THE 3UIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLLEGE OF ENGINEERING LOCAL MASS TRANSFER FROM CYLINDERS TO A TRANSVERSELY FLOWING GAS. T.. ' #~ I,,, Philip J. Birbara A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the University of Michigan 1961 April, 1961 IP-509

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ACKNOWLEDGEMENTS There are several people who deserve mention for their assistance in this dissertation. The members of my committee, DrsE DeRocco, Gordon, Sinnott, Tek, and Williams, each deserve thanks for their guidance throughout the course of this study, and for their helpful suggestions on the preparation of the manuscript0 I owe a special debt to Dro Gordon His generous donation of tifti and continual encouragement have contributed immeasurably to this study. He has been a ready and patient listener, an astute and constructive crtiic, and a fine friends Working with Dr, Gordon, I have learned the pleasures and satisfactions which research provides0 Through his guidance and example, he has had a profound influence. The writer is indebted to Arthur Platz for assistance during the experimental and calculational phases. The financial support of the ESSO Research and Engineering Trust Fund defrayed expenses and allowed me to devote my undivided energy to this study for 12 months I am indebted to the personnel of the Industry Program of the College of Engineering for their cooperation and assistance in the final preparation and reproduction of the manuscript0. Finally, to my parents for making this task possible, I dedicate this work0 ii

TABLE OF CONTENTS Page ACKNOWIEDGEMENTS s. o -. 0 > o o oo Do. o o o o o o o o o o oo o o ACKLIST OF TABLED M SX o o o o.. o. o o O o 0 0 o 0 Q0 0. 0.o0 0 0 0 0.o o o, o o 0 LIST OF TABLESOO.. O Q.0........ V................. LIST OF FIGURESoo o p O O O O o 0V a a a a a o o.. a. ~.vi ABSTRACT.O o aoa o. oo,o O Op p o a O oo00e 0 a o P O ix PART I MASS TRANSFERo oO 0 _.4O J 0i000o eOO. a. o1 'I INTRODUCTION.o,,.O a a. O O a 0 a.o.0000 o o 0 0.0, p0 Go. o. oO1 10 I -troduction6 a a.0 a a a a a a a a a ooa oo 1 2, Resume of Prior Worko.,,,, 0 o20 a 0.o0 o000 a o o0oo0 2 a Previous average heat and mass transfer studieso0. o 2.b Previous local heat and mass transfer studies...oo 5 c: Average experimental techniques-000000t0tc0o0000 8 d Local experimental techniques, P o *0 0 o00 0 o a O O 0 9 -3 Flow Chharacteristic Studies, 0,.,,.. o o 0 000000 ooo,.o 12 4. Effects of.Air Turbulence on Transfer Rates oO.........o 13 Effects of Surface Roughness0, o o 0 0 o. D15 6d Effects of Surface Temperature Distribution0 o oo o o o 15 70 Effects of Temperature on Mass Transfer Coefficients.0o 17 HII APPARATUSo o o.......oo..o,..* o o...oo o..o.0.0..o,, O. p18 III t EXPERIMENTAL PROCEDURE o o00 o o0 o0D 0O0 o 22 10 Preparations for a Run*0o a<<,op oooooo0ooo o0o 00000 22 29 Experimental Procedure During Run Periodso. o o o o, 23 IV, EXPERIMENTAL RESULTS o o0osoo o000 o o o o 26 1. Data.26 2d Correlation of DataO oo 0 0 o 0 0 0 0o0 28 V0o DISCUSSION OF RESULTSo...0..oooo0 oo....o..........o.ooo * 48 1 Ev'aluatiOn of Results 1 00....O..o.o0o 404o0o0o0 000 ', DT$G~,~dSSH~,R,O o%~i~s~B~b3FS o o a O O, a a a.O D G o a a O, O O,'0, 2, Comparison of Local Distributions with Other Investigations 0oo o 00 0s 00 0, o o0 0 0 0 f o 0 0 51 3 Comparison of j'Factors with Other Investigations.,.,. 1 PART II DETERMINATION OF VAPOR PRESSURES FOR NAPHTHALENE p-DIBROM1BENZENE, PROPIONAMIDE, AAD ANTHRACENE..... 67 VI TINTRODUCTION O o b o O D o.0 0 000o 68 Oii

TABLE OF CONTENTS (CONT D) Page VIEI EXPERIMENTAL EQUIPMENT o o o o o o o o o O O 000000000 69 IXo ESoULoTS0 0 0 0 0 0 oooo 0 0 ooooooooo 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0o 73 Xo DISCUSSION O RESULTD o o o o o o o o o o o o oooooo o o o o o o o o o o o o o o o o o o o o7 1o Details of Apparatus...00......ooooo ooo..oo..oooooooo 82 bo Air heatoing unitooooooooooooooooo oooooooooooooooo 82 30 Summary of Original a.nd Processed Data for Determination of Vtapor-Pressure 0ooooo.........oo...,o 91 4o Sample Calculations o O O o O o o o o o 000000000 92 ao Calculation of mass transfer coefficients o....oo.. 92 b Calculation of j-L actors o o o O o o o o o o o o o o 93 c Calculation of surface temperaturesooooo.......o. 94 do Calculation of diffusivities and Schmidt numbers~o 96 5o Calibrations.....,,.........00.00000000000000000000......000000000...00 102 NMENCATURE o o o o o o o o o o o o o o o o o o o o o o o o o o 0000000000 107 BIBSLTOCTRAPTIY0 0 o o 0 0 0 o 0 O 0 0 0 0 * 110 iv

LIST OF TABLES Table Page I Ratios of Local H'S to DSooo..O... ooooooooooo.... 29 II Comparison of Previous Local Heat and MassTransfer Studieso o oooooo ooooooooo oo oooo 53 III Studies Concerned with the Heat-Mass Analogy.. o,000. 64 IV Summary of Original and Processed Data for Mass Transfer Rates o...00..0ooo...... o o o0000.... o 86 V Summary of Original and Processed Data for Determination of Vapor Pressure o o o........ o oooo 91 VI Properties of Organic Solids for Determining Wet-Bulb Depression o o o o o o 0. o...0 0 0.. o o 96 VII "Wet-Bulb Depression" of the Organic Solidso,,Oo. ooooo 1 VIII Properties of Organic Solids for Determining Diffusivitieso 0 0 0 0 O, 0o o0oo000 o,000000000 0,0o000000 101 IX Schmidt Numbers and Diffusivities of the Organic Solids o o0 0 0 0 0 0 0 0 a 0 0 a 0 0 0o.0o 0 o a a 0 a Oo 101 v

LIST OF FIGURES F igure Page 1 Schematic Diagram of Mass-Transfer.Flow Equipment,e o e o o.9. 2 Diagrams of Test-Object Details o o 0,, o o o oo oo o o o o 20 3 Photographs of Equipmento o o b o 21 4 Data Sheet for Mss-Transfer Studies,0oo ooo,o,0oooooo 0 oo 25 5 Angular Variation of Mass-Transfer j-Factors at Constant Reynolds Numbero o o o oo ' a o o o 31 6a Polar Diagrams for Heat and Mass-Transfer j-Factor Distributions at Re 400 O.o o o D*.al o a a ' 32 6b Polar Diagrams for Heat and Masis-Transfer j-Factor Distributions at Re = 1000 o oo o a 33 6c Polar Diagrams for Heat and Mass-Transfer j-Factor Distributions at Re = 2000 O 0 0 0 a 0 0 00000 0 o o a o oo o o 34 6d Polar Diagrams for Heat and Mass-Transfer J-Factor Distributions at Re 400Q o o a a 35 7a Correlation of Local Mass-Transfer Data at Various Angles, Summary of Correlationso 00 o oo oo o 0 o o o O 36 7b Correlation of Local Mass-Transfer Data for 9 = 0o, 180 a 0 a 0 a OO o a O o b O to o o O % O a O a O a O a O a 37 7e Correlation of Local Mass-Transfer Data for e = 30Q Oo O 150ooooo oo~< o ' 38 7d Correlation of Local Mass-Transfer Data for = 600, 9, a 0 120 a a 39. Ahui1tui&, V'tirtibon of the ReynOlds Number Exponent. (n) o a n. O Oi o d f od o a o f oa o,, h, * o * d Q o o o * o * f ii u 40 9 Correlation Of Average Mass-Transfer Datao.,000,. ^,,,.00. 41 10b (.ktM/h) as a thatiob O6 Schmiat Number for 180=, 156, j 10 at RIe 2000~ ^^^d^bb ^ 42 lOb (k^/tl/h) &e a Functiohn of SCchnidt 3ibbdr for Q 4 60J, 306 00 &Ct Re 0OOba^oao^^b^o^o.^>^o, 0 43 vi

LIST OF FIGURES (CONT'D) Figure Page lla Temperature Variations of kc(Sc)0 5 for 09 1800, 15009 1200, 900 at Re = 20000oooo.0booooooooooooooooo 44 llb Temperature Variations of kc(Sc)005 for 9 = 60", 300, 0" at Re = 2000 ooooooaaooooooooooooo 45 12a Temperature Variations of the Mass-Transfer JD-Factors for 8 = 180o, 1500~ 1200, 90" at Re - 2000o 46 12b Temperature Variations of the Mass-Transfer jD-Factors for 9 = 60~, 30" 0 at Re = 20000 oo o o 47 13a Comparison of Previous Local Heat and MassTransfer Investigations for G = 0~.0000000000000000 54 13b Comparison of Previous Local Heat and MassTransfer Investigations for 9 = 30~ o o 5o o o oo 0oo 55 13c Comparison of Previous Local Heat and MassTransfer Investigations for G = 60~ooooooo o o o o o o o 56 13d Comparison of Previous Local Heat and MassTransfer Investigations for 9 = 90 0o o 000 o 0000000 57 13e Comparison of Previous Local Heat and MassTransfer Investigations for G 120OO~ o,ooooo oo 58 13f Comparison of Previous Local Heat and MassTransfer Investigations for 9 = 1500o 59 13g Comparison of Previous Local Heat and MassTransfer Investigations for 9 = 180 ooooooooo oo~ oo 60 14 Schematic Diagram of Vapor Pressure Equipment......... 70 15 Data Sheet for Vapor Pressure Studiesooooooooooooooooo 72 16a Correlation of Vapor-Pressure Data for Naphthalene, p-Dibromobenzene, and Propionamide, o o o 74 16b Correlation of Vapor-Pressure Data for Anthraceneoo... 75 17a Surface Temperature as a Function of Wet-Bulb Depression and Air Temperature for Naphthalene and p-Dibromobenzene..000000000000000000000000000.,00 99 vii

LIST OF FIGURES (CONT D) Figure Page 17b Surface Temperature as a Function of Wet-Bulb Depression and, Air Temperature for Propionamide and Anthraceneo OO O O O O o O 100 18a Calibration Curves for Rotameter Number lo o o o o. o. 103 18b Calibration Curves for Rotameter Number 2..ooo o oo 104 18c Calibration Curves for Rotameter Number 3.........oo 105 18d Calibration Curves Chromel-Alumel Thermocouple o oo.. 106 viii

ABSTRACT Local mass transfer rates into air from 30~ segments of a cylindrical surface were determined by: measuring the sublimation loss of a cast organic solid, The cylindrical test piece could be rotated through 360~ in increments of 30 ~ Tests were made with naphthalene, p-dibromobenzene, propionamide, and anthracene; Reynolds numbers of 400-4000; surface temperatures from 25-150~C; diameters of 1" and lo25"; and an estimated turbulence of less than 2%o The mass transfer data were obtained with the same geometry, equipment, and flow conditions as the heat transfer data of Churchill(4) The local and average transfer results were correlated by jD = B(Re)-n where B and n vary with angular position but are independent of flow rate and diameter, The standard deviations of the jDPS from the jD correlating lines and Churchill's JH correlations are 6o2% and 708% while the algebraic average deviations are -0.06% and 2o0% respectivelyo This confirms the heat and mass transfer analogy for the laminar and eddy flow regions of a cylindero At a Reynolds number of 2000, sublimation rates were determined over a temperature range of 125 C with the mass transfer j-factors decreasing less than 10% with increasing temperatures for all angles, A Schmidt number exponent of 1/2 in the j-factor equation is more representative of the data; than a value of 2/30 The vapor pressures of the four organic solids, determined by an air saturation technique, were correlated by log p = B - C/To ix

PART I MASS TRANSFER I INTRODUCTION lo Introduction Many important problems concern the transfer of material from one phase to another, Mass transfer from a cylinder is of interest because a cylinder resembles many components; and next to the flat plate, it is the simplest two dimensional case. Mass transfer studies have been concerned mainly with overall rates. Notable local mass transfer studies from cylinders to a transverse flow are those of Thoma,106) Klein(62) Powell and Griffiths,(84) and Winding and Cheney, (5) Since the equations for mass transfer are of the same form as those for heat transfer, it would be expected and has been shown that mass transfer can be used as an experimental analogue for heat transfer, An aim of this research is to test and calibrate the analogy and to complement Churchill and Briers(l5) heat transfer determinations under similar conditions o Most work on local mass transfer rates to gases has been at room temperature. Sublimation rates of four organics were measured over.a temperature range of 125~C which is. greater than any known work. In this investigation, the local mass transfer rates from 30~ segments of a cylindrical surface were determined by measuring the weight Loss of cast organics. The- angular positions of the test piece could be rotated through 360~ with respect to the transverse air flow in increments Df 30~. Tests were made with naphthalene, p-dibromobenzene, propionamide) and anthracene; a Reynolds number range from 400 - 4000; surface temperatures from 25 - 150~C; and an estimated turbulence of less than 2%. -1 -

-2 - 2. Resume of Prior Work a. Previous average heat and mass transfer studies The literature on heat transfer to cylinders with a transverse flow of air gives many theoretical and empirical equations with correlating heat transfer coefficientso One of the earliest is that of (7) Boussinesq(7) who proposed hD/k = o1015 tDupcv/k (1) This results from the Fourier heat conduction equation and assumptions of a film of uniform thickness, an incompressible and invis fliuid, and constant fluid propertieso Russell(89) has developed a similar equation and obtained data verifying the diameter and velocity effects indicated in Equation (l)o In 1914, King( ') used Boussinesq's assumptions to derive hD/k = 0 318 +.O.798 Dupc8/k (2) Langmuir(6) () contributed papers on both free and forced convection from cylinders ascribing the thermal resistance to an effective film. He correlated the forced convection data by a relation similar to Equation (1) Davis(l8) obtained the following equation including the viscosity hD/k = r[(Dupl/), (cl/k)] (3) For constant Prandtl number this reduces to hD/k:= (Dup/p) = *(Dupcp/k) = V(Dupcv/k) (4) Davis represented data for wires by Equation (4)0 Rice(87) used Hughes data for 0o164 - lol99 inch pipes to obtain hD/kf = 0o465 Dupf/f (5)

-3 -Fischenden and Saunders(29) successfully correlated the heat transfer data of Carpenter, King, Hughes, Taylor, Gibson, Reiher, and the mass transfer data of Thoma and Lohrisch by plots of log Nu. versus log Pefo Since Pe is the Product of the Prandtl and teyno~asnumbers, these correlations are expressed by Equation (3)o Ulsamer(107) correlated his data and those of Kennelly, King, Hughes, Reiher, and Vornehem by Num = B(Re)n (6) where physical properties are the mean of those at the gas and surface temperatureso The data of Hilpert(46), correlated by Equation (6), covered the largest range of diameters, 000079 to 5~9 inches~ When log Nu..isf plotted against log Re, the data fall on a series of straight lines with slight bends at log Re equal to 1.6, 3o6, and 4o6 coinciding with variations in:flow patternso With increasing Reynolds number, n increases and B decreaseso According to Ulsamer, for Re between 50 and 10,000, the values of n and B are 0.5 and 0o536; for Hilpert's correlation, n = o.466 and B = 00615, McAdams(0) correlated available data by Equation, (6) evaluating the physical properties at the film temperature, the average of the bulk and surface temperatures, For liquids flowing perpendicular to cylinders, Ulsamer(07) correlated his data by another form of Equation (3), Nu - E(Re)n(Pr)m (7) He recommended n m E Re = 0.1 to 50 0o385 0,31 Oo91 Re = 50 to 10,000 0050 0,31 0o60 A value of m = 1/3 is. often used.

In 1933, Chilton and Colburn 2)(13) presented the j-factor correlations which related heat and mass transfer and in some cases momentum transfer. The equations hD/k = I(Re, Pr) (8) kID/Dv = S,(Re, Sc) (9) become JH = (h/cpG),(Pr) = *(Re) (10) jD =-( kg- ': 3(sc (Re) (11) Assuming with Chilton and Colburn jH = (St)(Pr)2/3 (12) and dividing Equation (7) for m 1/3 by (Re)(Pr)l/3, there results Nu/(Pr)/3(Re) = E(Re)n-l= (St)(Pr)2/3 (13) jH = E(Re)n-l (14) Analogously D =E(Re)n (15) Chilton and Colburn plotted the data of Lohrisch for the absorption of water from air flowing across a fused caustic cylinder as. vs Reo The values of JD from Lohrisch were 10 to 15%:greater than accepted values for jHo An excellent summary of such mass transfer results appears Sherwood and Pigford(97)a The jD-factors calculated from the data of Powell on water vaporization, Lohrisch's water and ammonia absorption, Vint's liquid evaporation, London's et al water evaporation, and Winding and Cheney's naphthalene sublimation are in agreement with McAdams' jH versus Re curveo (72) Linton and Sherwood(7 dissolved cast benzoic and cinnamic acid cylinders placed transverse to a turbulent water stream verifying the 2/3 exponent on the Schmidt group for values up to 3000~

-5 -Bedingfield and Drew(4) correlated their psychrometric data for solids by JH = h/cpG(cptf/kf)0o56 = 0o281(D G/f)-0~4 (16) Jd =~ k /G( MfD)56= 0.281(DG/-~4 (17) They recalculated psychrometric measurements of Arnold, Dropkin, and Mark and found them to agree with Equations (16) and (17). Bedingfield and Drew did not include the data of Vint, Lohrisch, Powell, and Clapp because of inadequacies in presentation of data or experimental techniques. Giedt(36) measured the local heat transfer coefficients around a cylinder with a non-isothermal surfaceo The average Nusselt numbers agreed within 12% of Hilpert's for an isothermal surface, the greatest discrepencies occurring at the higher Reynolds numbers (Re>lo5xl0-5)o Churchill and Brier(l5) investigated heat transfer from cylinders at very high temperature differences proposing Num 0o60(Pr)1/3 (Reb)l/2(Tb/Ts)0.12 (18) b; Previous' local heat and mass transfer studies Local heat or mass transfer results for a cylinder are usually given as plots of Nusselt numbers versus angular position for a given Reynolds number, Lohrisch (74) measured ammonia absorbtion over 40~ segments; Drew and Ryan(23) steam condensation over 20~ intervals; Powell and Griffiths(84) water vaporization over 40~ segments; Churchill and Brier(l5) heat transfer over 30~ segmentsO The local heat transfer data of Fage and Falkner28) Small(98) Schmidt and.Wenner(92) obtained over segments.ubtendling 2~ to 15~, were presented as point values Krujilin and Schwab67) Giedt(36 Robinson and Han(8) measured local heat transfer coefficients by thermocouples in the-.- surf ace

the surface, Local transfer coefficients for sublimatigon are presented by (62) (115) Klein for ice by Winding and Cheney for naphthalene. Plots of log Nu versus log Re for given angular positions by Lohrisch, Klein, Krujilin and Schwab, and Churchill and Brier were linear with slopes varying with angular positiono Schmidt and Wenner, as well as Winding and Cheney, compare their data with those of Lohrisch, Drew and Ryan, Klein, Small, and Krujilin and Schwab at approximately Re = 40,000o Winding and Cheney, whose data agree with those of Small, have results about 50% greater than those of Schmidt and Wennero The plots of all these local Nusselt numbers, for D = 1 to 12 inches, versus angular position agree in shape. Schmidt and Wenner indiw cate the results of Drew and Ryan, Klein, and Lohrisch to be less reliable than their own due to experimental techniques. They suggest the high Nusselt numbers of Krujilin to be less reliable due to surface roughnesso Giedt compared two runs (Re = 101,300 and 170,000) with those of Schmidt at the same Reynolds numbers finding considerable disagreement, particularly in the rear of the cylinder. He attributes this to higher turbulence for his non-isothermal surface, Squire, as reported by Goldstein(39) theoretically derived.Nu = 1.14 PrO04i-eb Fsin R/G (19) near the stagnation point of the cylinder. For air, Pr = 0~74, at the stagnation point, this becomes Nu=. = lOlf Reb (20) The agreement of Equation (20) with the experimental measurements of Schmidt and Wenner, Giedt, Churchill and Brier, and Eckert and Soehng6n is exceptionally goodo

