ENGINEERING RESEARCH INSTITUTE THE UNIVERSITY OF MICHIGAN ANN ARBOR EVALUATION OF THE HUDSON ENGINEERING COMPANY AIR-TEST BOND-RESISTANCE APPARATUS Report No. 43 Edwin H. Young Assistant Professor of Chemical and Metallurgical Engineering Dennis J. Ward James R. Wall Marvin L. Katz William F. Conroy Walter R. Gutchess Research Assistants Project 1592 WOLVERINE TUBE DIVISION CALUMET AND HECLA, INCORPORATED DETROIT, MICHIGAN May 1956

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN - TABLE OF CONTENTS Page LIST OF TABLES iv LIST OF FIGURES v OBJECTIVE vi ABSTRACT vi I. INTRODUCTION1 SURVEY OF PERTINENT PUBLISHED PAPERS1 PROBLEM UNDER INVESTIGATION II. PREVIOUS WORK ON BIMETAL FINNED TUBES5 III> DESCRIPTION OF AIR-TEST APPARATUS IV. OPERATIONAL PROCEDURE 7 V. THEORETICAL CONSIDERATIONS 8 VI. SUMMARY OF PUBLISHED RELATIONSHIPS FOR AIR FILM COEFFICIENTS 14 VII. ANEMOMETER DUCT CORRECTION FACTOR 16 VIII. THERMONCMEER CORRECTION FACTORS 18 IX. BLOWER TURBULENCE EFFECTS 18 XO TEST DATA AND CALCULATION PROCEDURE 20 TEST DATA 20 CALCULATION PROCEDURES 25 XI. ANALYSIS OF ALL-ALUMINUM-TUBE DATA 25 DETERMINATION OF OUTSIDE-AIR FILM COEFFICIENT 26 DETERMINATION OF INSIDE STEAM-CONDENSING COEFFICIENT 29 XII. ANALYSIS OF BIMETAL-TUBE DATA 32 ii

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN - TABLE OF CONTENTS (Conci,) Page XIII. SENSITIVITY OF AIR-TEST APPARATUS 36 EXAMPLE 1 36 EXAMPLE 2 39 XIV. CONCLUSIONS AND RECOMMENDATIONS 41 REFERENCES 42 APPENDIX A - DERIVATION OF FIN RESISTANCE METHOD FOR A FOULED TUBE APPENDIX B - ANEMOMETER CORRECTION FACTOR OBTAINED FROM THE AIR-TEST APPARATUS APPENDIX C - DATA FOR THERMOMETER CORRECTION FACTORS APPENDIX D - DATA ON EFFECT OF SCREENS APPENDIX E - SUMMARY OF ALL-ALUMINUM TUBE DATA APPENDIX F - SUMMARY OF BIMETAL-TUBE DATA APPENDIX G - CALCULATION OF RUN NO., 481, USING SHORT-FORM, MODIFIED SHORT-FORM, LONG-FORM, AND MODIFIED LONG-FORM CALCULATION PROCEDURES APPENDIX H - CALCULATION OF BOND RESISTANCE VALUES FROM THE DATA FOR THE FIVE BIMETAL TUBES PRESENTED IN FIGo 15 44 50 52 54 56 58 60 65 iii

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN - LIST OF TABLES Table Page I TYPICAL TEST DATA 7 II ho AND ho FOR FINNED TUBE OF FIG. 4 11 III TYPICAL ALL-ALUMINUM-TUBE TEST DATA 23 IV TYPICAL BIMETALLIC-TUBE TEST DATA 24 V COMPARISON OF CALCULATED RESULTS OF RUN NO. 481 24 VI BOND-RESISTANCE VALUES FOR FIVE BIMETAL TUBES 33 iv

L ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN LIST OF FIGURES Figure Page 1 Schematic representation of heat flow across metallic contact areas. 2 2 Schematic diagram of test apparatus. 6 3 Efficiency of annular fins of constant thickness. 10 4 Fin resistance versus outside coefficient. 12 5 Calculated values of ho versus ho. 13 6 Calibration of anemometer in four-inch duct, 17 7 Temperature rise of the inlet air due to blower, radiation, and other effects. 19 8 Effect of screens on performance of tubes. 21 9 Effect of screens on the outside coefficient. 22 10 All-aluminum tubes; determination of exponent on velocity (ho = AVb). 27 11 Wilson plot for all-aluminum-tube data. 28 12 Air film coefficient as a function of air velocity. 30 13 Wilson plot for bimetallic tubes. 34 14 Combined heat transfer coefficient versus Vmax for various bond resistances, 35 15 Combined heat transfer coefficient versus Vface for various bond resistances. 37 16 Percent of resistance due to bond resistance for hi = 1000. 38 17 Percent of resistance due to bond resistance for hi = 2000. 40 v

L ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN OBJECTIVE The purpose of this investigation was to evaluate the Hudson air-test apparatus as a production-control device for bimetal high-fin tubes. ABSTRACT The results of this investigation indicate that (1) the Hudson air-test apparatus can be used as a production-control device if the sensitivity of the unit is acceptable and (2) a testing device having considerably greater sensitivity would permit closer production control of lowbond-resistance tubes. vi

- - ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN I. INTRODUCTION Bimetal integral aluminum spiral-finned tubes have found wide usage in a variety of heat transfer applications. For certain applications a liner is placed inside the aluminum finned tube. This may be done to protect the tube from corrosion or erosion. A small air gap, oil film, or other foreign matter between the liner and the finned-tube wall would cause an additional resistance to heat transfer. This additional resistance to heat transfer is sometimes referred to as "bond resistance" or "contact resistance." In heat transfer applications involving multilayer materials, no allowance is normally made for the interface resistance to heat transfer where the materials are in contact. Such a procedure is valid in the cases where the materials themselves have low thermal conductivities and are controlling the performance of the system. The assumption of no interface resistance presupposes the absence of gases or vacant spaces caused by blow holes, bubbles, rough surfaces, etc., which are likely to be present where two solid surfaces are brought into contact.I* Traces of poorly conducting materials between metals, such as oxide films or air, cause abrupt drops in temperature. Figure 1 schematically presents the heat flow pattern that exists at the interface of two metals in contact. The metal surfaces are actually in contact over a limited area. The void space may contain air, oil, or other foreign material. As indicated in the figure, when heat flows from one surface to the other the flux lines converge in the region of the area of contact. The area of contact can be increased by pressing the surfaces together. Pressing the surfaces together may cause the metal, at the point of contact, to be either elastically or plastically deformed. Several investigators have studied the effect of pressure on the contact surface area and on the heat transfer rate.2-7~9 The mathematical theory of elasticity and plasticity has been used to explain some of the heat transfer phenomena resulting from pressing the surfaces together. 26 *References are given on page 42. 1

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN Fig. 1. Schematic representation of heat flow across metallic contact areas. SURVEY OF PERTINENT PUBLISHED PAPERS The thermal resistance of metallic contacts apparently has been under investigation for quite a number of years. The problem was present in electrical switches357 and in the dissipation of combustion heat in lined cylinder blocks.2 One of the earliest investigations reported concerned the 4 heat contact between different parts of a cryogenic apparatus. The thermal conductance between two clean metallic surfaces in contact in a vacuum is of importance in the design of such an apparatus. Jacobs and Starr studied the thermal conductances between various clean surfaces in a high vacuum. The conductances were studied as a function of pressure and the investigation was limited to good heat conductors such as copper, silver, and gold. Since the quality and flatness of the surfaces considerably affected their results, they polished the surfaces to approximately optical flatness. They then found that the slightest trace of grease at the interface resulted in an increased conductance at room temperature and a decrease in conductance at low temperatures where the grease they found a linear relationship at the interface. The following became hard. For copper against copper between thermal conductance and pressure relationship fits their data: K = 0.08 P, (1) where K = thermal conductance, watts/cm2 ~C and P = contact pressure, Kg/cm2. 2