-7 -(79) MErtinelli et al.7 studied the data of Schmidt and Wenner proposing the empirical equation NuO = 1.14 Pr0O4 eb - (R/90)3] (21) This applies when the angular position is no greater than 80~ and the main stream turbulence is less than 1%. For air with a Prandtl number of 074, this reduces to NuG/Nuo - 1 - (G/9o)3 o~ < 9 < 80~ (22) Krujilin 66) theoretically derived Nug =pl() Pr /3R (23) The function 4i (9) was determined by numerical integration for a number of angles extending from 0~< 9< 90 and a Reynolds number range from 10,000 to 250,000o (26) Eckert )presents an equation based on the Squire derivation near the stagnation point of a cylindero For the stagnation point regionr a thermal boundary layer exists while the velocity outside the boundary, increases linearlyo Solution of the differential equations for the heat transfer coefficients to an isothermal cylindrical surface placed transversely to the fluid gives, h -Bk Ius/,p = Bk F/i (24) where F = us/x Expressed in dimensionless form Nux = /k B Usx/k (25).x usx~~~~~~~~~~~~<5

-8 - For potential flow around the cylinder, us- ad sin (2x/D) (26) Then for potential flow at the stagnation point, us- 4% b(x/D) (27) Substituting Equation (27) into Equation (25), there results Nu.O =hD/k = 2B Reb (28) B is a function of the Prandtl number, tabulated by Eckert(20), For air, Equation (28) reduces to Equation (21)o EckertIs calculations for the laminar boundary layer in the region 0~< 9 < 90~ agree with thb heat transfer data of Schmidt and Wennero c. Average experimental techniques Average heat transfer coefficients were measured by King(61) and Kennelly et alo58) who observed the heat loss from electric wires swinging around their long axis. The heat loss from electric wires, rods, and tubes with a transverse air flow were measured by Rice(87) Taylor(l03), Griffiths and Awberry4) Goukha41 Hilpert(46) Benke(5), Billman et aL(6), Comings et al(17) and. van der Zijnqn(l08) Hughes51), Carpenter(l), Hilpert(46), and Comings et all7 measured the condensation of steam in tubes obtaining average heat transfer coefficients. Gibson(35) circulated hot water through a tube measuring its temperature drop. Reiher(86) and Vornehem(llO)determined the heat transferred from hot air to cold water flowing through tubeso London et a1(76) used the transient behavior of a thermal capacitor to determine convective transfer from cylinders to gaseso The results agreed with the literature for steady state procedureso

Thoma(l06) and Lohrisch(74) investigated mass transfer from an ammonia-air flow to tubes of various sizes wrapped with blotting paper saturated with phosphoric acid Lohrisch(74) determined the transfer of water from air by the weight increase of sodium hydroxide rods, Mark(78), Arnold(l), and Dropkin(24) obtained psychrometric data for a variety of liquids from a cylindrical cloth surface measuring the liquid losto Powell(84) used cloth covered cylinders of several diameters in his wet-bulb studieso Comings et al(17) and Maisel and Sherwood(7) determined heat and mass transfer coefficients for cylinders. The latter studied the effects of turbulence. Winding and Cheney(ll5) measured the sublimation of naphthalene tubes placed transverse to a turbulent air stream. Bedingfield and Drew(4) obtained psychrometric data with volatile cylindrical solids as wet-bulbso Linton and Sherwood(72) present data on the solution of cast benzoic and cinnamic acid cylinders in turbulent water flow where the Schmidt number varied from 1000 to 3000 -(21) Dobry and Finn(1 obtained mass transfer rates at low Re; by observing the diffusion-limited electric current discharging at a cylindrical microelectrodeo' do Local experimental techniques As reported by Stanton(10), Jakeman measured the relative heat loss from an electrically heated metal strip attached to a cylindrical ebonite rodo He observed the heat loss from the back of the cylinder to be about one-half that from the front Similarly, Kirpitshev as reported by Krujilin and Schwab (67 made the same observation, Reiher(

measured the surface temperature distribution around a water cooled pipe placed transversely to a hot air stream. Lohrisch(74) wrapped 12 longitudinal strips of blotting paper saturated with phosphoric acid along glass tubes of various sizes. An air-ammonia stream flowed transversely to the cylindrical surface and the amount of ammonia absorbed was determined by titrationo As the ammonia was introduced into the air a short distance from the cylinder, there is doubt as to the homogeneity of the gaseous stream, Photos were taken of ammonium chloride clouds formed when the cylindrical surface was saturated with hydrochloric acido Fage and Falkner(28) presented data of local heat transfer and skin friction coefficients from the electrical input to a nickel strip subtending 2~o Drew and Ryan(23) reported variations in condensation rates and local heat transfer coefficients to air in 20O sectors of a vertical steam pipeo These results were similar to those of Lohrisch for ammonia absorbtiono Klein(62) studied the change in shape of ice tubes in a transverse stream of warm air, The average heat and mass transfer coefficients were obtained from the weight loss while change in dimensions gave local coefficients, Krujilin and Schwab(67) inserted a Ool mm thermocouple in a surface groove on a stream tube measuring the angular heat transfer variation in transverse air flow, They also measured the surface temperature of an iron cylinder by 32 peripheral thermocoupleso Small(97) used a thermopile in a steam heated cylinder to measure local heat transfer coefficients.

-11 -Powell and Griffiths(84) measured the vaporization of water to an air stream in 40~ sectors. Water circulated over the. wick covered surface. The evaporation was measured by the quantity evaporated in each sector and indirectly from the power required to maintain a uniform surface temperature by electric heaters in each sector, Highest rates were observed at the stagnation point, somewhat lower rates at 18o0 and a sharp minima at approximately 100~o Schmidt and Wenner(92) developed a method for local heat transfer measurements, Except for a narrow longitudinal thermally isolated sector of a steam heated tube, the cylindrical surface was maintained at the same constant temperature as the remainder of the surface by small electric heating coilso The heating element sector could be turned to any angle with respect to the air flow direction, Measurements of heat transfer and pressure distributions for 100 intervals are presentedo Winding and Cheney(ll5) and Klein(62) measured transfer coefficients from the change in dimensions of subliming solids, Giedt 36) investigated the variation of the heat transfer coefficients around a cylinder with a non-isothermal surfaceo An electrically heated nichrome ribbon 1" by 0,002" in cross section was wrapped helically around a 4" OoDo lucite cylindero Local heat transfer coefficients resulted from peripheral temperature variations and the electrical inputo A correlation between these results and the skin-friction distributions as indicated by the pressure variations was noted, Giedt, Krujilin(67) and Robinson and Han(88) observed no significant difference in the heat transfer coefficients When the surfrc6 teirpetAture distribution was n6t uniformo

Churchill and Brier(l5) measured;local heat transfer coefficients at gas temperatures varying from 580~F to 18000F and Reynolds numbers from 300 to 2300. The outer surface was maintained at approximately 100~F by circulating water through a hollow inconel cylinder. The radial temperature profile through a 30~ sector of the tube wall was measured permitting the calculation of the heat transfer coefficient, Robinson and Han(88) determined local heat transfer coefficients for cylinders in ducts of various widths, A 1,5" OoDo cylindrical tube with 19 thermocouples evenly spaced over one-half of the periphery was electrically heated. The radial temperature differentials and the thermal conductivity were used to calculate the heat flux distribution, The relative heat transfer distributions for a cylinder in a 6" wide duct are similar to those reported for free stream conditions, Eckert and Soehngen(27) used an interferometer to determine the temperature field around solid copper cylinders obtaining local heat transfer coefficients for 23 < Re < 597O Seban (93) measured local transfer coefficients from bakelite cylinders with nichrome ribbons wrapped on their surfaces for heating by electric dissipationo 3, Flow Characteristic Studies Drag coefficients for gases past cylinders have been measured by Wieslberger(ll2), Fage and Falkner(28), Delany and Sorenson(20) and Giedt(37), Similar to flow in pipes, they observed that the shear stress at low Reynolds numbers (< 1) varies as the first power of the velocity, The flow is completely laminar and only viscous forces contribute to the drago As the Reynolds number increases beyond 1, separation of flow from the cylindrical surface resultso This has been studied by a number of

techniques (Thoma, Green, Fage and Falkner, Giedt, etco)0 The point of separation is approximately 70~ for the laminar and 110~ for the turbulent boundary layerso Beyond the separation point eddies dissipate the kinetic energyo At small velocities the drag of the cylinder is mostly frictional resistance while at Re > 1000 mostly form resistance~ At the lower Reynolds numbers, the heat and mass transfer coefficients on the impact side are much greater than in the beck sideo As the Reynolds number increases, both coefficients increase becoming equal at ReP 5x10o5 4o Effects of Air Turbulence on Transfer Rates In 1925, Reiher(86) placed a grid upstream from a heated cylinder obtaining up to 50% increases in the heat transfer coefficients. Goukham et alo(41) located two 1.2 cm diameter cylinders 3 5 cm apart ul$tream from a 3o5 cm cylinder obtaining increases of 23 to 30%~ Loitsiansky and Schwab(75) observed 30 to 35% increases in the heat transfer coefficients to a 7 cm diameter sphere as the turbulence increased from 0o4 to 2~8% for 4x104 < Re < 102x105. McAdams(80) states that the heat transfer coefficient i} a tube bank is approximately 27% greater than that for a single cylinder under equivalent conditions, Fage and Falkner(28) indicated that the relationships between heat and mass transfer and surface friction are not altered by turbulence. Comings et alo(7) studied the effect of turbulence on both the heat and mass transfer. Evaporation of water in air was measured for 400 < Re < 20,000 and turbulence from 1 to 20%. The coefficients increased similarly with increasing turbulence~ The rate of increase is greatest at a turbulence of 2 to 4%. At Re = 5,800, the transfer coefficients vary little for turbulences of 7 to 25%. Increasing turbulence

-14 - at a constant Reynolds number, caused a maximum increase of 25% in the heat transfer coefficient. This was more pronounced at the higher Reynolds numbers. Giedt(37) measured the effect of turbulence on local heat. transfer and skin friction coefficients for 70,800 < Re < 219,000. Transfer coefficients increased 10~20% as the turbulence increased from 1 to 4%. For the 1% turbulence, the ratio of the average front half to the rear half heat transfer coefficient is 0.85 while for 4% turbulence it is lolo Using the evaporation from a cylinder, Maisel and Sherwood(77) were the first to observe the effects of intensity of scale on the transfer coefficiento They found little variation in the mass transfer coefficients with changes in scale levelso At Re = 1000 no change in coefficients was observed below an intensity level of 12%; while at Re = 5000, no effect was apparent below 4%. Like Comings et alo, they observed an increase in turbulence to be more effective at higher Reynolds numberso Van der Zijnen(l08) measured the heat transfer coefficients from wires and cylinders in both smooth and turbulent air flow, For 60 < Re < 25,800, the turbulence varied from 2 to 13% and the ratio of the turbulence scale to the cylindrical diameter varied from 0o31 to 240. The data were correlated by three independent groupso Reynolds number, intensity of turbulence, and (scale/diameter)O (59) Kestin and Maeder showed that slight increases in screen produced turbulence resulted in substantial increases in the heat transfer coefficiento

Seban(93) recently presented results on the effect of turbulence 55 on local transfer coefficients from cylinderse For 05x05 <Re<300xlO t^he increased turbulence resulted in increased heat transfer coefficients in the laminar boundary layer, an earlier transition to turbulence, and possible alteration in the character of the separated flowo No functional relationship was established specifying the increase in the heat transfer coefficient relative to the turbulence intensityo 5~ Effects of Surface Roughness Most experimenters attempt to work with "smooth" surfaceso In view of the Chilton-Colburn analogy,, roughness should increase the pressure drop, heat, and mass transfer at the same ratio, McAdams("80)reporte on. the experiments- of Cope who studied the effect of roughness in cooling water tubeso In the turbulent region, the pressure drop was varied to six times that of a smooth tube and the relative heat transfer was increased only 20 to 100%. Grimson(43) measured heat transfer to tube bundles with a transverse air flowo He noted an increase up to 20% in heat transfer.and flow resistance with increasing roughnesso 60 Effects of Surface Temperature Distribution Krujilin(66) measured local heat transfer rates from thick walled tubes providing a pronounced surface temperature variationr Defining a temperature ratio (T90-To~/Tmean), (the difference of temperature between the stagnation point and the 90~ positions divided by the mean cylindrical temperature), Krujilin observed no significant difference in local heat transfer coefficients for a cast-iron cylinder with a 303% temperature ratio and a porcelain cylinder with a 19% ratioo

(6) Billman et al) determined the variation in surface temperature by small thermocouples in the surface of a brass cylindero For 562 < Re < 4440 and average cylindrical temperatures between 125 and 315~ -F.a linear relationship exists between the heat transfer rate and the average surface temperature indicating that the surface temperature variations do not modify the flowo Giedt(36) measured the temperature and electrical input to a thin nichrome heating ribbon wound helically'around a cylindero A fourfold increase in the power caused the temperature gradients to increase from 4 to 8 times along the ribbon surface. No variation in local heat transfer coefficients was apparent for the different surface temperature distributions o Robinson and Han(88) investigated heat transfer from nonisothermal surfaces of banks of tubes to a forced transverse air flowo The distribution for a single cylinder was similar to that of GiedtO The effect of surface temperature distribution considered above were based on experiments with small surface to bulk temperature differenceso Churchill and Brier() measured heat transfer coefficients at high temperature differences and found that the mean coefficient varied as (Tb/Ts)0O12 with fluid properties evaluated at the bulk temperaturee Douglas and Churchill(22) successfully correlated the data of many investigators with high and low temperature differences by Equation (4) with fluid properties evaluated at the film temperatureo

7o Effects of Temperature on Mass Transfer Coefficients Kowalke, Hougen, and Watson(64) made a series of runs to determine the temperature effect on the ammonia transfer coefficient for the absorption of ammonia into water in. packed towers at constant mass flow rates, For 70-110~F, it was found that increasing the temperature diminished (Kga) by approximately 0o3% for each 1~C rise. For the absorption of ammonia in a 1" diameter packed tower from 70-95~F, Dwyer and Dodge(25) observed Kga decreases 1.2% for each 1~C increase. By variation of the water from 10 - 35~C, Molstad et al82) found the coefficients to decrease by 0,9% for each 1~C increase for the same system. Haslam, Hershey, and Kean(44) found that kg varied inversely as T14 for the absorption of NH3 into water on a flat surfaceO If the gas film is controlling, K should be practically independent of temperature according to correlations of the GillilandSherwood equation for packed towerso Explanations are lacking for the pronounced decrease of the transfer coefficient with temperature, Molstad et alpdetermined that for ammonia absorption the liquid film resistance is only 10-15% of the total, so that a large change of Kla with temperature should have little effect on Kgao Wilhelm(ll3) reports that Fischer observed that increasing the temperature decreased kg for the sublimation of benzoic acid tubes to air in tubes at high Reynolds numbers (lx105< Re < 4x105) at 25-45~Co The magnitude of the effect closely parallels that of Kowalke et alo

II APPARATUS The apparatus, Figures 1 and 2, includes an air control flow system with a pressure reducer and rotameter; a resistance furnace for heating the gas; an adiabatic "tube section" for measuring the gas temperature; and the test piece section which includes a heat shield surrounding the test pieceO Air at 100 psi is dried in one of the two parallel silica gel beds. The unused bed may be replaced, or dried without interruption of the the air to the test cylinder, The air is then measured and regulated by three parallel metering unitso Each contains a cutoff valve, pressure controller, bimetallic-element thermometer, a rotameter, and a needle valveo It then flows through a packed tube surrounded by an electrical. resistance furnace and then through another packed tube (adiabatic section) for measurement of the gas temperature before going -to the test piece The velocity profile, the scale and turbulence levels are maintained by two screens outside the adiabatic tube, The Inconel test cylinder, above the top screen, is shown in Figures 2 and, 3, It sits on a pair of brackets permitting rotation in 30~ increments, The cylinder has a removable boat for holding the material to be sublimed and parallel grooves for thermocouples adjacent to the boato The test piece is surrounded by a cylindrical heated shield with removable conical top for easy access to the test piece, To minimize radiation losses, the inner surface of the surrounding furnace is maintained at nearly the same temperature as the test objecto -18 -

I SCREENS HEATED SHIELDS ADIABATIC TUBE I H '0! TUBE OPEN -END Figure 1. Schematic Diagram of Mass-Transfer Flow Equipment.

1.25" DIAMETER TEST OBJECT SIDE VIEW HORIZONTAL LINES EXTENDING LENGTH OF TEST OBJECT 1.00" DIAMETER TEST OBJECT REPRESENT THERMOCOUPLE GROOVES SCALE: ___ 0 0.5 1.0 INCHES ISOMETRIC OF TEST OBJECT ~/ M O V -- REMOVABLE BOAT Figure 2. Diagrams of Test Object Details.

-21 - (a) View of Flow and Heating Units (b) Test Object in Run Position (c) Test Object with Boat Figure 3. Photographs of Equipment.

III EXPERIMENTAL PROCEDURE Optimum location of the test piece above the platinum screen was determined by Churchill(14) who employed a probing hot-wire anemometer at approximately 1-1/2" above the top screen. The hot-wire anemometer showed a uniform temperature, velocity, and turbulence zone in a cone with a base the size of the top screen and extending a distance from about 1/8" to approximately 8" above the top screeno Preliminary runs showed that slight variations in lateral, longitudinal, and elevational locations from Churchillgs optimum plane 1-1/2" above the top screen resulted in insignificant mass transfer differences. 1o Preparations for a Run Occasionally the test cylinder was polished to minimize thermal radiation, -Negligible staining of the Inconel surface was observed, The solid material to be sublimed is melted in a beaker and poured into the clean boato A smooth surface is accomplished by "shaving" and "curing",, A slight excess of material is cast and. then removed by shaving with a scalpel to give a smooth cylindrical surface. In curing, any uneven surface is preferentially sublimed in hot air, leaving a smooth surface The interior surface temperature of both the cylindrical and conical shields were regulated independently by Variacs and measured by a probing thermocouple, They were maintained within 5~C of the Inconel test pieceo

-23 - 2o Experimental Procedure During Run Periods The procedure was to~ a) pre-weigh the boat plus contents; b) insert the boat in the test piece, and make the run; c)' remove, cool, and weigh the boato A difference technique measured the mass transfer rate at the higher temperatures. This compensated for sublimation while approaching thermal equilibrium both after insertion and cooling prior to the final weighingo The difference of the two exposure times and weight losses, with other variables constant, furnished the steadystate mass transfer rate, Before the boat is placed in test position, aluminum foil is wrapped around it to reduce the material lost while approaching steady state temperatures, after which it is removedo At the end of the sublimation period, the hot boat is wrapped in foil, cooled in a desi —ir foil removed, and weighed, The time the foil is around the cylinder and the time allowed for cooling are identical for both runs of a pair. Temperatures were read by six thermocouples in about 15 secondso A sample data sheet is shown in Figure 4o When there was a significant variation in temperature or flow rate, the run was stopped and discarded, Some twenty runs were discarded due to unsteady state conditionso In all runs, the air pressure preceding the rotameter was fixed at 45 psia and the gas flow past the cylinder held at a series of Reynolds numbers of 400, 1000, 2000, and 4000. The test piece was rotated through 360~ in 30~ increments, Preliminary results indicated symmetrical mass transfer around the cylinder, Then most measurements were made at angular positions from 0~ to 180~ in 30~ increments,

Sumwmaries of results are given in Table IV. The numbers ascribed to the runs are assigned consecutively within the table and have no chronological connection,

DATA SHEET FOR MASS TRANSFER STUDIES D~rDATR- - -" id a -S -" —. nia Ma^rrsr~ MATERIAL TIME _ __(. __. I.. Io.|. FURNACE Vol ts Amop a _?P (mm HR GAS ROTA1METERS Gas */vFa_., - - _,,,;- -; Temn. OP CAS TEMPVRAOT TRE. Pot.TC-6 (mv)___ 6/ /k. k _ Ag _(OC___ ck ____ a4 IRc r. _ _-_t a s. Angle l, fy) TCcTP I (mv) - gs 4 TC-P (rVfia /^ /4^ /. & TC (my) / /0 -t %~BP~~jS I ig~PO I ': 2nC4.tmvls.. |nat 1w tcg.X (P' -___S-L3r)_eL-S Wt. lona (_ _., IL L 1 [ Ai L /. /,/~,.~fy -f =^ ai, a ~.,/,,. ai,,',ci -- -—. -1 —.-U I - CdI7 o- I - I ~DS3~~iCI~~ ~&LL"-~-d~-~~CL~~dl~-L~~. - — IYUIY - %FIQ IC i;vO~dz~Id~~~iI~u -L- lI~. C ( r r UI - U94( Aw Figure 4. Data Sheet for MaassTransfer Studies.

1V EXPERIMENTAL RESULTS lo Data Processing Dimensionless analysis is widely used in correlating heat, mass, and momentlm transfer datao The utility of dimensionless analysis is its ability to provide a relationship when the knowledge about the mechanism is incomplete. Mass transfer to fluids flowing past cylinders has been found to be influenced by -the mass velocity G, cylindrical diameter D, fluid viscosity 1, diffusivity Dv, and fluid density p, or k = (G, D, [ D, D p) (29) From dimensional analysis, this becomes kcD/Dv = ' [(DG/4)(p/p D) ] = J [(Re)(Sc)] (30) Analogously for heat transfer, hD/k = V [(Re)(Pr) ] (31) Eqaations (30) and (31.) may be rearranged to the j-factors for heat and mass transfer. D = kg Pbm M/G r(Sc) (32) JH = h/cpG t(Pr) 33) The mass transfer coefficient k is calculated by kg AW/ tA(pS - Pb) (34) Compared to Ps, Pb is negligible. In view of the relatively low vapor pressure of the organic solids, the inert film pressure is taken as the total pressureo The surface temperature of the subliming organic is taken to be the gas temperature less a small correction for the wet bulb depressiono -26 -

For steady-state, the heat received by the organic is equal to the latent heat of sublimation at the surface temperature, or 4kg(Ps - Pb) - h(Ta - Ts) (35) Since Pb is negligible compared to p,, Equation (35) can be rearranged to yield the surface temperature, = Ta- PsXskg/ (36) In the present study, the heat loss by radiation and conduction is negligible compared to that transferred by convection, Radiation and conduction losses are minimized by maintaining the surrounding heated shield and the test object at nearly the same temperature as the "subliming organico In Equation (36), (kg/h) is calculated from the j-factors. Assuming the equality of JH and jD, kg/h = (Pr/Sc)05 (l/cp MmPb ) (37) A value of O05 for the exponent of the Schmidt number is compatible with the data for lo79 < Sc <3005, discussed in Section V-Io The vapor pressures of naphthalene, p-dibromobenzene, propiona:m ide, and anthracene were measured by a gas saturation technique described in Part IIo Heats of sublimation were calculated by the ClausiusClapeyron equationo Diffusivities were calculated by the method proposed by Hirshfelder, Bird, and Spotz(47). For pairs of non-polar gases, Dv = [(1.492x13)T3/2 PrABp ] ( 1/MA + 1/MB) (38)

-28 - Diffusivity data for some of the organics in air are not available for the temperatures used in this study. For consistency, all diffusivities were calculated by Equation (38)o The gas viscosity was that of air, The physical properties for the Schmidt and Reynolds numbers were calculated at a film temperature, the average of the surface and mainstream temperatureso Negligible differences would have resulted if the surface or mainstream values were used. 2o Correlation of Data Appendix 2 contains the data and resultso Local j-factors, for a given Reynolds number, are given in Figures 5 through 60 Plots of log JD versus log Re with parameter of angular positions, 0~ to 180~0 are shown in Figures 7b - 7eo These are summarized in Figure 7a, Figure 8 gives the exponent on the Reynolds number for the equation, JD=B(Re)n, as a function of angular positiono Values of Churchill s heat transfer results are includedo Mist heat and mass transfer j-factors agree within 15%o Ratios of JH/JD for all angular positions are given in Table lo Table I contains the equations of the JD correlating lines determined from Figures 7b - do The standard deviations of the jD s for all positions are 6o2% from the jD correlating lines and 7Q8*% from Churchills JH correlationso

-29 - Table I Ratios of Local jH's to jD's Angle H/jD() jH/D Limits, (2) Standard Deviation __....................____ -(3) (4) S 0 1o01 090 - 1,18 6.2% 6.3% 30 1,04 0.91 - 1.12 5.1 6o3 60 lo01 0,89 - 1.15 5o9 5o9 90:094 0.86 - Lo06 5,8 708 120 0o98 0o89 - 1.18 6.9 705 150 0.92 0o84 - o02 5.1 10o8 180 0.97 0o87 - 1o10 7o3 9o0 (1) jH9 correlation line from Churchill and Brier jD' correlation line shown in Figs. 7b-d Ratio averaged from Re=400-4000 (2) / j correlation line J ', rrom data points ) (3) Deviations of JDPs from jD correlation. lines (4) Deviations of. JD s from jH correlation lines The runs, at a Reynolds number of 2000, were made with a wider range of variables than those at the other values. Included were cylindrical diameters of 1" and 1,25"; four organic solids; and surface temperatures ranging from 25-150~Co At Reynolds numbers of 400, 10009 and 4000, the temperature was close to 25~C and only naphthalene and p-dibromobenzene were sublimed over the temperature range 25-65~C; anthracene, over 105-150"Co The upper temperature limit for each solid is set by high sublimation rates altering the surface area in the runs, The average cylindrical mass transfer rates are obtained by integration of the local data and summarized in Figure 9, They are given by -0 -564 ( (39) j = o64 (. ) (39)..

Churchill s, J - 0,63(Re), ~5 and McAdams correlations are included for comparisono The exponent, 0,5, for the Schmidt and Prandtl numbers used in the j-factor relations is determined from Figures 10a and lOb, Values of h are obtained from Churchill's results Theory(4) requires the lines of these plots to pass through point P (Oo691 4o16) Thus when Sc = 0o69, the term (Pr/Sc) = 1 for air For this condition, Equation (37) can be written kgMPbmh = l/cp 4016 (40) Figures 12a and 12b show a slight decrease of the jD -factor with increasing temperature at Re = 2000o Most data points in Figures 6a-d and 7b-d are slightly displaced so that all the data may be clearly presented thereby preventing an objectional overlapping of points. In Figures 6a-d, these points are moved from the angular positions of 30", 60o, 90o~ 1200, 150~ and 180~ and. in Figures 7b-d from the Reynolds numbers of 400, 1000, 2000, and 4o000 The jD- factors in these plots are the actual calculated values

'"u ----- ------ - ------ ------ ----- ----- ------ ------ -/ --- — -— JH - 0.05 fr ir. Z c| 0.04 v, --- Re =1000 0 30 60 90 12 20 4\ /2/ 3 It.. 00 Re=2000 - _____ o o N /j r 0.02 Re:400 -0 30 60 90 120 150 180 210 240 270 300 330 360 6, DEGREES Figure 5. Angular Variation of Mass-Transfer j-Factors at Constant Reynolds Number.

Data for D-1.25" and 1.00". Symbol with attached dash (-) indicates D = 1.00" KEY o Naphthalene V p- Dibromobenzene Re =400 120~ 90~ 0o 30~ Figure 6a. Polar Diagrams for Heat and Mass-Transfer j-Factor Distributions at Re = 400. Data for 0 = 0~, 30~, 60~, 90~ 120~, 150~, and 180~.

-33 - 1800 I - Data for D=1.25" and 1.00". Symbol with attached dash (-) indicates 2.80 _ KEY 0 Naphthalene V p- Dibromobenzene Re = 1000 D 1.00 " - JD -— Ju 1200 900 30~ Figure 6b. Polar Diagrams for Heat and Mass-Transfer j-Factor Distributions at Re = 1000. Data for G = 0~, 30~, 60~, 90~, 120~, 150~, and 180~.

-34 - 180~ 150 0 x 3.15 2.80 Data for D=1.25" and 1.00"Symbol KEY 2.45. with attached dash (-) indicates 0 Naphtholene D/ D=- 1.00" __ 2.10 W V p - Dibromobenzene / >.75 A Propionomide El Anthroacene Re - 2000.% JH 2.10 1.75 1.40 1.0 6.70 035 Jx102 00 30~ Figure 6c. Polar Diagrams for Heat and Mass-Transfer j-Factor Distributions at Re = 2000. Data for 9 = 0~ 30~, 60~, 90~, 120~, 150~, and 180~. 160~

-35 - Data for D 1.25" and 1.00". Symbol with attached dash (-) indicates D- 1.00" KEY Naphtha lene 0 V Re 4000 1200 Figure 6d. Polar Diagrams for Heat and Mass-Transfer j-Factor Distributions at Re = 4000. Data for 9 = 0~, 30~, 60~, 90~, 120~, 150~, and 180~.

0.1.09.08.07 - -— i 300.06 -601.....05.004 --.00 U..00 -_ C.o,, 0 IL.006 300______ 2xl02 3 4 5 6 7 8 9 100 2 3 4 5 6 7 8 9 104 1.5 REYNOLDS NUMBER, Re Figure 7a. Correlation of Local Mass-Transfer Data at Various Angles, Summary of Correlations. of Correlations.

0.100.090.080.070.060..050 I.040 LU LL CO z <.030 I — C,.020 I0. ULi. cO.010 O.009 O.008..007.006.005.004 2xl0 I I 3 4 5 6 7 8 9103 2 3 4 5 6 7 8 9 10 2 REYNOLDS NUMBER, Re Figure 7b. Correlation of Local Mass-Transfer Data for G = 0~, 180~. Re = 400, 1000, 2000, and 4000. Data for

x LU. LL V) z () C, cn 2 0o G: 0 LL U') I 0.100.090.080.070.060.050.040.030.020.010.009.008.007.006.005.004 2xl02 A) 0:) I 3 4 5 6 7 8 9 103 2 3 4 5 6 7 8 9 104 2 REYNOLDS NUMBER. Re Figure 7c. Correlation of Local Mass-Transfer Data for 9 = 30~, 150~. Data for Re = 400, 1000, 2000, and 4000.

0.070.060.050 ^ 0N ' NAPHTHALENE v"^, v p- DIBROMOBENZENE.040 - A PROPIONAMIDE 040'" 1>' 1 <! < |0 t3 ANTHRACENE N. _ _ _ _ _ _ _ _ _ ___ _ - - JD.030 -- o I' I.020 z N (N I-.010 '60.009 ' w.008 I.c0 - ____ ___ ________ 004 Data for D=1.25" and 1.00". Symbol _______ ___ '~^ ~ with attached dash (-) indicates } 90~.003.002 2xl02 3 4 5 6 7 8 9 10I 2 3 4 5 6 7 8 9 04 2 REYNOLDS NUMBER, Re Figure 7d. Correlation of Local Mass-Transfer Data for 9 = 60~, 90~, 120~. Data for Re = 400, 1000, 2000, and 4000.

0.00 -0.10 KEY --- HEAT TRANSFER,(nH) -0.20 -- --- --- -- MASS TRANSFER, (n ) = B(Re)n = -0.30 w -0.40 0 0Q w -0.50 Cn o -0.6// w \ ct: -0.70 -0.80 -0.90 0 30 60 90 120 150 180 e, DEGREES Figure 8. Angular Variation of the Reynolds Number Exponent, (n).

z I., z 4 <) 2 z w C,) IUI_ 9 8 7 6 5 4 3 'THIS STUDY 9 8 7 -Me ADAMS(80) 3 2 -— I45-6-L 1.5 2 3 4 5 6 7 8 92 3 4 5 6 789 10 2.._ - REYNOLDS NUMBER, Re Figure 9. Correlation of Average Mass-Transfer Data.

CD H 0. E S 01:E v' x 0 II OQ Odo 0 0 0 [\ 0 O e o H 1 0 o 1-b $- 0 (D Pi ( t Y 8 5.0 = 1500 4.5 P 4.0 - 3.0 -- I A y —SLOPE OF -1/2 2.5 SLOPE OF-2/3 s 1'.5 1.0 I --- 0.6 0.7 0.8 0.9 LO 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.C SCHMIDT NUMBER, Sc 5.0 I I I 4.5 - = 120~ (THEORY REQUIRES LINE TOPASS P THROUGH THE POINT P) 4.0 3.5__ __ 3.0 2.5 s W m < -SLOPE OF - /2 2.0 KEY | - 0 NAPHTHALENE 1.5 V p - DIBROMOBENZENE - SLOPE OF-2/3 A PROPIONAM1DE 0L ANTHRACENE 1.0 E m 'L 0 E 21, ud 3 5.0 3.5 --- 3.0 2.0 3.C __ ---.-.._____ __. _____-PROPIONAMIDE 1.0 1 06 0.7 0.8 L 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5 SCHMIDT NUMBER, Sc 5.0 8=90~ 4.5 4.0, 3.5 3.0 2.5 SLOPE OF -1/2 2.0 SLOPE OF -2/3 -1.5 1.0 - I r\) I E lS m IC. E.., E S CID LL. o. E Y. 0.6 0.7 0.8 0.9 1.0 1.5 2.0 2.5 3.0 3.5 4.0 45 5.0 SCHMIDT NUMBER, Sc A 1 U.O 0.7 U.8.9 I.U L5 Z.U SCHMIDT NUMBER, Sc 2.5 3.0 3.5 4.0 4.5 53U

.-, (D i 0 E 0 o I 01 - 4.5 -60 4.0 35 3.0 - _ _ _ _ _^ -SLOPE OF-1/2 2.5 20 SLOPE OF-2/3 1.0 1.5 2.0 2.5 30 3.5 4.0 4.5 5 -0.6 0.7 0.8 0.9 1.0 1.5 2.0 25 3.0 3.5 4.0 4.5 5J E i I20 P 4.5 L _=30~ -- - 4.0.. 30 SLOPE OF-1/2 2.5 - SLOPE OF-2/3 I-c - - - ------- s^ 1.0.7 8 0.9 1.0 2.5 3.0 3. 06 0.7 0.8 0.9 1.0 1.5 20 2.5 3.0 3.5 4.0 4.5 5. 11t 0 O 03 0 CD 0 0 0 0 (D 1 -Fb D 0 SCHMIDT NUMBER, Sc 4.5 F 4.0 E 3.5 U-,- 2.5 2.0 SCHMIDT NUMBER, Sc I I SCHMIDT NUMBER, Sc

N..5 100 X o-,, -~~ --- —--- 200 40 60_80_100_120_140_160180 ~o,~C 0 T^ 175 125 Q - -— _____________ 20 40 60 80 100 120 140 160 180 T- TEMPERATURE,~C Figure la. Temperature Variations of kc(Sc)0'5 for 9 = 180~, 150~, 120~, 90~ at Re = 2000.

V-p- DIBROMOBENZENE,A- PROPIONAMIDE -AN4THRACENE _____^~~~ _. —____ __ ______ _~__ Re 2000 0.00 0o0.0005 0.0 --- OCT --- -. 0 J u- 0.0065 I0 180, 150, 120, at Re 0.2000.0060 0050: — ~0 0.0115 - 0? < 0.0105 0.0 0 95 -- -- -- V - -- -- -- -- -- -- -- -- --- -----— El 20 40 60 80 100 120 140 160 180 200 T - TEMPERATURE OC Figure 12a. Temperature Variations of the Mass-Transfer jD-Factors for 9 = 1800, 150 120, 90 at Re = 2000. I 4=0-1

00240 0.023C o 0.0220 (D Q021 y^ 0021 C co 0.0200 0.0190 Q027Q () 0.0260 0 0 - 0.0250 2 I < 0.0240 I 0.0230 0.0220 0.0290 0.0280 0 0 0.0270 <C 0 0.0260 Q0250 Q0240 v _ -- --- -- -- --- -- -- --- -- -- --- ---- KEY r ---- --- --- --- --- -- --- --- --- --- --- -- -- 0 - NAPHTHALENE, ---- --- ------ --- --- --- --- --- --- --- --- - V — p-DIBR OMOBENZENE,) _ — --- + A_ _ _ ___. _ A --- — - PROPIONAMIDE, II -- - - ^ ---- --- I -— ]-.... El-ANTHRACENE 0 _ ) ____ _ O _ 1 ____ ___ Re 2000 JD OC TO.,k(~~~~~ - l |. --- ---- ---- --— |~ ~ — SLOPE OF DATA, 1+ -------------------- 13 --- ---,,-..0 _ ________ _I___ _.____ I I 0 ~3 El —l -- -4 --- i" 2 A 1 i 4 4 1 4 4 4 4 4 4 -1 -I I I 4 20 40 60 80 100 120 140 160 180 200 T - TEMPERATURE,~C Figure 12b. Temperature Variations of the Mass-Transfer jD-Factors for G = 60~, 30~, 0~ at Re = 2000.