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN This equation indicates that in the case of optically smooth copper surfaces, doubling the interface contact pressure between the contacts doubles the thermal conductance. Weills and Ryder2 studied the thermal resistance of dry and oilfilled interfaces between flat surfaces of various metals. The experimental apparatus used consisted of two test blocks 3 in. in diameter by 3 in. long, stacked axially one on another between the platens of a hydraulic press. The upper block was inductivily heated and the lower block watercooled. The thermal conductance was obtained from measurements of heat flow and temperature gradient through the blocks. The effects of temperature, pressure, and surface finish were studied. The investigators found that the thermal resistance at the interface is decreased by increasing the temperature and pressure, by the inclusion of oil, or by plating the surfaces with a soft metal. As a result of their experiments, Weills and Ryder made the following conclusions: 1. The thermal conductance of a dry joint increases with pressure, linearly for steel, and generally exponentially for aluminum and bronze. 2. The thermal resistance of both dry and oil-filled joints decreases with a decrease in roughness of the surfaces. 3. At a given temperature, pressure, and roughness, the thermal resistance of both dry and oil-filled joints decreases in the order of steel, bronze, and aluminum. 4. The thermal resistance of a dry joint decreases as the temperature increases, For oil-filled joints, no consistent relationship was found. 5. The thermal resistance is about one-half as great for oil-filled joints as for dry joints at 10 psi. The effect of the oil decreases at higher pressureso The thermal resistance is decreased by copper plating one surface of a steel joint. 6. A hysteresis-like loop in the thermal conductance-pressure relation is obtained when the pressure is decreased following an increase in pressure 7. The presence of a film of oxide or other foreign material of low thermal conductivity could contribute to the thermal resistance of a joint. However, except for very low interface pressure, the oxide resistance appears to account for only a small part of the total resistance, The investigators also indicated that they believe that the area in metallic contact is directly proportional to the load during plastic deformation and to the two-thirds power of the 1 oad during elastic deformation. This 3

- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN opinion is based on the mathematical theory of elasticity.8 Centinkale and Fishenden considered the plastic flow of the metal at the interface when the surfaces are pressed together. These investigators concluded that when pressure is applied to the contact, the softer of the two metals will plastically flow until the average pressure at the contact interface is equal to the average resistance per unit area against indentation (Meyer hardness). If the pressure is subsequently reduced, the metallic flow is elastic and the area of contact is a function of the pressure to the two-thirds power. Kouwenhoven and Potter9 studied the thermal conductance of steelto-steel contacts under various conditions. The effects of pressure, temperature, and surface roughness were explored. The investigators assumed that the surface consisted of a series of parallel isosceles trapezoid ridges ("like a plowed field"), As the pressure at the interface is increased, the trapezoids are assumed to crush, increasing the contact area. They presented the following relationships for predicting the increase in contact area as a function of the original contact area and the relative height of the trapezoids: Af = Ao + 21 + 2 I^Ao + 2 (2) where Af = final contact area, Ao = initial contact area, and = decrease in trapezoid height as a result of pressure. Since A is the area of contact, 1/A is a measure of the resistance to heat flow. The influence of pressure was found to be greater for rough surfaces In general, Kouwenhoven and Potter's results agreed with those of Weills and Ryder.2 Brunot and Bucklandl1 investigated the thermal conductance of blocks of laminated steel. They also found that the effect of pressure was considerably greater in the case of rough surfaces and concluded that contact resistances vary widely depending on smoothness, contact pressure, thermal conductivity of the metal, and thermal conductivity of the material between the metal surfaces. The published data referred to above form a useful basis for the investigation of bond resistance to heat transfer in bimetal tubes. The concept of treating the effect of the bond as a separate resistance to heat transfer is a fundamentally correct approach to the problem. The reciprocal 4

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN of the bond resistance is the conductance of the bond. PROBLEM UNDER INVESTIGATION The Hudson Engineering Company designed and built a unit to test the performance of finned tubese A copy of the blueprints used to build this unit was obtained from that company, A similar unit was built at The University of Michigan for evaluation by the project. The evaluation of this unit involves the determination of its ability to detect and measure in a reproducible manner the bond resistance of a tube. The sensitivity of the device to differences in bond resistance between different tubes is an important control criterion of the unit. II. PREVIOUS WORK ON BIMETAL FINNED TUBES Project Reports No.26 and No. 34, entitled "Development of a Test for Bond Resistance to Heat Transfer in Bimetal Finned Tubes" and "Effect of Root Wall Thickness on Bond Resistance to Heat Transfer of Bimetal Tubes," respectively describe a test method for bond resistance, In this method water was circulated by natural convection on the outside of the finned tube being tested, and steam was condensed or water was pumped inside the tube. The main conclusions reached in these reports were: 1. The described test method was suitable for measuring bond resistance 2. Root-wall thickness apparently had no effect on bond resistance. III, DESCRIPTION OF AIR-TEST APPARATUS A schematic diagram of the test equipment is presented in Fig. 2. The test unit essentially consists of a centrifugal blower for blowing air perpendicular to a steam-heated finned tube. An American Blower type 75H was used for this purpose. Provisions were made for measuring the inletsteam temperature and pressure, and the inlet- and outlet-air temperatures. A Taylor vane-type anemometer, model No. A413, was used to measure the discharge-air velocity. To prevent the accumulation of noncondensables, steam was continuously bled from the system. Straightening vanes were placed between the blower and the tubes 5

- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN Anemometer Plate Steam Steam 4 Inlet-Air - Thermometer Vanes -Blower Fig. 2. Schematic diagram of test apparatus, 6

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN being tested in order to remove large-scale turbulence created by the blower. The inlet-air thermometer was placed above the vanes and about 6 in. below the finned tube. The outlet-air temperatures were measured using a thermometer placed above the orifice plate but below the anemometer, The thermometers were calibrated against a thermometer calibrated by the Bureau of Standards., The steam-pressure gage was calibrated against a 100-in. Merriam mercury manometer, IV. OPERATIONAL PROCEDURE Steam was first purged at a rapid rate through the tube to remove inside fouling, The pressure was then set at 10 psig for all experimental runs. Approximately 20 min were allowed for the equipment to reach equilibrium. A stopwatch and the anemometer were then started simultaneously, after which inlet- and outlet-air temperatures, and steam-temperature and -pressure readings were recorded at 1-min intervals for a total of five readings. The stopwatch and anemometer were then simultaneously stopped and their readings recorded. Steam was then again purged at a rapid rate through the tube to remove any condensate in the tube. The test procedure described above was repeated and the temperature data were compared with the previous measurements to ascertain that equilibrium had been reached. Typical test data are given in Table I. TABLE I IYPICAL TEST DATA Run No,. 414 Date of Run 12-20-55 Anemometer reading = Anemometer time = Tube Designation No. 17 All-aluminum tube 9100 ft 5 min 4,9 sec Inlet-air thermometer reading = 27.06~C Calibration correction to thermometer Correction due to radiation and other Actual inlet-air temperature = Outlet-air thermometer reading = 48.66~C Calibration correction to thermometer Actual outlet-air temperature = = -0o09 o effects = 25.970C = = -_0o03~C 48,63~C = -1.00~C 78.75~F 119.55~F Steam pressure = 10 psig Barometer reading = 752.0 mm Hg Barometer temperature = 18~C 7

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN V THEORETICAL CONSIDERATIONS The overall coefficient of heat transfer is defined as Q = UoAoATm, (3) where Q Uo Ao ATm The bimetal tubes U0 = - = heat transferred, Btu/hr, = overall coefficient of heat transfer, Btu/hr/~F/ft2 based on outside area, = outside heat transfer area, ft2, and = mean-temperature driving force, ~F. overall coefficient of heat transfer is further defined for as 1 t (4) h 1 + rf + rO( A )+ rm ()+ rb ) + ri (A)+ i A) where h' = outside film coefficient, Btu/hr/~F/ft2, rf = fin resistance (see Equation 5), Btu/hr/~F/ft2, rm = root-wall metal resistance, Btu/hr/~F/ft2, Am = log mean heat transfer area, ft2, rb = bond resistance, Btu/hr/~F/ft2, AL = outside area of the liner tube, ft2, ri = inside fouling resistance, Btu/hr/OF/ft2, Ai = inside heat transfer area of liner tube, ft2, and hi = inside film coefficient, Btu/hr/~F/ft2. The fin resistancell1-2 is defined by Equation 5~ The de: of this relationship is given in Appendix A, rf = [r A+ E i rivation (5) 8

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN - where ro = outside fouling resistance. The fin-resistance concept as presented by Carrier and Andersonl: is convenient to use where repetitive calculations are encountered, The method is an alternate procedure which can be used in place of that used in previous reports, Following the procedure used in the earlier reports, the overall coefficient of heat transfer would be written as iAo' (6) 0 =) 1 + A +, h + ro + r + rb() ri() + hi (i ) (6) where ho = outside heat transfer coefficient based on Ao. A comparison of Equation 6 with Equation 4 indicates that the following substitution has been made: [h1 = + rf|] (7) The relation between ho and ho is given by ho Aeq = ho Ao. (8) The equivalent area is a function of the efficiency of the fin and may be determined by Aeq = Ar + Ef Af, (9) where Ar = root area, ft2, Ef = fin efficiency, Fig. 3, 1 and Af = fin area, ft2. In the range of air velocities encountered in the operation of the air test, the values of the air-side coefficient, ho, vary from 6 to 10. The corresponding fin efficiencies vary from 97% to 92%, respectively. -A typical bimetal finned tube has a fin OD of 2.00 in, a root diameter of 1.10 in., and a fin thickness of 0.019 in., The root area, Ar, for such a tube is 030 ft2/ft length of tube. The area of the fin, Af, is 3.29 ft2/ft, and Ao is 3.59 ft2/ft. By Equation 9, Aeq = 0,30 + 3.29 Ef for Ef = 0.92% Aeq = 0.30 + 3529 (0.92) = 3533 ft2/ft and 9