V DISCUSSION OF RESULTS 1o Evaluation of Results The results correlate well with the heat transfer data of Churchill using an exponent of 1/2 on both the Schmidt and Prandtl numbers. The agreement of the heat and mass j-factors is significant in view of the differences in methods and mechanisms0 Employing hot wire anemometer explorations, Churchill confirmed the presence of uniform turbulence in the vicinity of the test object. Maisel and Sherwood(77) found no variation in the mass transfer rates below a turbulence of 12% for Re = 1000; while at Re = 5000, no effect was noticed below 4%, The work of Baines and Peterson(2) relating turbulence levels to screen dimensions indicates a turbulence of less than 2% in the present work. Figures 5 through 8 show the agreement of the local heat and mass transfer j-factors. High values are observed in the impact region, somewhat lower at the back, and minima at about 120~-150~ from the stagnation pointo At Re = 400, the minima occurs at 150~ which decreases to 120~ for Re = 4000. Similar distributions of skin friction coefficients have been found(26, 37) From Figures lOa and lOb, it is evident that the 2/3 power of the Schmidt number is too large while 1/2 is more representativeo An accurate value for the Pr exponent cannot be obtained from heat transfer to gases because the Prandtl number varies littleo In the Bedingfield and Drew(4) investigations of mass transfer from cylindrical surfaces, an exponent of 0.56 is obtained. The data of Gilliland and -48 -

-49 - Sherwood(38) support this value. In these studies, the Schmidt number is varied from 0o5 to 2o5. In packed beds, Gaffney and Drew(32) observed that the j-factor increased with the 0o58 power of the Schmidt number which varied from 150 to 13,000o However, in pipes the studies of Linton and Sherwood(72) for Schmidt numbers between 1000 to 3000 and Lin et al^1) for the transfer from flowing electrolytes to the surface of an electrode where Sc varied from 325 to 3100 give a 2/3 exponent on the Schmidt number. Carberry(9) shows that a fixed exponent should not cover a large variation of the Schmidt numbero Instead a variable exponent from 1/2 to 2/3 with increasing Schmidt number is proposed. A firm choice for a constant exponent cannot be madeo The surface temperature was taken as the gas temperature minus a small wet-bulb correctiono This correction was calculated by the heat and mass transfer analogy. If the relation were in error, this would introduce only a slight error in the surface temperature which is used to obtain the vapor pressure and mass transfer coefficient~ In the present investigation the heat transfer coefficient was not determined~ No direct comparison with other local.measurements, except ChurchillVs, is possible since they were at other flow rateso At a Reynolds number of 2000, sublimation rates were determined over a temperature range of 125~Co Since experiments evaluating the effect of temperature on mass transfer coefficients are limited, it must be approximated from available correlations, Gilliland and Sherwood(38) and others confirmed that the mass transfer coefficients can be described by the dimensionless equation, k D/D - const (Re)a(Sc)b (41)

-50 - Equation (41) may be written as c (b)s )(DL- c (Re) (S) = const (Re)a(Sc)b(42) u, Dvp U By definition, D = kc (Sc)05 const (Re)a-1 (Sc)b-05 (43) u For the conditions of this investigation where b = 0O5 and the Reynolds number is constant, the jD - factor would be expected to be temperature independent, The temperature dependencies a:the physical properties involved in the above equations are p a 1/T - for air D, a T1095- according to the Hirschfelder et a (47) technique t ac T0O75- for air G a T0 75_ for constant Re where Goxp T075T u a T175- since u = G/p (T075)(T'1) = T1~75 p The effect of temperature on the Schmidt factor to the 005 power is then (Sc)O05 a (T-0020)0o5 T-010O At a constant Reynolds number, there then results from Equation (41) kc aC T1~95 x T-010 = T1.85 or kc(Sc)~o5a Tl185 x T-10O=Tlo75 Similarly, from Equation (43) jD O T~00 Temperature variations of kc(Sc)O 5 for given angular positions are shown in Figures lla and llb. The dashed lines with the predicted

-51 - variation of T- 75 are included and within experimental limitations give a fair representation of the data. A slope with T1 50 is far more in accord with the data, A closer study of these data indicates considerable scatter with a slight increasing variation of k with increasing g temperature for each of the organic solids. Figures 12a and 12b show that jD decreases less than 10% over the 125~C temperature range for any position and may be taken as constant. 2. Comparison of Local Distributions with Other InvestigatiOns Only a few studies of local measurements of heat transfer and none of mass transfer are reported for Reynolds numbers of the present investigation. In Table II are references to other local transfer studies together with their ranges and methodso The distributions can be classified into the pre-critical, critical and the post-critical Reynolds numbero In the pre-critical region, all j-factor distribution curves have maximums at the stagnation point, G 0, and decrease to minimuma at approximately 90~-120~ nearly coinciding with the point of separation of the laminar boundary layer from. the surfaceo The curves continue to gradually increase to a second maximum at the rear stagnation point, G 180~o For large Reynolds numbers, the rear stagnation maximum is the greater due to the eddy motion of fluid behind the bodyo In the critical and post-critical regions, the distribution in the forward region, G < 90~ is similar to that for pre-critical flowo However, the first minimum occurs between 80 an.d 95o and is attributed to a transition from laminar to a turbulent boundary layer, The sharp maximum between 100~ to 1200, is apparently

-52 - due to increasing turbulence in. the boundary layer and vorticity sheet. The second minimum, at about 1.40~ coincides with the separation point of the boundary layer from the surface. The distribution curves increase gradually from here to a maximum at the rear stagnation point. This is ascribed to a circular motion of fluid going from the joining point (where the two branches of fluid join behind the cylinder) towards the separation point of the boundary layer. Increasing turbulence causes a decrease in the critical. Reynolds number. Distributions obtained in this study and other investigations are given in Figures 13a to 13go From the published data, heat and mass transfer j-factors were calculated in 30~ increments Most of the precritical data give linear plots of log j versus log Re with slopes varying with angular position. For the studies spanning the critical range, linearity is apparent for the front of the cylinder while the data in the rear often are scattered. For these plots, straight lines are drawn by sight. Unfortunately the 30~ segmental average transfer distributions particularly in the rear half at the higher Reynolds numbers do not indicate the lobes of the distribution curveo In view of the meagerness of data points, nearly al l j-factor distributions are calculated f'rom the graphical results which in certain instances could only be approximately determined. This is true partic~ularly for the study of Krujilin and Schwab(67) who presented smooth distributions for Reynolds nzmbers of 1000, 2000, and 4000 in small graphso In Figures 13a through 13d, studies including the present agree on the impact half, while on the rear discrepencies are appreciabl.e As an example, the plots for the data of Eckert and Soehngen(27) at low Reynolds numbers from 23 to 597 agree satisfactorily with the present study

-53 - Table II Comparison of Previous Local Heat and Mass-Transfer Studies Constants (B & n) for j-Factor Equation, j = B(Re)-n, for Various Angular Positions Reynolds Number & Cylindrical No. Study Turbulence Level Diameters * Methods and Comments Constant 0~ 30~ 60~ 90~ 120~ 150~ 180~ 1 This study 400 < Re < 4000 1.00",1.25" Sublimation of organic solids from 30~ B 0.817 0.860 0.899 1.330 0.685 0.069 0.0204 Turb. < 2% (est.) 2 Churchill,S.W. & J.C. Brier, 300 < Re < 2300 CEP Sym.Ser.No.17,51,57 Turb. < 2% (est.) (1955) cylindrical segments. 1.00" Heat transfer from radial temperature profile through 30~ sector of tube wall 1.49" Measured steam condensation over 30~ segments. Data only given for Re=39.000. 0.5",1", Employed interferometer to determine 1.5" radial temperature field around cylinder. n 0.451 0.466.496 0.635 0.624 0.279 B 0.847 0.947 0.842 1.602 0.715 0.064 n 0.456 0.477 0.486 0.671 0.592 0.293 0.101 0.0224 0.117 3 Drew,T.B. & W.P.Ryan, Trans.AIChE,26,118(1948) 4 Eckert,E.R.G. & E.Soehngen, Trans.ASME,74,343(1952) 5 Fage,A. & V.M.Falkner, Gr. Brit.Aero.Res.Com.Rept. & Memo.No.1408(1931) 6 Giedt,W.H.,Trans.ASME,71, 375(1949);J.Aeronat.Sci., 18,725(1951) 7 Klein,V.,Arch.Warmewirstch. u.Dampkessekw.,15,150(1934) 8 KruJilin,G. & B.Schwab, Tech.Physics USSR,2,312 (1935) Report Distribution at Re=39,000. 23 < Re < 597 Turb. not reported 5.89" 70,800 < Re < 219,000 4" Turb.approx. 2.25% and < 1%. 8,000 < Re < 75,000 Turb. not reported 20,000 < Re < 75,000 4.4 Turb. not reported Heat transfer rates measured from electrical input to a nickel strip substending 2. (Linearity not apparent.) Measured temperature variation around heated cylinder by heating ribbon wrapped helically around surface. (4% Turb. not included.) Measured change in dimensions of subliming ice cylinders. Thermocouples inserted in surface grooves of steam heated tube. B 1.182 1.124 0.954 1.289 0.498 0.396 0.430 n 0.516 0.518 0.527 0.656 0.614 0.549 0.510 B 0.171 0.168 0.0977 0.00551 1.048x10-4 0.00341 0.00566 n 0.330 0.331 0.297 0.067 -0.290 0.014 0.046 B 2.687 2.330 1.753 0.0788 0.01524 0.0473 0.0671 n 0.582 0.573 0.568 0.338 0.180 0.243 0.261 B 1.776 1.761 2.178 1.473 0.921 0.638 0.574 n 0.538 0.545 0.578 0.592 0.511 0.452 0.427 8a 8b 1060,2080, & 4020 Turb. not reported Krujilin,G.,Tech.Physics 6,000 < Re < 425,000 USSR,5,289(1938) Turb. not reported B 3.389 3.598 2.575 1.141 0.562 1.171 0.676 n 0.539 0.655 0.628 0.649 0.518 0.571 0.479 B 0.497 0.439 0.239 0.0416 0.0553 0.505 1.374 n 0.408 0.407 0.382 0.260 0.243 0.407 0.478 B Re > 130,000 0.108 0.138 n 0.277 0.281 B 0.758 0.679 0.581 0.273 0.0274 0.00769 0.0222 n 0.454 0.450 0.456 0.459 0.238 0.016 0.099 9 Lohrisch,W.,Forsch.Gebiete 5,000 < Re < 25,000 5cm Air-Ammonia stream absorbed on 12 longiIngenieuw.,No.322,45(1929) Turb. not reported tudinal strips of blotting paper saturated with phosphoric acid. 10 Powell,R.W. & E.Griffiths, Relative rates of evaporation from nonaTrans.Inst.Chem.Engrs., gonal prism approximating a cylinder were London,13,175(1935) measured. No quantitative data appear in the article. 11 Robinson,W. & L.S.Han, Report distribution 1.5" Heat transfer distributions in ducts Proc.Midwest Conf. Fluid at 21,300 determined from radial temperature difMech.(2nd Conf.), 349, ferenials. Results for single cylinder (1952) similar to (12). 12 Schmidt,E. & K. Wenner, 8,290 < Re < 426,000 5cm,10cm, Measurementsof heat transfer distribuNACA TM 1050,1943 Turb. not reported 25cm tion from steam heated tube presented in 10~ intervals. 13 Seban,R.A.,Trans.ASME, 50,000 < Re < 300,000 1.2'51.87" Bakelite cylinders with Nichrome heating Series C, 82,101(1960) Turb. from 1-3% ribbons wrapped on their surfaces. Influence of turbulence intensity on local heat transfer studied. 14 Small,J., London Phil 22,400 < Re < 84,100 4.5" Thermopile embedded in steam heated tube Mag.,19,251(1935) Turb. not reported used to measure the distribution. 15 Winding,C.C. & A.J. 10,600 < Re < 32,000 1.49" Measured change in dimensions of sublimCheney,Jr., IEC,40, Turb. not reported ing naphthalene cylinders. 1087(1948) B n B n 1.132 1.076 0.765 0.01434 0.00970 0.0348 0.494 0.479 0.484 0.194 0.097 0.204 Re > 120,000 0.0700 0.247 1.516 0.514 0.272 0.324 0.1761 0.303 B 1.131 1.177 0.876 0.00446 0.0384 0.1968 n 0.459 0.471 0.467 0.026 0.183 0.313 B 1.910 1.801 1.068 1.360 0.1219 0.1086 n 0.543 0.544 0.516 0.611 0.330 0.282

.3001 - I- F 11 1 Ii I F IIIZI(4) 2 21 E I 1 (4)/i i i i 1111 i I i lli o n n ------ - ^ I- - - - ------ --- -- - - - _ --------- -- - - - _ --------- -- - - - _ _ -------- -- - - - -. - - 8 =0.100 nOR KEY _ ---_ - MASS TRANSFER, JD HEAT TRANSFER, JH.040 (I) tL4J I 18a) II.020.010.008.006 7117 __________ ____ - -1 ____ - - ____ _____ ____ i \J1 -pI7.004.002 '1d).001 - 10I 02 103 104 105 1o6 REYNOLDS NUMBER, Re Figure 13a. Comparison of Previous Local Heat and Mass-Transfer Investigations for 9 = 0~. See Table II for explanation of numbering system.

.300.200.100.080.060.040 In o I L_.020 (4) -300 KEY. ---- MASS TRANSFER,j ___- _ (2) - -- ---- HEAT TRANSFER,JH H (80) ' -, (,9) (12) ~... 17-.5) ' _6) __ _.Bb) ---- -- - - _ _ _ _ _ ---- -- - - _ _ _ _ _ ---- __ _ _ _ _ _ _ _ ______ _ _ _ _ _ _ _ ______ _ (iz ) _ _ _ _ _~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~,..010.008.006.004.002.001 \J1 <n ',./! 10 l2 13 4 10 0 10 6 I0 REYNOLDS NUMBER, Re Figure 13b. Comparison of Previous Local Heat and Mass-Transfer Investigations for 9 = 30~. See Table II for explanation of numbering system.

.300.200 (4) ---- ----- 0=600.100 - KEY.080 -- MASS TRANSFER, JD.60 HEAT TRANSFER, JH -.040 C', o.020 0 -(12).010 __-5).008 1 -I - i ( I i I -_.006.004 (7) -",,^(6)..002 112).001 -- i0 d0 103 10 10 10 REYNOLDS NUMBER, Re Figure 13c. Comparison of Previous Local Heat and Mass-Transfer Investigations for a = 60~. See Table II for explanation of numbering system. \-1

.300.200.100.080.060.040 KEY -- - MASS TRANSFER, JD HEAT TRANSFER, H I-.020.010.008.006 -- (.15) (8b)- (8)_.004 (13) 102) - 10 05 (6) (8b).002 — ~__.001d ---- 0 -. iO- 06 0 REYNOLDS NUMBER, Re Figure 13d. Comparison of Previous Local Heat and Mass-Transfer Investigations for 9 = 90~. See Table II for explanation of numbering system. I \n J I<

.300. --- ---.200 8 120~.100 -- KEY.080 (4) - -- --- MASS TRANSFER, JD.060 1 - l- L HEAT TRANSFER, JH ---.040 cn <U-~~~~ ~~~ — o.020 -- (2), 0 (8a).006 F I II II___I___F_ TT -1___I____________.010 - 1010.008 (8b) (8) (13).002 REYNOLDS NUMBER, Re Figure 13e. Comparison of Previous Local Heat and Mass-Transfer Investigations for 9 = 120~. See Table II for explanation of numbering system. I CI Oo

(-) '"'3.300.200 8 = 150~.100 5 - KEY.080 (4) MASS TRANSFER, JD.060 ---- HEAT TRANSFER, JH.040 (80).020 (2) (I)N.O 0 __ __ "- -- *010 - ----- -- -- _~ — --—..3) -.-~008 ---------— Z --- —--------—..- ~ —_- (e^ ------— (9)O.006 (14) (7):..004 - (8b) 6] - - - - - -12)-.002 ~nnm.......00 ---- - - - I - --- -- - - _ _ --- -- - __d --- -- - _ _ _ --- - - - _ I \ I k 10 id' 10i 10 10~ 10o REYNOLDS NUMBER, Re Figure 13f. Comparison of Previous Local Heat and Mass-Transfer Investigations for 9 = 150~. See Table II for explanation of numbering system.

.300...- -.200 8=180~.100 - (4).08o KEY.060 -- - --- MASS TRANSFERJD.040 - - _____ ___ __ ___^ ___ ____ -___ ______ ___ __ _ ___ _ _____ _ ---- HEAT TRANSFER J H (8a).020.(1) (8b).010.(.) _-_ — 'I_3 - -- _.006.004 ------ --- — ____ — ------ --- — _ ___ — ------ --- — __8) --- —-- --- b ___,^^ ---^ — _______.004 6) (,) o 0!-) I "I O 0 I '(12.001 L 10 2 I0 3 I0 4 10 5 10 6 10 REYNOLDS NUMBER. Re Figure 13g. Comparison of Previous Local Heat and Mass-Transfer Investigations for O = 180~. See Table II for explanation of numbering system.

for 0~ to 135~ with increasing disagreement for 135~ to 180~o Evidently the rear of the cylinder is more sensitive than the front half to the process conditions. The agreement of various studies is good in light of dissimilar techniques used including sublimation, absorption, and heat transfero 30 Comparison of j-Factors with Other Investigations The assumption of the equality of JH and jD has been used to predict mass transfer from heat transfer data and vice versao The validity of this assumption has not been adequately proved. A verification would be helpful. in interpreting data such as from heterogeneous catalysis, absorbers, packed and fluidized beds, Table LI contains references to studies of the heat-mass analogy together with comments and suggested ratios of (jH/iD) The table indicates the equivalence of the j-factors for flow past objects including cylinders, spheres, disks, and flat surfaces. The studies of Ranz and Marshall(85), Sogin9 Furber, (3) and Jakob et al, (5) contribute convincing support to the ppximae eality he roheat and mass transfer j-factors averaged for the whole surface areao For wetted-wall columns, the (jH/jD) ratios differ, Sherwood's9 comparisons indicates that the ratio may vary from 0o62-1o Opposed to Sherwood's results are those of Barnett and Kobe (3) which indicate that the heat transfer data without simultaneous mass transfer are 24% greater than the mass transfer data, Cairns and Rope(8)indicate the equivalence of the j-factors at low humidities fo the flow of air and water within a wetted-wall column, Overall evaluation of the transfer processes within

-62 - the wetted-wa.l. columns indicates a (JH/JD) ratio less than one for laminar Reynolds numbers and approaching unity with increasing.Reyno.lds numbers o For wall to fluid transfer within packed beds' the equivalence of JH and JD for turbulent flow was verified by Yagi and. Wakao(16) o For transfer between the packing and fluid within packed beds, the jHo (19) factor is greater than jDo The recent study of DeAcetis and Thodos ( indicates, contrary to previous assumptions, that the temperature of the packing surface is not the same as the adiabatic saturation temperaturle of the incoming air for the evaporation of water in air, For the case where the adiabatic saturation temperature is assumed, a value of (jH/JD) equal to 1.08 is obtained, The independent heat and mass measurements of DeAcetis and Thodos give values of (H/JiD) from. i.17 to 3006 with an average of 1o51o A decreasing ratio was noted with increasing Reynolds numbers. The authors note that the wet-bul b temperature is reached at the higher intersticial velocities, thus it may be inferred that (jH/jD) would approach 1o08 at the high velocities In the Wilke and Hougenll4) fixed bed experiments, it was observed that the solid particles rapidly reached the adiabatic saturation temperature so that it was necessary to limit the bed height to a few particle diameters to prevent the outlet gas from becoming saturatedo Surface temperatures higher than the adiabatic case (from 0o8 to 1020~F for DeAcetis and Thedos) have a marked increased effect on (JH/JD) in that JH increases while 3D decreases Additional support that the (JH/JD) ratio is greater than unity for packed beds is supplied by the chemical reaction (91) experiments of Satterfield and Resnick, A ratio of 1o37 is reported for packed beds while 109 is observed for reaction in a cylindrical tube

-63 - fabricated from the same catalytic metal as the bed packing. Gordon(40) compares the data of many investigators relating independently obtained jH and jD- factors to Reynolds numbers for fixed beds of spheres. The plotted data points, covering wide ranges of variables, indicate that jH is consistently greater than jDo The ratio (jH/jD) may be approximated by lo5. Independent measures of heat and mass transfer in the same fluidized column are reported by Kettering et al () The results were calculated on the basis of many questionable assumptions. Wamsley and Johanson(llO) discuss weaknesses inherent in the Kettering et alo investigationo Recalculation of the heat transfer coefficients by using the adiabatic saturation temperature of inlet air as the fluidized bed temperature gives an average (jH/jD) ratio of lo09o Since the magnitude of the heat transfer coefficient and the transfer mechanism is not established with certainty(111), the (jH/jD) ratio for fluidized beds remains in doubt. Satterfield et a1 (90) attribute the heat and mass j-factor differences from. their tube studies too (1) a temperature gradient and. simultaneous heat and mass transfer, (2) the effect of counter and bulk diffusion, (3) thermal diffusion, or (4) and effectso These four conditions may possibly account for discrepencies noted in other investigationso Nusselt as noted in Eckert(26) indicates that if heat and mass transfer occur separately in geometrically similar fields with the same boundary conditions for each case, the principle of similarity may be applied to predict the transfer of one from measurements of the othero Eqiuations for heat and mass transfer occurring separately and simultaneously have been derived by Nusselto For low solute concentrations, the simpler equations for separate fields is usually applied, It is possible