ENGINEERING RESEARCH INSTITUTE UNIVERSITY OF MICHIGAN - I.0 I \l11111 1 1 1I1I1Z 4-" —— ~~~~~~~~~~~~~~~~~~~~~~~~I - I I I Y/2 A p. A - - _ -I I 0.7 \\ I 0.6 XX XI Ik. z w Lii 0 IL 14 c 0 - - - - - - VX -^S I NA - - - __ __ __ __ __ I__I I __ __ _ 9% - z " O. [ 0. 0.2 ) ~I~ I~~~~~~~~~~o~~~~ f, c - 0 1.0 2 H (+ r.e) KY KT' " 2.0 3.U FIGURE 3. EFFICIENCY OF ANNULAR FINS OF CONSTANT THICKNESS 10

7- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN Ao Aeq 3259 355 33 1.08 For Ef = 0.97%, Aeq = 0.30 + 3.29 (0.97) 3.49 ft2/ft and Ae Aeq 3.59 3.49 = 1.03 ho = 1,08 ho for Ef = 92% and ho = 1.03 ho for Ef = 97%. A plot of Equation 5 giving the fin resistance, rf, in terms of ho, ro, and fin efficiency, Ef (using Fig. 3), is given in Fig. 4. In order to use this figure, h6 must be known; In the laboratory experimental research work, ho is obtained directly. Table II presents the fin efficiencies. equivalent areas, and ho as a function of ho for the tube described in Fig. 4 0 - TABLE II ho AND ho FOR FINNED TUBE OF FIG. 4 ho Ef() AeqAeq rfho Ao 600 27.5 0.881 0.329.00382 197.5 400 34.0 1.420 0.396.00374 158.1 200 47.5 1.862 0.520.00463 103.8 100 62.5 2.355 0.656,00523 65.5 50 7500 2.765 0.772.00594 38.5 25 86 0 3.130 0.874.00588 21 8 10 9350 3.360 0.910.00684 9.35 O 100.0 3 59 1.000 O The values of ho venience in Fig. 5. and h' given in Table II are plotted for conan h Equation 4 indicates that the overall coefficient of heat transfer is equal to the reciprocal of the sum of the individual resistances to heat 11

n -,L Fin resistance of an aluminum finned tube having the following dimensions' Do=2.00 Inches Dr=1.14 Inches Y =0.019 Inches N =9 Fins / Inch m Z T3 C) z m z Cv m m z C' I: i I n Hro 1o 0 x.4 I5~~~~ ~~~~ __ __!...L......______ - _ 2 -- -- -- -- - - ~ ~ --- - --- -- - - - - -- - - -- -- - - _ _ 2~~~~~~ c: z m In zI oo C -- z 2 3 5 7 9 10 20 50 100 200 500 I[T]' + r' ho 0 Fig. 4. Fin resistance versus outside 10 coefficient. I

- - - - -00 Q801 1 ho vs ho for aluminum tube _ having: __ Do= 2.00 l"e __ Dr- I. 14" Y =0.019" N =9 fins/inch _ 20 P8 F co -olc~~ --- -— 400 — 300 2 ----- 1 __ _ -200150 1.0 2.0 5.0 10 20 50 100 200 500 1000 Fig. 5 Calculated values of h versus h Fig..5. Calculated values of ho versus h. m z (A) z m m z 7) m m C. 3: z m 70 < -< t1 z I Z I

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN transfer. In the case of the tubes tested, the outside fouling resistance, ro, and the inside fouling resistance, ri, were for all practical purposes zero. The new tubes had clean fins and, as described in the previous section, steam was used to clean the inside of the tubes, Therefore, Equation 4 reduces to 1 1 Ao \ ), AA) U1 h__ + rf + rm (An + rb AL' hi (Ai)' (0) where 1/Uo = overall resistance to heat transfer, Btu/hr/~F/ft2. In this simplified case where ro = 0, the abscissa of Fig. 4 becomes ho. In most heat transfer studies, values of U0 are obtained directly. Other resistances or coefficients are calculated by subtracting out known resistances obtained from Wilson plots, wall temperatures, or empirical equations. From the above equations and discussion it can be seen that if one wishes to study any particular resistance to heat transfer, such as bond resistance, the other resistances involved should be minimized. If this is done, variations in 1/Uo will reflect variations in the resistance being studied. If other resistances besides the one being studied are large and also vary, such variations can easily mask the variations of the resistance under study. This subject is developed further in Section XIII of this report. In the air-test apparatus the velocity of the air past the finned tube affects the outside-air film coefficient of heat transfer, A review of the literature (see Section VI) indicates that the variations in air film coefficients are correlated in the following form: ho = aVb. (11) The various values of a and b obtained by different investigators are summarized in Section VIo VI. SUMMARY OF PUBLISHED RELATIONSHIPS FOR AIR FILM COEFFICIENTS A survey of the technical literature since 1942 indicates the following equations for air-side coefficients for tubes: 1. Norris and Spofford:14 14