Table III Representative Studies Concerned with the Heat-Mass Analogy Type Study Study Comments jH/jD J/jD Limits.~ ~ ~ ~ ~ ~~~~~~~~~~~~~~~~~~~HJ.J.L..m..i_,, Cylinders (normal flow) *This study Dobry,R. & R.K.Finn, IEC, 48, 1540(1956) *Comings,E.W.,J.T.Clapp, & J.F.Taylor,IEC,40,1076(1948) Spheres Disks Flat Surfaces Wetted-Wall Columns (diffusion controlled chemical reaction in tube) Sherwood,T.K.,IEC,42,2077 (1950) *Ranz,W.E. & W.R.Marshall, CEP,48,141 and 173 (1952) Sherwood, T.K.,IEC,42,2077 (1950) Linton,M. & K.L.Sutherland, Chem.Eng.Sci.,l2,214(1960) *Hsu,N.T. & B.H.Sage,AIChE Journ.,3,405(1957) Garner,F.H. & R.D.Suckling, AIChE Journ.,4,114(1958) *Sogin,H.H.,Trans.ASME,80, 61 (1958) *Heertjes,P.M. & W.P.Ringens, Chem.Eng.Sci.,5,226(1956) *Furber, B.N.,Proc.Inst.Mech. Engrs.(London),168,847(1954) *Jakob,M.,R.L.Rose, & M. Spielman,Trans.ASME,72,859 (1950) Sherwood, T.K.,IEC,42,2077 (1950) *Barnett,W.I. & A.Kobe,IEC, 33,436(1941) *Cairns,R.C. & G.H.Roper, Chem.Eng.Sci.,4,97(1954) Sherwood,T.K.,IEC,42,2077 (1950) *Satterfield,C.N.,H.Resnick, & R.L.Wentworth,CEP,50,460 (1954) Local mass transfer measurements for 30~ segments compared r1.0 0.84 - 1.18 with analpgous heat transfer results of Churchill and (3) Brier. (15) The H and JD distributions nearly coincide for the chosen experimental conditions. Mass transfer to a cylinder at low Re(< 10) agree with the -s1.0 heat transfer measurements of Davis.l 8) Studied effects of air turbulence for heat and mass transfer 1.0 from cylinders. Even though results are widely scattered, it is evident that the heat transfer data are consistent with the mass transfer results. Compares literature values with McAdams' generalization for -a 1.0 0.85 - 1.30 flow transverse to a cylinder. (3) Correlations of heat and mass transfer obtained from drop 1.0 0.8 - 1.2 temperatures and evaporation rates. Data obtained from (1) Re = 0 - 200. Comparison of Maisel's data (jD) with McAdams' (JH) shows -1.10 0.95 - 1.35 that the JH line is slightly higher than JD by approxi- (3) mately 10%. This paper compares the transfer predicted from theory of 1.0 a laminar boundary layer with experimental results for heat and mass transfer. Agreement noted between JH and JD. Agreement indicated between thermal and material transfer 1.0 in turbulent gas streams (Re from 1530 to 4200). Comparison of JD values obtained with JH from McAdams suggest -l1.15 that the analogy is applicable. Values of JD are approximately 15% higher. Sogin shows that his mass transfer results coincide with the 1.0 data for heat transfer by convection in-an identical configuration. Heat and mass transfer data obtained for the evaporation of __1.0 0.81 - 1.32 four liquids in air. (2) Presents heat and mass transfer data on humid air flowing 1.0 0.55 - 1.55 over a plane containing an isolated cooled region. (2) Heat and mass transfer results obtained by discharging hot 1.0 0.75 - 1.20 air from a continuous slot parallel to a plane surface. (4) Compares mass transfer data with McAdams'representation for -1.0 0.80 - 1.35 flow over flat plates. Agreement is satisfactory. (3) Heat and mass transfer data obtained. Results show that 1.24 0.90 - 1.60 JH/JD = 1.24. Their mass tragsfer data are 13% less than (4) Gilliland and Sherwood's (3. An equivalent basis for H20 vaporization with (38) give JH/JD = 1.10. Simultaneous heat and mass transfer data obtained with flow m1.0 0.77 - 1.37 of air and water. For low humidities JH = JD. (2) Compares many sets of mass transfer data with McAdams' heat ol 0.60 - 1.00 transfer correlation for flow of gases through pipes. All (3) data lie from 0 - 60% above the McAdams' line. The rates of simultaneous heat and mass transfer in a gas- 1.09 0.94 - 1.24 solid diffusion controlled chemical reaction (decomposi- (1) tion of H202) were measured with the flow of H202 vapor through a cylindrical tube.

-65 - Table III (Cont'd) Representative Studies Concerned with the Heat-Mass Analogy Type Study Study Comments jjH/D Limits Container (liquid-solid *Hixson,A.W. & S.J.Baum, Equations correlating heat transfer data for several liquids 1.29 1.06 - 1.58 agitation systems) IEC,33,1433(1941) Packed Beds Gamson,B.W.,G.Thodos,O.A. Hougen,Trans.AIChE,39,1 (1943) Wilke,C.R. & O.A.Hougen Trans.AIChE,41_,445 (395) Taecker,R.G. & O.A.Hougen, CEP,45,188(1949) *DeAcetis,J. & G.Thodos, IEC,52,1007(1960) (diffusion controlled *Satterfield,C.N. & H. chemical reaction) Resnick,CEP,50,504(1954) Gordon,K.F., Paper presented at Chem.Eng.meeting, Washington,D.C.,1960 (wall to fluid in a *Yagi,S. & W.Wakao,AIChE packed bed) Journ.,5,79(1959) Fluidized Beds *Kettering,K.N.,E.L. Manderfield, & J.M.Smith, CEP,46,139(1950) Wamsley,W.W. & L.N.Johanson, CEP,50,347(1954) in a series of geometrically similar agitators is similar in form to the expression correlating mass transfer data in the same equipment. Present data on drying of wet cylinders and spheres randomly packed with through air circulation. It is shown that JH/JD = 1.08. However, since the surface temperature is assumed equal to the wet-bulb temperature of the entering air, ths ji's given are not based on independent measurements. Sherwood(94C shows that JH can be calculated from jD. (1) 1.08 The temperature of water evaporating from spherical catalyst 1.51 1.17 - 3.o6 carriers has been measured directly, and it was found that (2) the surface temperature is the same as the wet-bulb temperature only at the high air velocities. The reaction mentioned above was observed in a bed packed with 1.37 1.29 - 1.45 spheres of the same catalytic metal. (1) For fixed beds of spheres, the data of many investigators re- ^1.5 lating to JH and JD factors are presented. Approximately 1000 data points from 20 investigations indicate that j-H/jD W1.5. Heat and mass transfer from tube wall to fluids flowing through 1.0 0.75 -1.50 packed beds were determined separately. It was found that (4) JH = JD in the turbulent region. Heat and mass transfer between solid particles and the gas 11.68 10.94 - 12.42 stream were measured for desorption of water from silica- (1) gel and activated alumina fluidized in air. Irregularly (see comments shaped particles were assumed to be equivalent spheres. Tem- of Wamsley et peratures of the gas were determined by bare thermocouples al. next ref.) immersed in the bed. The solid temperature was assumed constant and equal to the equilibrium temperature of the gas leaving the fluidized column. (Temps. 10-20~F higher than the adiabatic saturation temps. were recorded.) Recalculated heat transfer coefficients of Kettering et al. 1.09 by assuming the adiabatic saturation of the inlet air as the temperature of the fluidized bed. The jH-factors decreased from the original values by factors from 4.83 to 24.6 increasing with increasing Re and decreasing particle size. The average decrease of this ratio being 10.65. Thus the recalculated JH/JD ratio becomes 11.68/10.65 = 1.09. Footnotes * indicates independently measured heat and mass transfer data (1) calculated from average deviations of JH and iD (2) calculated from maximum and minimum JH's and JD's (3) ratio of JD extremes to JH from specified source (4) calculated from jD and iH extremes of correlating line

-66 -that differences between jH and jD may be caused by lack of field similarity. No other explanations for the disparity between the jH and jD factors, particularly for packed beds, can be advanced, Further studies in which heat and mass transfer data are obtained under similar physical circumstances in packed beds (fixed and fluidized) areneeded to determine the limitations of the (JH/JD) ratio. Particular attention should be devoted to ascertaining the surface temperature of the packings.

PART II DETERMINATION OF VAPOR PRESSURES FOR NAPHTHALENE p-DIBROMOBENZENE PROPIONAMIDE, AND ANTHRACENE -67 -

VI INTRODUCTION Unsatisfactory literature values for vapor pressures, disagreeing in some cases by a factor of two, necessitated measuring the vapor pressures of Naphthalene, (crystal reagent, Baker an.d Adamson) p-Dibromobenzene, (practical grade, Eastman) Propionamide, (highest purity, Fischer Scientific) Anthracene (highest purity, Fischer Scientific) They were determined by the air saturation method where a measured volume of air is saturated by passing through a bed of the solid at a definite temperatureo The amount sublimed is determined by the weight loss. The vapor pressure is then calculated from the gas lawso The heat of sublimation is obtained from the ClausiusClapeyron equation, x = -Rd(ln p)/d(l/T) (44) -68 -

VII EXPERIMENTAL EQUIPMENT The equipment, shown in Figure 14, consists of~ a) a silica gel bed for drying the air; b) an air flow control and measuring system; c) a constant temperature bath; d) a U-tube holding a bed or the organic solid; e) instruments to measure pressure, temperature, and cumulative air flowo The air feed system contains a cut-off valve, pressure regulator, thermometer. Bourdon pressure gauge, rotameter, and needle control valve, A nest of three stirred baths maintained the U-tube to +01oOCo The outermost, made by Precision Scientific, has three independently controlled 1 KW heaters. The middle bath is a battery jar whose temperature is maintained by a 1/4 KW heater controlled by a mercury thermostat. The unheated inner bath is a 3 liter stainless steel beaker. The air flows through copper tubing submerged in each batho The U-tube bed, 5/8" IoD, and 10" long, is in the stainless steel beaker. A manometer gives the.outlet bed pressureo The air from the bed goes to a series of three bubblers prior to a wet test meter. Temperatures are determined by calibrated porcelain-jacketed thermocouples -69 -

-70 - SCHEMATIC DIAGRAM OF EQUIPMENT FOR DETERMINATION OF VAPOR PRESSURE @ L bTLI Figure 14. Schematic Diagram of Vapor Pressure Equipment.

VIII EXPERIMENTAL PROCEDURE The solids were pressed into 1/8", 1/4", and 1/2" spheres by punches and dies (F. Jo Stokes CO )o The temperature of the middle bath was maintained slightly above those of the other baths for improved steady state conditions, The temperature fluctuations decreased from the outermost to the inner bath o After the packed U-tube was weighed and inserted in the inner bath, it equilibrated with the bath for approximately 15 mino before passage of airo In all runs, the air through the bed was less than 1 ft3/hr. The air pressure was reduced from. 90 to 30 psig prior to the rotametero Constant flow was maintained, The U-tube was 'stoppered to reduce loss prior to post-weighing, Preliminary tests indicated that the weight loss of the bed while exposed to the atmosphere during the loading and recovery operations was insignificant, Approximately ten experimental runs at different temperatures were made for each of the organic solids, The runs were from 5 to 15 hourso Operating temperatures, bed and atmospheric pressures, and air flow rates were periodically recorded, A sample data' sheet is shown in Figure 15, -71 -

DATTA SHEE;T FOR VAPR PRZ~SSURE DiMr~W ONON DATE - ce. We 20 MATHRIZAL_ TIME S.., BEAKR OTIKE BATH," f, ^, ml T,-, ' -- 1 1. W. (Hours) (IV) ( C) (IT) ( C) (my) ( C) (UV) (~C) I! I I 1- l e I _______ — r —' — s.,4^ ^ _ = 2 ^. _4 _ -mlm~ A 74m & ----- 1^ I.? 6ZIg ______ la I ------— 1g___ -______, - __ ------- ^-V =; 5 &t, ------,,7f, ^ ZS. — ^-g^___________________________~~~ _____ ~ YLL ~_I aJ7.i^ ^-r, <.c^ ^it^ I - ________ PR3SSURSs Pmal (m W) A210sifOBHIC (loan Hg).AB2EfL~U2SI (mm hg) AIR PLOW "RggPEWRSR UNITS PRESS g.-. (psig) WR.T VOLUME (ou tt) (our Hg) I -1 I VT. LOBS WRP LOSS... mu (gas) (gms) (gi) / /o 7C / - 2. o 7Z7.5 7'~ e7-E-D s0 wVED f=~ 0^,Vk~2 6 0 7/z /230 37.s Figure 15 Data Sheet for Vapor Pressure Studies

IX RESULTS The original and processed data are summarized in Table V. The data are correlated by plots of log p versus 1/T shown in Figures 16a and 16bo The following represent the least-square lineso 1) Naphthalene log p = 11.61705 - 3786o64/T 2) p-Dibromobenzene log p = 11o73772 - 3885 20/T 3) Propionamide log p = 10.45681 3543 20/T 4) Anthracene log p = 9 07248 - 3827 42/T The respective average deviations are 0o64%, 2o40o, 0o36%, and 2o16%o Heats of sublimation calculated by the Clausius-Claperyon equation are MATERIAL ae. (BTU/lb-mole) 1) Naphthalene 31,112 2) p-Dibromobenzene 32,044 3) Propionamide 28,417 4) Anthracene 30,132 -73 -

10 1.0 I E E u) U) c: (0 hr 0 a.. ---NAPHTHALENE PROPIONAMIDE — - ___ \_v_-, pDDIBROMOBENZENE KEy \ 1) Bedingfield a Drew (4) 2) This work \ 1 3) Bedingfield a Drew (4) _ 4) This work \\. 5) I.C.T. (53) 6) Thatcher et ol (104) \\ 7) Jordon (55) \\ (this line is extropoloted from higher temps. where Propionomide exists in the liquid state.) \ 8) This work 70 65 60 55 50 45 40 35 30 25 20 DC — I [I, 1I 1-I, II II I i 11 I, I 0.1 0.01 2.80 2.85 2.90 2.95 3.00 3.05 3.10 3.15 0 3/TOK-I 3.20 3.25 3.30 3.35 3.40 3.45 Figure 16a. Correlation of Vapor-Pressure Data for Naphthalene, p-Dibromobenzene, and Propionamide.

I0 1.0 E w IJ (0. 0 o a >: 4). IC.(3 ANTHRACENE KEY, i) Mortimer 8, Murphy (83) -| 2) This work 3) Jordan (55) 4) I.C.T. (53) 160 155 150 145 140 135 130 125 120 115 I10 OC I) IMorime a Muph (83 I I I 0.1 nnl 2.300 2.300 2.350 2.400 2.450 10 / T OK 2.500 -I 2.550 2.600 2.650 Figure 16b. Correlation of Vapor-Pressure Data for Anthracene.

X DISCUSSION OF RESULTS The accuracy of the temperature is probably not better than +0.l~C at 100lC, and the error is less at the lower temperatureso The sublimed weight was determined to the nearest 0.1 mg and pressures (atmospheric and bed outlet) to the nearest 1 mm Hgo According to the JD correlation(40), the 10" bed is estimated to achieve saturation to within 10-5% for all vapor pressure runs, Except for naphthalene, there is disagreement with some of the results of other investigators as shown in Figures 16a and 16bo For p-dibromobenzene, the results are in agreement with those of Bedingfield and Drew but not those in the International. Critical Tables. It should be noted that Bedingfield and Drew used the air satuiration technique for both p-dibromobenzene and naphthalene, No experimental vapor pressures at the temperatures of interest were found in the literature for propionamideo The straight line shown in Figure 16a is extrapolated from higher temperatures where propionamide exists as a liquid. Since the log p vs 1/T plot increases slope when going from liquid to solid, it is expected that the experimental line would lie below the line extrapolated from the liquid, as was found.

XI SUMMARY 1o By simulating the heat transfer arrangement of Churchill with one for mass transfer, it was possible to compare local mass transfer by convection with heat transfer under similar conditions. The apparatus included an air flow system; a furnace for heating the air; an adiabatic tube for measuring the air temperature and developing uniform and low turbulence; and a test piece surrounded by a heating shieldo The organic solids were cast and a smooth surface obtained by shaving the curing. Local mass transfer from 30~ cylindrical segments were measured from sublimation losses, Tests were made with naphthalene, p-dibromobenzene, propionamide, and anthracene; Reynolds numbers from 400 to 4000; surface temperatures from about 25-150 ~C diameters of 1" and 1o25"; and an estimated turbulence of less than 2%o The local mass transfer results were correlated by jD= B(Re)'-n where the values of B and n vary with angular position but are independent of diameter and air flow rateo Most local ja-factors are within 15% of Churchill's jH-factors, confirming the analogy between heat and mass transfer. The standard deviations of the JDIs are 602% from the JD correlating lines and 78% from Churchill's JH correlationso From 4x10 < Re < 4x103, the average jD-factors are expressed by j = o064 (Re)-0~5 The average jD-factors are greater than the average jH-factors of Churchill, -0 5 JH 0 6653(Re), 5 and McAdams but agree within 15%o -77 -

At a Reynolds number of 2000, sublimation rates of the four organics were measured over a temperature range of 125~Co The j -factor which decreased less than 10% with increasing temperature for all angles, may be taken as constant.. The Schmidt numbers of the four organic solids ranged from. 1.79 to 3o05. The results indicate that 1/2, rather than 2/3, is a more representative value of the Schmidt number exponent in the j-factor equations 2. Appreciable disagreement in literature values for vapor pressures required that the vapor pressure of the solids used in the mass transfer studies be determined. Vapor pressures were obtained.by an air-saturation method, A measured volume of.air was saturated by passing through a U-tube bed, 5/8" OoDo and 10" long, of solid spheres situated within a constant temperature bath maintaining the bed to +0ol~Co The amount sublimed was determined by weighing. The vapor pressures were then calculated from the gas lawso Approximately 10 runs, 5 to 15 hours long, were made at different temperatures for each solid. For all runs, the air rate through 3 the bed was less than 1 ft/hro The vapor pressures were correlated by equations of the form, log p B-C/T. The least-square values of B and C are~o MATERIAL B C Naphthalene 11.61705 3786 64; p-Dibromobenzene 11o73772 3885020 Propionamide 10o45681 3543.20 Anthracene 9 07248 3827.42 Heats of sublimation were obtained from the Clausius-Clapeyron equation.

XII CONCLUSIONS Local mass transfer rates from 30~ segments of a cylindrical surface were determined from the weight loss of naphthalene, p-dibromobenzene, propionamide, and anthracene. Tests were made with cylindrical diameters of 1" and 125"t Reynolds numbers from 400 to 4000; surface temperatures from about 25 - 150 C; and an estimated turbulence of less than. 2', The following conclusions were reached~ 1o Most measured jD - factors agree within 15% of the independent jHr correlations determined by Churchill and Brier, The standard deviations of the jD's for all positions from the determined jD and Churchill and Brier s jH correlating lines are 602% and 7o8% respectively. This confirms the heat and mass transfer a;nalogy for the laminar and eddy flow regions of a cylindero The local mass transfer were correlated by jD = B(Re)n 2where B and n are independent of the Reynolds number o 2. The area average rates can be expressed by jD - 064(Re)-05 which may be compared with jH 0.63(Re)-0o5 as found by Churchill and Brier for small temperature potentials~ This shows agreement to within 2%o 30 An exponent of 1/2 for the Sehmidt number in the j-factor is more representative of the data than 2/3. 4~ At a Reynolds number of 2000, no appreciable variation of local jD - factors for a temperature range of 125~C is apparent o

-80 -5o The vapor pressures for naphthalene, p-dibromobenzene, propionamide, and anthracene were determined and satisfactorily correlated by, log p = B - C/To

XIII APPENDICES

-82 - 1o Details of Apparatus a, Air supply system Parallel silica gel units consisted of two vertical pipes 3" IoDo by 61 high dehumidified the air stream During a run, air flows through one of the two beds The other bed may be dried or replaced without interrupting the air flow. Each of the tubes is externally wrapped with an insulated chromel resistance heating wire and asbestos insulationo The water absorbed by the gel is removed by slowly passing a stream of air through a hot bed heated by surrounding heating wireo The center and right panels shown in Figure 3a contained three sets of regulating and indicating components. Each set contained a cutoff valve, a pressure regulator of the bleeding type (Nulmatic 40E50), a bimetallic-element thermometer (Weston 228-C), a Bourdon type pressure gauge (Duragauge 4-1/2'"), rotameter (Fischer Porter B-5N259 B-4A25, B2-26-250), and needle valve for controlling the flowo The rotameter fluctuated little, if at all, during a runo Rotameter calibrations for air at 700F and 45 psia are presented in Figures 18a-c. Since the air regulator reduced the pressure from 100 psi to 45 psia in all mass transfer runs, the calibration curves were used directly with a small correction applied for deviations from 700Fo b Air heating unit As shown in Figure 1, the air heating unit consists of a high temperature tube furnace containing a 2"? I.oD and 3" OoDo by 36" silicon carbide Globar element with watr cooled contact plates, temperature controller, and transformer unit.