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN ho = C1 (Vmax)"5 (12) 2. Lemmon, Colburn, and Nottage:l Uo = C2 (Vmax)0'53 (13) 3. Jameson16 (for various finned tubes): hto = C3 (Vmax)060 (14) 0.69 ho = C4 (Vmax)' (15) h = C5 (Vma)0 675 (16) 0 ho = C6 (Vma)0655 (17) ho = C7 (Vmax)0718, and (18) ho = C8 (Vmax)0'666 (19) 4. Kays and London17 (for various finned tubes): Fig. 92, ho = Cs (Vmax)0'8 (20) Figv 93, ho = Clo (Vmax)0'763, (21) 0076 Fig. 94, ho = Cil (Vmax)' (22) Fig. 95, ho = C12 (Vmax)059, and (2) Fig. 96, h = C(13 (Vmax)0.72. (24) 0 5. Katz, Beatty, and Foust:18 Uo = c4 (Vmax)053. (25) 6. Schmidt19 (first row of finned tubes in a tube bank): h' = C15 (Vmax)0'29 (26) ho = C16 (Vmax)047 (27) ho = 17 (Vma)0'41 (28) ho = C18 (Vmax)0'525, and (29) ho = C19 (Vmax)0.44 (30) 15

ENGINEERING RES$EARCH INSTITUTE * UNIVERSITY OF MICHIGAN An examination of Equations 12 through 30 indicates that the power (exponent) on the maximum velocity varies from 0.29 to 0.8. Most of the exponent values appear to be in the neighborhood of 0.65. It should be pointed out that the above equations do not contain the value of the constants C1 through C19 because the data were obtained on a wide variety of tubes in various test arrangements and were reported in many forms. Many of the exponents reported above were computed from the published data and curves. VII. ANEMOMETER DUCT CORRECTION FACTOR In the early stages of this investigation it was observed that the air film coefficients obtained on the air-test apparatus were considerably higher than those published in the Katz, Beatty, and Foust articlel8 and in the correlation report.20 Some of the data published in the correlation report were for tube banks one row and two rows deep. The Katz-Beatty-Foust data were obtained on single tubes, one-row banks, and two-row banks. As a result of this discrepancy an investigation on the influence of a 4-in. duct on the Birams type vane anemometer was undertaken. Report No. 5721 was issued as a result of this investigation. Figure 3 of that report (p. 12) indicates that the actual amount of air flowing through the 4-in. duct is 66% of that indicated by the anemometer. Early air-test results (using the 66% duct correction factor) indicated that the exponent on the velocity term for all-aluminum tubes was about 0.35 This value was considerably lower than that expected, since the literature indicated that the probable value would be in the neighborhood of 0.6. As a result of this situation an independent check of the anemometer correction factor for a 4-in. duct was made with the anemometer in the airtest apparatus. Steam condensate was collected and air-side and steam-side heat balances were obtained. The results verified the 66% correction factor. The actual value obtained by this latter method was 65.3%^ Figure 6 presents the test curve. The test data are summarized in Appendix B. It was concluded that the duct correction factor is an essential correction that must be taken into consideration in analyzing the air-test data. It was also concluded that the low value of the velocity exponent could not be explained by an error in the anemometer duct correction factor. Two other possible factors could explain all or part of the low exponent. These are: (a) thermometer error due to radiation or other factors; (b) airturbulence factors. These are discussed in Sections VIII and IX of this report. 16

1 — - 1 I I I I I I I C-/ n mrvh 4) w 4) E 0 E 0 ~L44 4) rC 0 LaL C') m 4) U) 0 4) 44 0 4) 7 1900 1800 1700 - 1600 -- 1500 1400 1300 W 1200 SLOPE=1.531 1100 1000 900 900 ~____l ___________________________________ m z n m m z ~3 m m I I — 4 — I "1 0 3: z m 03.1n Z Jr 500 600 700 800 900 1000 1100 1200 ACTUAL SFM OF AIR Fig. 6. Calibration of anemometer in four-inch duct. 1300

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN VIII, THERMOMETER CORRECTION FACTORS The possibility of radiation from the hot finned tube to the inlet-air thermometer was experimentally investigated. This was done in the following manner. A second inlet-air thermometer was placed in the ambient-air stream going to the blower. It was observed that there existed a significant difference between the temperature readings. It was apparent that part or all of this difference might be accounted for by the energy added to the inlet-air stream by the blower. If only part of the difference was due to the blower, the remaining portion would be due to radiation or possibly to conduction of heat from the test tube to the wall of the apparatus and finally by convection to the air in the neighborhood of the thermometer. To determine the blower effect, the tube was not heated and the air thermometers were read with varying air velocities. A calibration curve was established giving the temperature rise of the air due to the blower as a function of the air velocity past the tube. Analogous test data were obtained for the condition in which the tube was heated. The results of these two series of tests are presented in Fig. 7 and the test data are tabulated in Appendix C. It was concluded that these correction factors are significant and must be taken into account when analyzing air-test data. This situation could be avoided by redesigning the air-test apparatus so as to relocate the inlet-air thermometer in such a manner that no such correction is required. IX, BLOWER TURBULENCE EFFECTS The centrifugal blower used in the air-test apparatus tends to discharge the air against the back wall of the duct going to the tube. As indicated in Section III of this report, straightening vanes were installed between the blower discharge and the tube being tested. These straightening vanes were of the "egg-crate" variety. Discussions with professors of fluid dynamics in both the Engineering Mechanics and the Aeronautical Engineering Departments indicated that the straightening vanes were undoubtedly ineffective in removing all of the centrifugal blower effects. Further discussions with the above personnel indicated that one or two screen grids would be required to smooth out blower disturbances. 18

Z -J w z 4 m Z er m er, radiation.C) 7i m m C) n Z -— 1 </ -I= C= 0 m ________ 0 2r000 radiation, Z 1500 VMAf FT/MIN Fig. 7. Temperature rise of the inlet air due to blower, and other effects. i

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN Initially one 30-mesh screen was inserted above the straightening vanes Later a second 30-mesh screen was inserted about one inch above the first screen. The data obtained from an all-aluminum tube in the air-test apparatus with no screens, one screen, and two screens, (inserted as described above) are tabulated in Appendix D. The data are presented graphically in Fig, 8 where the reciprocal of the overall heat transfer coefficient (1/Uo) is plotted vs the reciprocal of the maximum velocity to the o04 power. The power on the velocity was determined from all of the all-aluminum test data and is described in Section XI. The data presented on Fig. 8 were obtained from two separate series of tests. A separate series of tests indicated that it is necessary to clean thoroughly the inside of the tube prior to testing in order to obtain reproducible results. The cleaning was accomplished by blowing live steam through the inside of the tube for about one-half hour. Since this cleaning procedure had not been used on the tube in the initial test measurements made to determine the effects of the screen, a second series of tests were run with an all-aluminum tube cleaned on the inside in the above manner to check the effects of the screens on the tube performance. The results of the second series, also presented on Fig. 8, indicate that the first tube was fouled during the runs made with no screens present in the apparatus. From the data in Fig. 8 it appears that the fouling probably present on the inside of the tube was essentially removed during or following the tests made with no screens present, as it does not appear significant in the one-screen and twoscreen data. The effect of the screens on the outside-air film coefficient is presented in Fig. 9 where the outside-air film coefficient is plotted vs the maximum air velocity on logarithmic coordinates. As shown on this figure, one effect of the screens is to reduce the outside coefficient 11.5%.l The use of screens between the blower and the tube being tested tends to level out the uneven disturbances created by the blower. Since the flow characteristics produced by different blowers would in general not be the same, some method must be used to eliminate blower effects in order to obtain comparable results between air-test apparatuses using different blowers. The use of screens can accomplish this purpose. X. TEST DATA AND CALCULATION PROCEDURE TEST DATA The test data taken on all-aluminum and bimetal tubes in the air-test apparatus consisted of the inlet- and outlet-air temperatures, the anemometer reading and anemometer time, and steam and atmospheric pressures. Typical test 20