-83 - Two 6 KVA transformers operating on 220 volt, 2 phase 60 cycle power supply voltage from 20 to 100 voltso An ammeter indicates the current to the primary power transformero The terminals of the heating element are water cooledo A spring loaded plate holds the electrical contact plate, the carbon block, and Globar element in place and allowing thermal expansiono The Globar is surrounded by refractory brick insulation which is surrounded by 4" of rockwool in a cabineto The furnace temperature is maintained by an electronic controller (Whelco 292)o The thermocouple of 24 gauge platinum and 10% rhodium-90% platinum wire is 1/8" outside and 12" below the top of the Globaro After the metering system, the air passes through a tube of three sections. The first or heat transfer section, at the bottom of the furnace, is 38" in length, 1-3/4" OoDo by 1-5/8" I Do; the middle or throat section is 6" in length, 11/16" OoDo by 1/2" I oDo; the third or adiabatic tube section, projecting above the furnace, is 6" long with a square cross section 2" OoDo by 1-3/4" I.oDo The throat section is surrounded by a cast refractory inside a split zircotube of the same OoDo as the heat transfer tubeo The whole assembly, containing the three sections, is set within the Globar element, being maintained in place by the projecting corners of the square adiabatic section resting upon transite sheets which lie on the spring loaded plateo The adiabatic tube section is surrounded with 1" of high temperature insulation and 2" of low temperature insulationo The heat transfer section is packed with 1/4" alumina sphereso A manometer determines the pressure drop across the furnaceo To prevent

-84 - bed movement of the alumina spheres, the tightly packed bed is held by a retaining screen located immediately below the throat tube sectiono The adiabatic section establishes the gas temperature, a uniform velocity and a low turbulence level for the air flowing past the test piece. It is filled with. 1/4V alumina spheres held in place by screenso The combination of two 52 mesh platinum screens mounted on the outlet of the adiabatic- section and separated by 1/4 furnished a uniform velocity profile and low turbulence level, about 2%o The air temperature is determined by a 24 gauge butt-welded chromel-alumel thermocouple with the junction located 1/4?! below the center surface of the lower platinum screen. Within the adiabatic tube, the bare thermocouple wire is inserted in a O09 mm IoDo by lo5 mm OoDo porcelain tubeo This section is surrounded by insulationo The top layer of alumina spheres contacting the lower platinum screen are covered with platinum foil thereby minimizing radiation losseso Because of the negligible heat losses, the temperature of the packing 1/4?1 below the level of the lower screen is assumed equal to the exit air stream. The upper layers of the alumina spheres are arranged to provide a nearly flat velocity profileo c. The mass transfer test unit The inconel test piece is shown in Figures 1 and 2O The cylindrical portion is 3-1/2" in length by 1-1/4" in diametero The test piece was machined from 2" inconel bar stock then cut longitudinally in half for inserting thermocouples within the test unit and for ease in constructing a niche to contain the boato Two set screws on each end extension hold the test piece together. The organic material in the boat subtends 30~ and is

-85 - 1-1/4" longo Removal of the boat is facilitated by winged screws inserted in two holes on each end of the 1/16" thick boato A longitudinal set screw through the cylinder holds the boat in position, Along the flat interior faces are five parallel grooves for the 40 gauge chromel-alumel thermocoupleso The junctions of the thermocouples are all located in the same cross-sectional plane as shown in Figure 2~ The thermocouples are butt-welded and coated with an electrical insulating enamelo The thermocouple leads from the test piece are insulated with asbestos braided tubingo The potentiometer (Leeds and Northrup. Model 8662) is read to within 2 microvolts, corresponding to Ool~Co The thermocouples were calibrated against NoBoSo thermometerso An electrically heated shield, 12" long by 12" in diameter, reduces radiation losses by maintaining its surface at approximately the temperature of the test pieceo The shield bottom contains a 2-1/2"' square hole in its center to allow the air from the square adiabatic tube to flow past the test pieceo Bolted to the base of the shield are a pair of 1" right angled steel brackets to support the test pieceo A truncated conical heated shield, above the cylindrical heated shield, has an altitude of 10" and diameters of 12" and 1-1/2.o To reduce radiation losses, the exit air leaves the conical shield through three parallel disoriented screens, 1/2" apart, then passes to a vent blowero Both shield temperatures are regulated independently by Variacs. A probing thermocouple indicated the shield's temperatures which are regulated to the test piece temperatureo

-86 - 2. Table IV Summary of Original and Processed Data for Local Mass Transfer Rates for Re = 400, 2000, 4000 (cylindrical diameter = L") g No. Material B AW t T i Ts Ps lb-moles (Sc)11/2 lb-moles. Material Re (mg) (min) (oC) (oC) (OC) (mm Hg) hr-ft-2-atm hr-ft -2 1 Naphthalene 180 400 6.0 420 26.3 26.2 26.1 0.09084 0.0542 2 " 180 " 5.4 420 25.8 25.8 25.6 0.08697 0.0510 1.57 7.40 1.57 7.40 0.0115 0.0108 3 4 0 6.5 0 " 6.4 L80 2000 5.9 lo0 25.7 25.5 25.5 0.08590 0.261 100 26.0 25.9 25.8 0.08850 0.249 120 23.5 23. 23.4 0.06994 0.242 5 6 1.57 7.40 0.0554 1.57 7.40 0.0529 1.57 36,8 0.01033 1.57 36.8 0.01117 1.57 36.8 0.C'2243 1.57 36.8 0.00224 180 " 6.6 120 23.9 23.9 23.8 0.07242 0.262 0 " 7.5 60 24.3 24.2 24.2 0.07565 0.570 0 r 6.8 60 24.2 24.0 24.1 0.07470 0.524 7 8 9 10 11 12 " 180 4000 9.3 I" 180 " 9.0,, 0 i" 6.4?0" 7.0 100 25.3 25.2 25.2 0.08326 0.384 1.57 74.0 0.00815 100 25.4 25.4 25.3 0.08404 0.370 1.57 74.0 0.00785 30 a5.6 25.6 25.4 0.08453 0.870 1,57 74,0 0,0185 30 25.7 25.6 25.5 0.08590 0.936 1.57 74.0 0.0199 Summary of Original and Processed Data for Local Mass Transfer Rates for Re = 400 (cylindrical diameter = 1.25") k g w t T Ti Ts Ps (Sc)/2 b-les No. Material O (mg) (min) (0C) (OC) (OC) (mm Hg) lb-moles lb-mole JD hr-ft-2-atm hr-ft-2 13 Naphthalene 14 15 16 p-Dibromobenzene 17 18 Naphthalene 19 20 p-Dibromobenzene 21 22 Naphthalene 23 24 p-Dibromobenzene 25 26 Naphthalene 27 28 29 p-Dibromobenzene 30 31 32 Naphthalene 33 34 p-Dibromobenzene 35 180 4.0 3.7 " 4.0 4.0 " 4.4 150 4.2 4.4 " 5.0 5.0 120 5.1 5.0 t 6.1 6.3 90 4.5 5.0o " 5.0 6.1 " 8.6 5.7 420 23.6 23.6 23.5 0.07055 360 23.7 23.6 23.6 0.07177 360 24.2 24.2 24.1 0.07470 360 23.7 23.6 23.6 0.04373 360 24.0 24.0 23.9 0.04491 300 26.5 26.4 26.3 o.09245 300 26.5 26.5 26.3 0.09245 400 23.9 23.8 23.8 0.04451 350 24.3 24.2 24.2 0.04655 240 26.2 26.2 26.0 0.09005 240 26.5 26.4 26.3 0.09245 265 26.2 26.2 26.1 0.05620 265 25.9 25.8 25..8 0.05468 170 23.7 23.6 23.6 0.07117 180 23.8 23.8 23.7 0.07177 170 23.8 23.8 23.7 0.07177 145 26.4 26.4 26.3 0.05720 200 26.0 26.0 25.9 0.05518 145 25.8 25.7 25.7 0.05420 0.0372 0.0399 o.o4lo 0.0380 0.0407 o.0418 0.0453 0.0420 0.0459 0.0651 0.0620 o.0612 0.0650 0.1025 0.1078 0.1130 0.1100 0.1165 0.1085 0.1725 0.1851 0.1732 0.1736 1.57 1.57 1.57 1.59 1.59 1.57 1.57 1.59 1.59 5.88 5.88 5.88 5.88 5.88 5.92 5.92 5.88 5.88 0.00993 0.01064 0.01095 0.01027 0.01100 0.01108 0.01201 0.o1134 0.01241 0.01726 o. o644 o.o164 0.0175 0.0274 0.0288 0.0302 0.0295 0.0313 0.0291 1.57 5.92 1.57 5.92 1.59 5.92 1.59 5.92 1.57 5.88 1.57 5.88 1.57 5.88 1.59 5.92 1.59 5.92 1.59 5.92 60 6.3 120 25.5 25.5 25.3 0.08404 " 7.0 120 25.8 25.7 25.6 0.08697 t 6.8 120 24.8 24.8 24.7 0.04890 7.1 120 25.2 25.2 25.1 0.05088 1.57 5.92 o.o458 1.57 5.92 0.0492 1.59 5.90 0.0466 1.59 5.90 0.0468

Table IV (Cont'd) Summary of Original and Processed Data for Local Mass Transfer Rates for Re = 400 (cylindrical diameter = 1.25") (sontinued) oranW t T T T Ps k (SC1/2 b -moe No. Material 9 l(mg) (m ) ) ) ( () -moles JD (mg (in) (o) (OC) (oc) (mm Hg) hr-ft_2-atm hr-ft_ 36 Naphthalene 30 6.3 100 25.2 25.2 25.1 0.08245 0.211 1.57 5.90 0.0561 37 " " 5.6 100 25.0 25.0 24.9 0.08110 0.1908 1.57 5.90 0.0508 38 p-Dibromobenzene " 6.8 120 23.8 23.6 23.7 0.04410 0.1920 1.59 5.88 0.0519 39. " 7.8 120 24.3 24.2 24.2 0.04655 0.209 1.59 5.88 0.0565 40 Naphthalene 0 8.8 120 26.3 26.1 26.1 0.09084 0.223 1.57 5.92 0.0591 41 " " 6.3 100 25.9 25.8 25.7 0.08775 0.198 1.57 5.92 0,0525 42 ",, 6.6 100 25.8 25.8 25.6 o.o8697 0.209 1.57 5.92 0.0554 43 p-Dibromobenzene " 9.0 140 23.8 23.8 23.7 0.04410 0.218 1.59 5.88 0.0589 44. " 8.5 140 24.1 24.0 24.0 0.04532 0.201 1.59 5.88 0.0510 45 " " 8.6 140 24.0 24.0 23.9 0.04491 0.204 1.59 5.88 0.0551 Summary of Original and Processed Data for Local Mass Transfer Rates for Re = 1000 (cylindrical diameter = 1") k Gm No. Material AW t T Ti Ts Ps lb-moles (Sc)1/2 Lb-moles JD (mg) (min) (oC) (oC) (oC) (mm Hg) hrft-2_atmhrr-ft2 46 Naphthalene l80 8.1 300 25.5 25.5 25.3 0.08404 0.1110 1.57 18.4 o.oog48 47 " " 8.0 300 24.8 24.7 24.7 0.07930 0.1160 1.57 18.4 0.00991 48 " 7.5 260 25.2 25.2 25.1 0.08425 0.1205 1.57 18.4 0.0103 49 p-Dibromobenzene " 6.6 200 25.7 25.6 25.6 0.05371 0.1149 1.59 18.4 0.00995 50 " " 7.3 200 25.5 25.5 25.4 0.05229 0.1307 1.59 18.4 0.0113 51 " ' 7.3 200 25.9 25.9 25.8 0.05468 0.1248 1.59 18.4 0.0108 Summary of Original and Processed Data for Local Mass Transfer Rates for Re = 1000 (cylindrical diameter = 1") AW - t To. TjT_ kg Gm aW t Tg Ti T s lb -moles (Sc) 1/2 lb -moles JD So.9materim hr-f J No. MateriaL (mg) (min) (~C) (OC) (~C) mm ng) hr-fttz-atm hr-ft-2 52 Naphthalene 150 5.8 260 23.8 23.8 23.7 0.07177 53 i 5.7 260 24.0 23.9 23.9 0.07305 54 p-Dibromobenzene 6.2 24 4.2 24.0 24.1 0.04590 55 " 6. 240 24.2 24.2 24.1 0.04590 56 Naphthalene 120 6.6 260 25.4 25.2 25.2 0.08326 57 6.5 260 25.6 26.6 25.4 0.08473 58 6.9 260 25.5 25.5 25.3 0o084o4 62 6.8 155 24.4 24.3 24.3 0.07630 63 III 7.4 155 24.8 24.8 24.7 0.07930 64 p-Dibromobenzene 8.1 135 25.7 25.6 25.6 0.05371 765 it I 8.4 160 25.6 25.4.255 0.05300 66 Naphthalene 60 8.0 100 26.5 26.4 26.3 0.09245 67 I 8.8 100 26.4 26.2 26.2 o.o0965 68 p-Dibromobenzene 8.4 85 25.5 25.5 25.4 0.05229 69 1it 7.6 85 25.3 25.3 25.2 0.05136 70 Naphthalene 30 8.2 100 24.2 24.2 24.1 0.07470 71 iIt 8.7 100 24.2 24.2 24.1 0.07470 72 p-Dibromobenzene 11.2 85 26.3 26.2 26.2 0.05667 73 U i 9.8 85 25.7 25.7 25.6 0.05371 74 Naphthalene 0 8.9 100 23.7 23.5 23.6 0.07177 75 9.1 100 24.0 24.0 23.9 0.07370 76 8.0 100 24.1 24.0 24.0 0.07370 77 p-Dibromobenzene 8.3 85 24.1 23.9 24.0 0.04532 78 9.5 85 24.1 24.1 24.0 0.04532 79 t 9.o 85 24.1 24.1 24.0 0.04532 0.1072 0.1035 0.1050 0.1153 0.1052 0.1018 0.1086 0.1015 0.1085 o.189 0.199 0.208 0.209 o.185 0.298 0.331 0.354 0.326 1.57 1.57 1.59 1.59 1.57 1.57 1.57 1.59 1.59 1.57 1.57 1.57 1.59 1.59 1.57 1.57 1.59 1.59 18.4 0.00915 18.4 0.00883 18.4 0.0090S 18.4 0.00996 18.4 0.00oo898 18.4 0.00868 18.4 0.00927 18.4 0.00877 18.4 0.00937 18.4 0.0161 18.4 0.0170 18.4 0.0178 18.4 0.0180 18.4 0.0160 18.4 0.0254 18.4 0.0283 18.4 0.0306 18.4 0.0282 18.4 0.0322 18.4 0.0343 18.4 0.0377 18.4 0.0347 18.4 0.0365 i8.4 0.0364 18.4 0.0319 18.4 0.0348 18.4 0.0399 18.4 0.0378 0.378 1.57 0.402 1.57 0.436 1.59 0.402 1.59 0.428 0.426 0.375 0.403 0.462 0.438 1.57 1.57 1.57 1.59 1.59 1.59

-88 - Table IV (Cont 'd) Summary of Original and Processed Data for Local Mass Transfer Rates for Re = 2000 (cylindrical diameter = 1.25") AWt W, Tg Ti Ts p 9kg~ k ( G- o M lb-moles ), (Sc)l/2 kg(Sc)12 k<(Sc)1/2 Ib moles I^OF No. Material 8 (mg) (mg) (min) (Oc) (Oc) (Oc) (mm Hg) hft fthr 2 g()l/2 k()l/2 le JD lb-OF PItu-atm 80 Naphthalene 180 6.4 0.0 135 24.2 24.2 24.1 0.07470 0.1763 68.6 1.57 0.277 107.7 29.4 0.00942 2.352 81 7.8 0.0 135 25.2 25.1 25.1 0.08245 0.193 75.4 1.57 0.304 L18.4 29.5 0.0103 2.565 82 " 8.0 0.9 11 54.2 54.0 52.3 0.9480 0.188 80.1 1.56 0.292 125.0 31.7 0.00920 2.326 83 " 9.7 1.0 11 56.8 56.5 54.4 1.128 0.211 90.5 1.55 0.327 140.3 31.8 0.0103 2.602 84 "" 9.4 1.0 11 55.8 55.5 53.7 L.062 0.218 93.3 1.55 0.338 L44.6 31.8 0.0106 2.688 85 p-Dibromobenzene 9.0 0.0 14o0 25.3 25.2 25.2 0.05136 0.187 73.1 1.59 0.298 116.2 29.5 0.0101 2.486 86 " 9.0 0.0 14o0 24.8 24.8 24.7 o.04890 0.196 76.5 1.59 0.312 121.6 29.5 0.0106 2.601 87 7.8 0.8 7 56.3 56.2 54.8 0.7724 0.194 83.3 1.58 0.306 131.6 31.8 0.00962 2.392 88 " 7.3 0.8 7 55.7 55.7 54.2 0.7320 0.190 81.5 1.58 0.300 128.8 31.8 0.00943 2.343 89 Propionamide 8.4 0.6 20 63.5 63.3 62.0 0.7592 0.248 108.9 1.34 0.333 145.9 32.3 0.0103 3.011 o90 " 8.2 0.7 20 64.3 64.2 62.7 0.7968 0.238 o104.7 1.34 0.305 L40.3 32.4 0.00941 2.881 91 Anthracene " 5.5 0.1 40 111.6 111.5 ll.4 0.1306 0.205 103.3 1.75 0.359 180.8 35.6 0.0101 2.258 92 "" 4.9 0.1 40 110.2 110.0 110.0 0.1201 0.198 99.4 L.75 0.347 174.0 35.6 0.00975 2.181 93 8.7 1.2 7 150.5 150.3 149.0 1.007 0.212 117.2 1.73 0.367 202.8 38.1 o0.009og64 2.182 94 "" 8.9 1.4 7 152.5 152.2 150.8 1.100 0.193 107.2 L.73 0.334 185.5 38.3 0.00873 1.976 95 Naphthalene 150 4.6 0.0 110 25.3 25.3 25.2 0.08326 0.1385 54.1 1.57 0.218 84.9 29.5 0.00738 2.343 96 ' 6.o 0.0 120 26.7 26.5 26.5 0.09490 o.1453 57.0 1.57 0.228 89.5 29.6 0.00772 2.450 97 " 8.0 0.0 180 25.5 25.5 25.4 0.08473 0.1460 57.1 1.57 0.229 89.6 29.5 0.00777 2.470 98 " 12.3 o.8 22 54.5 514.3 52.6 0.9734 0.148 63.2 1.56 0.231 98.6 31.7 0.00730 2.331 99 "" 10.1 0.9 17 55.5 55.2 53.4 1.034 o.144 61.6 1.56 0.225 96.1 31.7 0.00710 2.267 100 p-Dibromobenzene 3.7 0.0 80 24.0 24.0 23.9 0.04491 0.1540 59.9 1.59 0.245 95.2 29.4 0.00833 2.615 101 " 4.4 0.0 100 23.7 23.6 23.6 0.04373 0.1504 58.5 1.59 0.239 93.0 29.4 0.00824 2.554 102 " 6.8 0.9 10 52.5 52.5 5L.4 0.5752 0.1533 65.2 1.58 0.242 103.0 31.6 0.00767 2.422 103 "" 8.o 1.0 10 514.3 54.2 53.0 0.6614 0.1582 67.6 1.58 0.250 o106.8 31.7 0.00790 2.491 104 Propionamide 12.7 0.7 40 64.2 64.0 62.6 0.7908 0.184 80.9 1.34 0.246 o108.4 32.4 0.00760 2.835 105 ' 7.6 0.5 25 62.6 62.5 6L.1 0.71o4 0.193 84.5 L.34 0.259 113.2 32.2 0.00o805 2.992 106 Anthracene " 5.5 0.1 60 o109.4 109.3 109.2 o.1144 0.156 78.1 1.75 0.273 136.7 35.4 0.0077 2.199 107 "" 5.8 0.1 60 111.9 111.7 111.7 0.1329 o.142 75.8 1.75 0.249 132.7 35.6 0.0070 1.991 108 " 10.5 1.0 12 151.2 151.0 149.6 1.037 0.151 83.6 1.73 0.261 144.6 38.2 0.00oo68 1.973 o109 9.4 o.8 12 148.0 147.8 146.7 0.8977 0.158 86.9 1.73 0.273 150.3 38.0 0.0072 2.076 110 9.9 0.8 12 148.4 148.2 147.0 0.9116 0.L65 90.8 1.73 0.285 157.1 38.0 0.0075 2.168 N. Material Mt AM t Tg Ti T P b-moles k (Sc)/2 kg(Sc)1/2 kc,(SC)/2 bmoles _ Plc-atm 111 Naphthalene 112 113 114 115 p-Dibromobenzene 116 117 118 119 Propionamide 120 121 " 122 Anthracene 123 124 " 125 126 127 Naphthalene 128 129 130 p-Dibrombbenzene 131 132 Propionamide 133 134 Anthracene 135 136 120 6.1 0.0 7.2 0.0 " 10.0 0.9 8.5 0.7 5.2 0.0 3.9 0.0 6.2 0.9 6.8 0.8 9.6 0.4 7.4 0.6 " 10.4 0.6 6.4 0.1 8.1 o0.1 7.7 0.7 7.3 0.8 7.1 0.7 90 4.5 0.0 9.5 l.o 8.0 0.9 7.1 0.8 7.8 0.8 8.9 0.7 " 8.2 o.6 " 5.1 0.1 " 7.4 1.0 9.9 1.4 165 25.2 25.0 25.1 0.08245 165 27.0 26.9 26.8 0.09741 16 57.3 57.0 54.9 1.L80 20 53.0 52.8 51.3 0.8725 150 23.6 23.6 23.5 0.04335 100 24.9 24.7 24.8 0.04956 10 55.3 55.2 53.9 0.7130 10 55.2 55.0 53.8 0.7063 40 62.5 62.3 61.1 0.7104 30 64.2 63.9 62.6 0.7908 40 63.9 63.7 62.3 0.7747 100 108.9 108.8 108.7 0.1109 100 111.7 111.5 111.5 0.1313 12 150.4 150.1 148.9 1.002 10 152.0 L51.7 150.4 1.079 10 150.8 150.6 149.3 1.022 70 25.1 25.0 25.0 0.08182 10 56.1 55.8 53.9 1.080 10 53.2 53.0 51.5 0.8855 7 55.3 55.2 53.9 0.7130 7 55.1 54.9 53.7 0.7000 20 63.2 63.o 61.7 0.7420 20 62.7 62.5 6L.2 0.7155 40 109.6 109.4 109.4 0.1158 7 147.6 147.5 146.3 0.8806 7 151.5 151.2 149.9 1.053 0.1240 0.1235 0.133 0.123 0.1193 0.1175 0.1111 0.1270 0.157 0.138 0.153 0.112 0.121 0.116 0.119 0.124 0.217 0.217 0.221 0.189 0.214 0.267 0.257 0.214 0.202 0.228 48.4 1.57 0.195 48.5 1.57 0.194 57.2 1.55 0.206 52.2 1.56 0.192 46.3 1.59 0.1900 45.8 1.59 0.1870 47.6 1.58 0.1757 54.4 1.58 0.201 68.7 1.34 0.210 60.7 1.34 0.186 67.2 1.34 0.205 56.0 1.75 0.196 61.0 1.75 0.212 64.1 1.73 0.201 66.0 1.73 0.206 68.6 1.73 0.215 84.7 1.57 0.340 93.0 1-55 0.336 94.0 1.56 0.343 81.0 1.58 0.298 91.6 L.58 0.338 117.1 1.34 0.358 112.5 1.34 0.344 107.2 1.75 0.374 110.0 1.73 0.350 126.3 1.73 0.395 76.0 76.1 88.7 81.4 73.6 72.8 75.2 86.0 92.1 81.3 90.0 92.4 106.8 110.9 114.2 118.7 133.0 144.2 146.6 128.0 144.7 156.9 150.8 187.6 192.0 218.5 29.5 29.6 31.9 31.6 29.4 29.5 31.7 31.7 32.2 32.3 32.3 35.4 35.6 38.1 38.2 38.2 29.5 31.8 31.6 31.7 31.7 32.3 32.2 35.4 37.9 38.2 0.00661 2.430 0.00656 2.412 0.00646 2.410 0.00609 2.250 0.00646 2.346 0.00635 2.302 0.00555 2.026 0.00634 2.315 0.00652 2.818 0.00575 2.470 0.00635 2.738 0.00554 1.829 0.00596 1.965 0.00528 1.760 0.00540 1.801 0.00563 2.028 0.0115 2.591 0.0106 2.404 0.0109 2.463 0.00941 2.101 0.0106 2.379 0.0111o 2.912 0.0107 2.812 0.0106 2.130 0.00925 1.878 0.0103 2.103

-89 -Table IV (Cont'd) Summary of Original and Processed Data for Local Mass Transfer Rates for Re = 2000 (cylindrical diameter = 1.25") oWt No. Material AWg) (mg) tWc t Tg Ti (mg) (min) (~C) (oc) Ts Ps kg kc (oc) (mm Hg) lb-moles ft/hr ir -ft-2-atm Gm (S)1/2 kg(Sc)l/2 k(S)/2 b-les JD h hr-ft-2 lb-OF Btu-atm 137 Naphthalene 138 139 140 141 " 142 p-Dibromobenzene 143 144 145 146 147 Propionamide 148 " 149 Anthracene 150 151 152 " 153 154 Naphthalene 155 156 157 158 159 " 160 p-Dibromobenzene 161 162 163 164 60 7.3 7.1 " 10.3 " 10.4 11.2 " 10.0 8.6 " 13.3 12.3 13.7 " 10.1 9.5 " 11.8 " 9.2 " 10.0 11.8 " 12.9 30 9.9 " 10.6 9.3 8.9 13.3 11.4 " 6.9 6.9 " 12.4 " 12.7 13.1 0.0 0.0 0.0 1.4 1.5 0.0 0.0 1.5 1.8 1.7 1.1 1.4 0.2 0.2 0.2 1.3 1.4 0.0 0.0 0.0 1.2 1.6 1.3 0.0 0.0 1.8 1.5 1.3 70 25.0 25.0 55 25.9 25.8 100 24.2 24.2 5 58.2 57.9 5 58.5 58.1 60 26.6 26.5 60 24.8 24.8 6 55.1 55.0 4 58.4 58.2 5 57.1 56.9 12 62.7 62.5 10 64.7 64.4 40 112.3 112.2 40 109.0 108.8 40 109.1 109.0 5 149.4 449.3 5 152.3 152.0 70 25.2 25.2 60 27.0 26.9 60 26.4 26.3 5 53.4 53.2 5.5 57.3 57.0 5.5 54.7 54.5 45 24.8 24.8 40 25.3 25.2 4 56.8 56.7 5 54.0 54.0 6 52.5 52.5 24.9 0.08110 25.7 0.08775 24.1 0.07470 55.6 1.243 55.8 1.264 26.5 0.05874 24.7 0.04890 53.7 0.7000 56.6 0.8933 55.5 0.8150 61.2 0.7155 63.0 0.8140 112.1 0.1361 108.8 0.1117 108.9 0.1124 147.9 0.9529 150.6 1.089 25.1 0.08326 26.8 0.09741 26.2 0.09165 51.6 0.8921 54;9 1.180 52.7 0.9824 24.7 0.04890 25.2 0.05136 55.2 0.7934 52.7 0.6460 51.4 0.5752 0.355 0.406 0.380 0.400 0.423 0.424 0.438 0.421 0.440 o.440 0.507 0.482 0.422 0.399 0.432 0.436 0.418 0.469 0.502 0.467 0.476 0.498 0.516 0.468 0.503 0.500 0.519 0.511 138.6 158.9 147.9 172.2 182.3 166.4 170.9 180.2 190.0 189.4 222.0 212.2 212.9 199.6 216.2 232.2 232.0 183.2 197.2 183.1 202.5 214.0 220.2 182.6 196.6 215.1 221.5 217.2 1.57 1-57 1.57 1.55 1.55 1.59 1.59 1.58 1.57 1.57 1.34 1.34 1.75 1.75 1.75 1.73 1.73 1.57 1.57 1.57 1.56 1.55 1.56 1.59 1.59 1.57 1.58 1.58 0.557 0.637 0.597 0.620 0.656 0.675 0.696 0.665 0.690 0.691 0.680 0.645 0.739 0.698 0.756 0.755 0.723 0.737 0.788 0.734 0.743 0.772 0.805 0.745 0.800 0.785 0.820 0.809 217.6 249.5 232.2 266.9 282.6 264.6 271.7 284.7 298.3 297.4 297.5 284.3 372.6 349.3 378.4 401.7 401.4 287.6 309.6 287.5 315.9 331.7 343.5 290.3 312.6 337.7 350.0 243.2 29.5 29.5 29.4 31.9 31.9 29.5 29.5 31.7 31.9 31.8 32.2 32.4 35.6 35.4 35.4 38.0 38.2 29.5 29.6 29.6 31.6 31.8 31.7 29.5 29.5 31.8 31.7 31.6 0. 0189 0.0216 0.0203 0.0194 0.0206 0.0228 0.0236 0.0210 0.0216 0.0217 0.0211 0.0199 0. 0208 0.0197 0.0214 0.0199 0.o0189 0.0250 0.0266 0.0248 0.0235 0.0242 0.0254 0.0252 0.0271 0.0246 0.0258 0.0256 1.984 2.269 2.131 2.068 2.186 2.370 2.448 2.190 2.274 2.281 2.596 2.453 1.955 1.858 2.012 1.892 1.804 2.109 2.249 2.093 1.998 2.077 2.159 2.104 2.262 2.085 2.171 2.145 A wt Awc t Tg Ti (mg) (mag) (min) (~C) (~C) (T ( ) b;; kg k ( /2 T, Ps lb-moles fthr (S0)1/2 (Oc) (mm Hg) hr-ft-2-atm 165 Propionamide 166 167 168 Anthracene 169 170 171 172 173 Naphthalene 174 175 176 177 p-Dibromobenzene 178 179 180 181 Propionamide 182 " 183 Anthracene 184 185 186 30 10.9 1.4 10 64.3 64.0 11.0 1.3 10 63.9 63.7 1.2 1.2 12 62.7 62.5 11.7 0.2 40 109.2 109.2 12.4 0.2 40 110.5 110.3 12.0 0.2 40 110.7 110.5 12.5 1.5 4 151.2 150.8 13.2 1.7 4 152.8 152.5 0 9.5 0.0 60 25.1 25.0 11.3 1.6 4.5 55.2 55.0 10.2 1.5 4.5 54.2 54.0 13.2 1.9 4.5 58.4 58.1 6.6 o0.0o 36 25.2 25.2 6.0 o.o 33 25.5 25.5 11.9 1.7 4 55.5 55.3 12.5 1.8 4 56.2 56.0 10.6 1.4 10 62.9 62.7 10.6 1.3 10 62.5 62.3 7.6 0.2 20 112.4 112.2 6.6 0.2 20 109.3 109.3 12.4 1.6 4 148.4 148.2 13.8 1.8 4 152.0 151.7 62.7 62.3 61.2 109.0 110.3 110.5 149.6 151.1 - 25.0 53.1 52.3. 55.8 25.1 25.4 54.1 54.7 61.4 61.o 112.2 109.1 147.0 150.4 0.7968 0.7747 0.7155 0.1130 0.1223 0.1237 1.037 1.116 0. 08182 1.010 0.9480 1.264 0.05088 0.05229 0.7255 0.7655 0.7258 0.7054 0.1369 0.1137 0.9116 1.079 253.8 1.34 0.606 266.3 1.34 0.562 246.0 1.34 0.562 0.504 252.3 1.75 0.494 248.1 1.75 0.473 237.7 1.75 o*0.527 291.8 1.73 0.511 284.0 1.73 0.511 0.535 209.0 1.57 0.587 250.8 1.56 0.563 240.0 1.56 0.548 236.1 1.55 0.539 210.5 1.59 0.520 203.3 1.59 0.526 225.4 1.58 0.522 224.1 1.58 0.613 268.6 1.34 0.638 279.3 1.34 0.535 270.0 1.75 0.558 279.4 1.75 0.586 322.5 1.73 0.551 305.7 1.73 Gkg Mm kg(Sc)l2 (c)/2 c)l/2 b-moles JD hr-ft-2 lb-OF Btu-atm 0.773 340.0 32.4 0.0238 2.362 0.814 356.8 32.3 0.0251 2.488 0.753 329.6 32.2 0.0234 2.315 0.882 441.5 35.4 0.0249 1.888 0.864 434.2. 35.5 0.0243 1.846 0.827 416.0 35.6 0.0232 1.762 0.910 504.8 38.2 0.0238 1.830 0.884 491.3 38.3 0.0231 1.770 0.840 328.1 29.5 0.0284 2.370 0.916 391.2 31.7 0.0289 2.419 0.879 374.4 31.6 0.0278 2.328 0.850 366.0 31.9 0.0266 2.245 0.857 334.7 29.5 0.0290 2.387 0.827 323.2 29.5 0.0280 2.303 0.831 356.1 31.7 0.0262 2.168 0.825 354.1 31.8 0.0260 2.145 0.821 359.9 32.2 0.0255 2.487 0.855 374.3 32.2 0.0266 2.589 0.937 472.5 35.6 0.0263 1.964 0.976 489.0 35.4 0.0276 2.o60 1.015 557.9 38.0 0.0267 2.015 0.953 528.9 38.2 0.0250 1.885

Table IV (Cont'd) and Processed Data for Local Mass Transfer Rates Summary of Original for Re = 4000 (cylindrical diameter = 1.25") W t Tg Ti Ts Ps/ GM No. Material T T (ra Goles) No. M(mg) (min) (C) (~C) (OC) (mm Hg) lb-r-s hr-t-2e 187 188 189 190 191 192 193 194 Naphthalene it p-Dibromobenzene tt 180 9.0 tl 9.0 " 10.2 i" 9.4 150 5.9 I" 6.1 T" 8.6 t" 9.0 120 23.8 120 23.5 100 24.2 100 24.2 100 24.1 100 24.0 130 23.8 130 23.6 23.7 23.7 0.07177 23.5 23.4 0.06994 24.2 24.1 0.04590 24.2 24.1 0.04590 0.288 0.296 0.332 0.306 1.57 1.57 1.59 1.59 Naphthalene p -D ibromobenzene.t 24.0 24.0 23.7 23.5 195 196 197 198 199 200 201 202 203 Naphthalene p-Dibromobenzene it Naphthalene tl p-Dibromobenzene i. 120 7.2 " 77.8 it 6.4 1" 6.7 90 9.0 "i 7.3 It 9.3 t 12.6 " 10.5 200 200 130 130 24.5 24.4 24.7 24.6 24.6 24.6 24.8 24.8 24.0 23.9 23.7 23.6 24.4 24.6 24.5 24.7 24.6 24.4 24.3 25.1 25.0 0.07370 0.07305 O. 04410 0.04373 0.07698 0.07832 0.04785 0.04890 0.07832 0.07698 0.07630 0.05088 0.05036 0.221 0.230 0.225 0.236 1.57 1.57 1.59 1.59 0.129 0.136 0.154 0.158 0.244 0.262 0.259 0.288 0.240 1.57 1.57 1.59 1.59 1.57 1.57 1.57 1.59 1.59 58.8 58.8 58.8 58.8 58.8 58.8 58.8 58.8 59.0 59.0 59.0 59.0 59.0 59.0 59.0 59.0 59.0 0.00769 0.00791 0. oo898 0.00827 130 24.7 100 24.5 130 24.4 130 25.2 130 25.1 24.5 24.5 24.3 25,0 25.0 204 205 206 207 208 209 210 211 212 213 214 215 216 217 Naphthalene It p-Dibromobenzene Naphthalene p-Dibromobenzene 11 Naphthalene tp t! p-Dibromobenzene it 60 9.7 " 10.3 " 10.3 I" 9.7 30 9.9 10.8 8.7 9.1 60 60 45 45 50 50 33 33 25.3 25.3 25.2 0.08326 25.0 24.9 24.9 0.08110 26.4 26.3 26.3 0.05720 26.1 26.1 26.0 0.05567 25.5 25.5 25.3 0.08404 25.5 25.5 25.3 0.08404 25.9 25.8 25.8 0.05468 25.8 25.8 25.7 0.05420 0.538 0.585 0.599 0.580 0.648 0.709 0.722 0.762 0.707 0.690 0.800 0.758 o.660 0.776 1.57 1.57 1.59 1.59 1.57 1.57 1.59 1.59 1.57 1.57 1.57 1.59 1.59 1.59 59.0 59.0 59.2 59.2 59.0 59.0 59.2 59.2 59.0 59.0 59.0 59.0 59.0 59.0 0.00590. 00614 0.00608 0.00638 0.00344 0.00368 o. oo415 0.00423 0.00649 0.00697 0.00690 0.00776 0.00648 0.0143 0.0156 0.0161 0.0156 0.0172 0.0189 0.0194 0. 0205 0.0188 0.0184 0.0213 0.0204 0.0178 0.0209 0 O 0 6.8 33 24.9 6.9 33 25.4 " 7.7 33 24.9 7.8 33 24.3 " 8.3 39 24.7 " 8.1 33 24.5 24.8 25.2 24.8 24.3 24.5 24.5 24.8 25.2 24.8 24.2 24.6 24.4 0.08401 0.08326 0. 08401 0.04655 0.04824 0.04739

-91 - 3. Table V Summary of Original and Processed Data for Determination of Vapor Pressures No. Material tb Pa Pb Vt Vd Tm Pm Vc nc W Ps (OF) (mm Hg) (cu ft) (OF) (mm Hg) (scf) (gr-mol) (gr) (mm Hg) 1 p-Dibromobenzene 65.5 741 746 4.14 4.03 74 741 3.62 4.56 2.6627 1.847 2 62.2 740 745 4.16 4.04 75 740 3.62 4.56 2.0787 1.439 3 " 60.0 741 747 4.13 4.02 75 741 3.60 4.54 1.7235 1.200 4 58.6 738 743 4.12 4.01 73 738 3.59 4.52 1.4112 0.982 5 " 56.8 739 744 4.18 4.05 76 739 3.62 4.56 1.2659 0.875 6 " 54.0 740 745 4.14 4.02 75 740 3.60 4.54 1.0561 0.734 7 " 45.9 741 746 5.00 4.85 75 741 4.35 5.48 0.6365 0.368 8 " 27.3 736 742 12.65 12.25 77 736 10.87 13.70 0.2751 0.0632 9 " 26.5 749 744 13.58 13.10 75 749 11.88 14.97 0.2694 0.0575 10 25.3 745 750 13.46 13.06 75 745 11.78 14.84 0.2465 0.0528 11 24.8 747 752 18.90 18.40 73 747 16.69 21.03 0.3325 0.0503 12 Naphthalene 62.0 736 741 4.09 3.98 73 736 3.64 4.59 1.6265 2.049 13 61.3 739 744 4.13 4.01 75 739 3.61 4.55 1.5101 1.931 14 59.8 737 742 4.17 4.05 75 737 3.64 4.59 1.4184 1.790 15 " 59.5 743 749 4.18 4.06 74 743 3.68 4.64 1.3602 1.718 16 " 56.7 744 750 4.16 4.04 75 744 3.67 4.62 1.0650 1.362 17 51.2 746 751 4.60 4.46 77 746 4.03 5.08 0.7537 0.870 18 " 30.1 745 751 L3.19 12.78 77 745 11.55 14.55 0.3426 0.1380 19 " 28.5 746 752 14.74 14.32 75 746 13.03 16.42 0.3219 0.1151 20 25.6 747 753 14.68 14.25 75 747 12.98 16.35 0.2397 0.0862 21 25.2 746 752 14.53 14.09 76 746 12.80 16.13 0.2280 0.0830 No. Material tb a Vt Vd Tm Pm Vc nc W Ps (OF) (mm Hg) (cu ft) (OF) (mm Hg) (scf) (gr-mol) (gr) (mm Hg) 22 Propionamide 23 " 24 " 25 " 26 " 27 " 28 Anthracene 29 " 30 31 " 32 " 33 t 34 I 35 l 36 " 37 " 38 " 39 68.3 744 750 4.34 4.21 67.4 738 744 4.40 4.26 65.8 745 751 4.08 3.97 62.4 745 751 4.28 4.15 60.5 742 748 4.01 3.89 57.6 743 748 4.84 4.69 156.1 731 731 3.56 3.44 153.4 732 732 3.50 3.38 151.2 731 731 3.67 3.55 149.8 729 729 3.87 3.74 148.2 730 730 3.87 3.72 143.7 728 728 3.92 3.80 128.9 730 730 8.58 8.32 119.8 735 735 7.78 7.53 110.9 737 737 8.78 8.48 109.2 736 736 8.32 8.05 107.4 735 735 10.14 9.83 105.9 740 740 10.58 10.26 76 744 3.78 76 738 3.80 73 745 3.59 75 745 3.74 75 742 3.49 75 743 4.22 77 731 3.03 78 732 2.98 78 731 3.12 77 729 3.29 76 730 3.28 75 728 3.35 75 730 7.35 77 735 6.67 78 737 7.53 77 736 7.14 76 735 8.74 76 740 9.17 4.76 0.5582 4.79 0.5227 4.52 0.4364 4.71 0.3603 4.40 0.2916 5.32 0.2873 3.83 1.3135 3.77 1.1673 3.94 1.1067 4.16 1.0622 4.14 0.8786 4.23 0.8073 9.29 0.7913 8.43 0.4420 9.51 0.2891 9.02 0.2452 11.04 0.2725 11.59 0.2556 1.203 1.110 0.992 0.786 0.678 0.552 1.421 1.284 1.163 1.055 0.878 0.787 0.352 0.218 0.1270 0.1132 0.1027 0.0924

-92 - 4o Sample Calculations The original data sheet is reproduced in Figure 4o ao Calculation of mass transfer coefficients The mass transfer coefficient kg is kg = W/A (ps - po) t (45) The rate9 AW/t, is calculated for the weight-loss data. The final weight subtracted from the initial weight gives the weight-loss for the "test run propero" The "preliminary run" mainly accounts for the sublimation loss during the unsteady state periods between the two weighings. This loss is negligible for both p-dibromobenzene and naphthalene with the temperature in the 25~C rangeo AWt = initial wto - final wto 153o562 - 1553459 - Oo0103 gm AW = AWt - AW 10o5 - 0Oo0 10o3 mg t c where AWc "preliminary run" sublimation loss The rate AW/t, is 10o3/45 -= 0229 mg/mn The surface temperature is necessary to determine pso Plots of the surface temperature versus the air temperature are given in Figures 17a and 17bo The temperatures are recorded on the data sheetso The averaged air temperature, Ta9 is 26o4~Co Referring to Figure 17a9 the "wet-bulb depression," (Ta - Ts), is Ool~C for Ta = 26.4. The surface temperature is (264 - Ool) = 26o3~Co At 2630~C, the vapor pressure, Ps, is Oo05720 (Figure 16a)o

-93 - Compared to Ps, Pb is negligible and is neglectedo The surface area is rtDxL/12 -:(1l25in)(lo25in)/12(l44 in2 284 x 10-3 ft2 ft2 Substituting into Equation (45), =(2 29x -4 gr min 1 lb) 1 mole( 1 1 1 kg(2.29x10 n)(60 r) ( 456gr) 2359 lb ) 2m84x10-53 I 1 1 - )(760 mmHg) Oo0572 mm Hg atm kg=0 599 lb-mole/hr-ft2-atm lb.-mole ____)29 K ft kc=kgRTs=(Oo599 )(1310 3-atm )(2994 K) 2350 h hr-ft -atm lb-mole - ~K bo Calculation of jD-factors The jD-factor is defined by Equation (46), JD -kgM Pbm/G)(S)05 (46) The mass velocity is determined from the rotameter reading and corrections for pressure and temperatureo indicated SCFM (530)(Pr) 1 Gm= ( SCF/lb-mole ) (T)(45) (cross-sectional area) (7) The pressure at the rotameter, Pr 'was 45 psiao The temperature, T, fluctuated slightly around 5355~F Thus the calibration correction term under the square root in Equation (47) is minuteo indicated SCFM = 8010 ft3/min Pr - 45 psia T = 536~R cross-sectional area = 2o12 x 10-2 ft2

Substituting Gm - (810o/386)( (530 (45)/(53)(5 5 (45) )(1/2.12 x 10-2)(60 hr Gm ='59o2 lb-mole/hr-ft2 which gives Re = 40000 For p-Dibromobenzene, (Sc)Oo5 l159 (Section d) Then D = (0o599)(1) (lo59)/(59~2) 0o0161 dimensionless Co Calculation of surface temperatures For steady state conditions, an energy balance is Xkg(PS - Pb) = h(Ta T) (48) Neglecting Pb and rearranging Ts -a Psskg/h (49) Assuming the identity of the heat and mass transfer j-factors, JD = (kgMmPbm/G)(p/)DV)0~5 = JH (h/cpG)(ep ik)0~5 (50) Rearranging Equation (50), kg/h (l/cpPbm) (PD/)-O 5(cp/k)0~5 - (1/cpMmbm)(Sc)-O05(Pr)05 (51) For air at 70 ~F, cp = 00238 BTU/lb-~F Mm = 28 85 lb/lb-mole Pbm = 760 mm Hg Pr = 0o69 dimensionless

-95 - Substituting 1 _ ~C kg/h ~( 1 ))0.69)0.5 ( 0 5 (o0238)(28.85)(706o) o8 OF (8o7661 x 10-5)(Sc)-0 5 mole-C (52) BTU-mm Hg The factors involved in calculating (kg/h) are nearly independent of temperature variations over the experimental temperature limitso For this reason9 (kg/h) is taken to be a constant for each of the organic solidso In the case of p-dibromobenzene, (Sc)Oo5 = 158; consequently, kg/h - (807661 x 10-5)/(1.58) = 55483 x 10-5 moleC (5 BTU-mnm Hg Substituting into Equation (49), Ta T = (kg/h)(Ps)(Xs) = (5o5483 x 10-5)(ps)(Xs) ~c (54) Similar results for naphthalene, propionamide9 and anthracene are summarized in Table VIo If the surface temperature of the subliming p-dibromobenzene surface is 25~C, the wet-bulb depression, (Ta - Ts), is at 250~C ps = 0o05038 mm Hg Xs = 32,044 BTU/lb-mole (from Clausius-Clapeyron equation) Equation (54) becomes Ta - Ts (5o5483 x l0-5)(005038)(32,044) = 0,090 = o10~C The results of the wet-bulb depression calculation are presented in Figures 17a and 17bo

-96 - TABLE VI PROPERTIES OF ORGANIC SOLIDS FOR DETERMINING WET-BULB DEPRESSION (kg/h) (Ta - Ts) Material (Sc)0O5 mole- ~F/BTU-mm Hg ~C Naphthalene lo56 5.6194 x 10-5 5o6194 x 10-5PsXs p-Dibromobenzene 1.58 5o5483 x 10-5 505483 x lO-,5psXs Propionamide 134 6o5422 x 10-5 6o5422 x 10-SpsXs Anthracene 1.74 5 0383 x 10-5 5 0383 x 10-lOpXs do Calculation of diffusivities and Schmidt numbers The diffusivity was calculated by the method of Hirschfelder et alo (47) For pairs of gases Dv - ((1.492 x lO53)(T)5/2/(p)(rAB)2())( 1/MA + 1/MB ) (55) The collision function, 0, is a function, of k, T, and CAB. Hirschfelder et al. have tabulated 0 for values of kT/EABO The factors ~AB and rAB are calculated from values of the critical volumes and temperatures of the solids. The critical constants are calculated by Equations (56) and (57) developed by Meissnero (8) Tc T 20~2(TgB)0o6o 1435- 1.2(P) + 10o4(RD) + A (56) Vc 0.55(1o5(P) + 9 - 4o34(RD) )1.155 (57) P = parachor term RD = molar refraction term

Using values of dibromobenzene, P and RD tabulated by Meissner, Tc C6H4Br2, are calculated as follows and Vc for p Structual Components 6 carbons 4 hydrogens to carbon 2 bromines 3 double bonds 1 six membered ring Totals Parachor (P) 55.2 61.6 138.0 57.0 0.8 314o2 Molar Refraction (RD) 140508 4 400 17o730 5.166 0 000 41.804 For p-dibromobenzene, TB = 494 ~K A - 10, P 5314o29 RD 41.804 Substituting these values into Equations (56) and (57) Tc 757~K = 1363~R Vc 399 cc/g-mole = 6.39 ft3/lb-mole The radius of the p-dibromobenzene molecule and the factor E/k are e/k -- 0.75Tc = 075(1361) = 1022~R r = 330(Vc)1/35 - 330(6.39)1/3 = 6o13 A (58) (59) For air, r = 3063 A, and s/k = 179~R rA = 1/2(rA + rB) = 1/2(6-13 + 3.63) = 4.88 A (6o) eAB/k= (l/k) (i 1 x e ) = (1022 ) (179) = 428 ~R (61)

-98 - Substituting into Equation (55) Dv (1.492 x 10l3/1(4o88)2)(\ (l/235o9) + (1/2885) )((T)3/2/(S)) Dv = (10235 x 10-5)(T)3/2/(O) ft2/hr For a given temperature the diffusivity of p-dibromobenzene through air at 1 atm is found by substitution in the above relationshipo For pdibromobenzene9 kT/CAB = T/428o At T = 528~R, kT/GAB = 1o233 = 0o658 Therefore, Dv = (1o235 x 105) (528)3/2/(o~658) = 0.228 ft2/hr A summary of similar calculations appears in Table VIIIo Tabulation of diffusivity values for the selected temperatures are presented in Table IX, The dimensionless Schmidt group is defined by Sc = //pDv (62) The values of the viscosity and density of the gaseous mixtures were 'taken to be those of air obtained from (56)~ Calculated Schmidt numbers are in Table IX. The Schmidt number was determined at a temperature intermediate between those of the surface and mainstream. Since the Schmidt number is almost independent of temperature~ negligible numerical differences would result if the reference temperature were taken at the surface or mainstream value o

o0 2.C o I.E l.4 I.C 0.E 0.2 0o I 0.1 I-0 0 23 3 4 2 3! I 62 61 3R. 60 -59 -58 57 - 56 o,-~ -55 -54 -53 - 52 51 60 I VO TS, ~c,,,,A NAPHTHALENE 27 26 25 I - I I I i 24.20 ol, I-P IP.10 28 ------ 27 p- DIBROMOBENZENE I _ _ I I| [ It 1 - I_ _ _ _ _ 2 6 o0.~ 0o 25 0 0,x J C --- 23 23 24 25 Ts,C 26 27 24 25 26 27 Ts,C Figure 17a. Surface Temperature as a Function of Wet-Bulb Depression and Air Temperature for Naphthalene and p-Dibromobenzene.

U) 0~ ~-p~ I-P 157 156 155 154 153 15 152 151 150 149 148 I 0 0 To To TS,~ 1.8 o o~ 1.6 1 1.4 1.2 112 - III o 0~ 110 -109 - 108 113 Ts,C Ts,C Figure 17b. Surface Temperature as a Function of Wet-Bulb Depression and Air Temperature for Propionamide and Anthracene.

-101 - Table VII "Wet-Bulb Depression" for the Organic Solids Material Ts Ta-Ts Ta Material Ts Ta-Ts Ta Material Ts Ta-Ts Ta Naphthalene 23.0 0.119 23.1 " 25.0 0.145 25.1 " 27.0 0.176 27.2 50.0 1.35 51.4 52.0 1.60 53.6 " 54.0 1.88 55.9 " 56.0 2.21 58.2 I".58.0 2.58 60.6 p-Dibromobenzene 27.0 0.111 27.1 "t 50.0 0.900 50.9 " 52.0 1.07 53.1 54.0 1.26 55.3 56.0 1.49 57.5 58.0 1.75 59.8 Propionamide 60.0 1.22 61.2 62.0 1.41 63.4 64.0 1.62 65.6 Anthracene 108. 0.167 108.2 t" O110.0 0.188 110.2 " 112.0 G.212 112.2 " 146.0 1.29 147.3 " 148.0 1.42 149.4 " 150.0 1.57 151.6 " 152.0 1.72 153.7 154.0 1.89 155.9 p-Dibromo- 23.0 0.0742 23.1 benzene T =- Surface Temperature (~C) T = Ail Temperature (oC) 25.0 0.0909 25.1 Table VIII Properties of Organic Solids for Determining Diffusivities Material TB (OR) TC (OR) VC (ft Mm ro (A) c/k (OR) D ft2 B c c\mole/ \ moleJ. Dv (: ) Naphthalene 884 1351 6.56 128.16 6.17 1013 1.265 x 10-5 x T3/2/ p-Dibromobenzene 890 1363 6.39 235.92 6.13 1022 1.235 x 10-5 x T3/2/0 Propionamide 875 1223 4.00 73.1 5.23 919 1.678 x 10-5 x T3/2/0 Anthracene 1131 1657 9.14 178.22 7.21 1242 1.017 x 10-5 x T3/2/0 Air 238.2 1.326 28.85 3.63 179 Table IX Schmidt Numbers and Diffusivities of the Organic Solids Material Material Temp.(Oc) Naphthalene p-Dibromobenzene Propionamide Temp. (C) Anthracene Dv Sc Dv Sc Dv Sc Dv Sc (ft2/hr) (ft2/11r) (ft2/hr) (ft2/hr) 20 0.234 2.50 0.228 2.56 0.319 1.83 30 0.252 2.46 0.244 2.54 0.341 1.82 40 0.268 2.44 0.262 2.50 0.364 1.80 50 0.284 2.44 0.277 2.50 0.386 1.80 60 0.306 2.42 0.298 2.45 0.414 1.79 70 0.320 2.41 0.312 2.45 0.432 1.79 100 0.289 3.08 110 0.304 3.07 120 0.320 3.05.130 0.384 3.05 140 0.352 3.02 150 0.368 3.00

5o Calibrations -102 -

-103 - 260 240 220 200 E 180 E 160 C(3 Z c 140 W 120 u i) t. n 100 m - 80 60 40 20 0 METERED AT 45 PSIA 8 70 OF (calibrated with wet test meter ) Fischer and Porter rotometer Tube B-4A25 Float BSX-41-A _~~.. 0 2 4 6 8 10 STD. C.F.M. AIR AT 14.7 P.S.I.A. PRESSURE 8 70 ~F 12 Figure 18a. Calibration Curves for Rotameter Number 1.

-104 - 260 240 220 200 180 E E 160 0 z 140 w ' 120 w J u 100,/) w Im 80 1 -60 40 20 0 I METERED AT 45 P.S.I.A. 8 70 ~F (calibrated with wet test meter) __ I I I — d -- Fischer and Porter rotameter Tube B-5N25 Float BSX-51-A 0 1 2 3 4 5 STD. C.F.M. AIR AT 14.7 P.S.I.A. PRESSURE 8 70 OF 6 Figure 18b. Calibration Curves for Rotameter Number 2.

-105 - 260 240 220 200 180 E E 160 Z 2 140 w, 120 -_J 0 C) 100 ro - 80 60 40 20 0 METERED AT 45 PSIA. 8 70 OF (calibrated with wet test meter ) l / I Fischer and Porter rotometer Tube B2-26-250 '~/.~~ ~Float BSX - 20 D____ ___i 0 0.2 0.4 0.6 0.8 STD. C.F.M. AIR AT 14.7 P.S.I.A. PRESSURE 8 70 OF 1.0 1.2 Figure 18c. Calibration Curves for Rotameter Number 3.

0 -10 (a 0 0 o E z 0 U w nr 0 U O c) -20 -30 -40 -50 OI Is^!Thermocouple Calibrations ----—......... _determined with Potentiometer Model #8662 '\ Ss) 0Ser. No. 729427 and N.B.S. Calibrated Thermometers '~.Os ________^___._ o 0 -60 -70 0 I 2 3 4 5 6 7 8 THERMOCOUPLE READING, (millivolts) Figure 18d. Calibration Curves Chromel-Alumel Thermocouple.

NOMENCLATURE a area of interphase contact per unit volume, ft-l 2 A area, ft B constant cp heat capacity at constant pressure, BITULb-~F cv heat capacity at constant volume, BTU/lb-~F C constant D diameter, ft D molecular diffusivity, ft2/hr E constant f friction factor, dimensionless F ratio of Us/x, 1/hr G mass, velocity, lbs/ft -hr Gm molar mass velocity, lb-moles/hr-ft2 h heat transfer coefficient, BTU/ft2-hr-~F jD ((kgMmbm/G)(Sc) 5, dimensionless jH (St)(Pr)0O5, dimensionless k thermal conductivity, BTU/ft-hr-~F kc mass transfer coefficient, ft/hr k mass transfer coefficient, lb-moles/hr-ft2-atm K over-all mass transfer coefficient, lb-moles/hr-ft2-atm L length, fto m exponent M molecular weight, lbs/lbmole n exponent N mass transfer rate, lbs/hr -107 -

10o8 -Nu Nusselt number, (hDv/k), dimensionless P total pressure, mm Hg p partial pressure of one component in a gas mixture, mm Hg Pr Prandtl number, (epl/k), dimensionless rAB arithmetic average of radii of two molecules, Angstroms R gas-law constant, 0, 728 ft3-atm/lbomole!~R Re Reynolds number, (DG/p), dimensionless Sc Schmidt number, (pi/ Dv.) dimensionless St Stanton number> (h/cpG),. dimensionless t time, hr T absolute temperat'ure OR u linear velocity, ft/hr V gas volume, ft3 W weight loss, lb-moles x distance from stagnation point ft Greek angular position, degrees X latent heat of sublimation, BTU/lb-mole viscosity, ibsM/ft-hr p density, lb/ft3 collision function calculated by Hirschfelder et al (47) p function to be determined Subscripts a air ave average b bulk bm inert component

-109 -c corrected d dry f film (arithmetic average) i inconel surface L -liquid phase m integrated mean s surface t total Abbreviations CFM cubic feet per minute Ib pound force IbM pound force log common logarithm, base 10 In natural logarithm, base e NoB So National Bureau of Standards SCFM standard cubic feet per minute at 70~F and l4o7 psia

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