ENGINEERING RESEARCH INSTITUTE 0.16 Legend o - One screen test no. I 0.15 - One screen test no. - X- No screen test no. I - No screen test no. ET 0.14 0.1 3 0.12: 0.1 I 0.10 0.09 0.08 * UNIVERSITY OF MICHIGAN X i I vO.4 Fig. 8. Effect of screens on performance of tubes. 21

- ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN 20 18 16 14 12 No Screen,Clean Tube No Screen, Dirty Tube:-o 6 1^1 / / l l [ One Screen,Clean Tube 6.-_-~ —--- 3600 Vm Fig. 9. Effect of screens on the outside coefficient, 22

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN - data obtained on an all-aluminum tube (No. 16) are given in Table III. Table IV includes typical test data obtained on a bimetallic tube (No. 36). As can be noted from a comparison of Tables III and IV, the measurements taken were the same for both types of tubes, differing only in the experimental values obtained. A summary of all of the all-aluminum test data for this report is given in Appendix E. Appendix F contains a summary of the bimetallic-tube test data. The test data obtained in the earlier runs without two screens were not used in this evaluation report. TABLE III TYPICAL ALL-ALUMINUM-TUBE TEST DATA I Tube No. 16 Barometer reading Barometer temperature Orifice size Anemometer reading = Anemometer time = Run No. 481 = 73. 2 mm Hg = 20.2~C 4 in. 9200 ft 4 min, 21.8 sec Inlet-air thermometer reading Correction for radiation and other effects Thermometer calibration Inlet-air temperature Outlet-air thermometer reading Thermometer calibration Outlet-air temperature = 28.98~c = -100~C =+0.07 =28.05~C =82.50F =48.735C = -o.o4~c =48.69~C = 119.65~F I Steam pressure = 10 psig CALCULATION PROCEDURES Four different calculation procedures had been used at one time or another to analyze the air-test data. The four methods have been referred to as (1) short form of calculation, (2) modified short form, (3) long form, and (4) modified long form. Sample calculations for each of the above procedures are given in Appendix G for Run No. 481. The results of these calculations are given in Table V. The differences among the four calculation procedures are as follows: 23

- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN TABLE IV TYPICAL BIMETALLIC-TUBE TEST DATA Tube No. 36 Barometer reading Barometer temperature Run No. 508 = 720.8 mm Hg = 258~0C Orifice size Anemometer reading Anemometer time = 4 in. = 8995 ft = 3 min, 57,7 sec Inlet-air thermometer reading Correction for radiation and other effects Thermometer calibration Inlet-air temperature Outlet-air thermometer reading Thermometer calibration Outlet-air temperature = 30,8O0C = -1.00C =+O.09~C = 2989~c = 85.8~F =47.90~c =-0.030 = 4.870C = 118. 1F Steam pressure Steam temperature = 10 psig = 114.1~C = 257.4~F TABLE V COMPARISON OF CALCULATED RESULTS OF RUN NO. 481 Calculation Procedure Short Form Modified g Modified Short Form Long Form Short Form Long Form Vface 980 646 672 672 max --- --- 1790 1790 Uo (liner OD) 174.5 120.5 118.5 124.8 Uo (outside) --- --- 8.68 9.13 ho (liner OD)* 205 134 151.5 139.5 *Calculated assuming all resistances except air film equal 0.00085, based on liner area. 24

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN 1. The short form of calculation does not take into account (a) the density correction on the anemometer, (b) the effects of the duct on the anemometer, (c) corrections on the inlet-air thermometer due to radiation and other effects, or (d) differences in tube geometry. 2. The modified short form of calculation is the same as (1) above except that the effect of the duct on the anemometer reading is taken into account. 35 The long form of calculation is the same as (1) above except that items (a), (b), and (d) are taken into account. No correction is made on the inlet thermometer for radiation and other effects. 4. The modified long form of calculation takes into account all four (a, b, c, and d) of the above factors. As indicated in Table V, significant differences can exist among the results obtained from the four procedures. The modified long-form type of calculation is believed to give the most significant heat transfer result. This method of computation was used to compute all overall coefficients given in this report. XI. ANALYSIS OF ALL-ALUMINUM-TUBE DATA The overall coefficient of heat transfer can be computed using the data given in Appendix E by Equation 35, making proper allowance for anemometer and inlet-air-temperature corrections. The overall coefficient of heat transfer is related to the individual resistances by Equation 4. Equation 4 can be rearranged to give 1 1./A o \/A0 A Ao\ Ao\ -U — +r f + r (A )+ rm ( )+ rb + ri + AO (31) U0 h+ tAAeqmA Ar A Ai hi\Ai/ For an all-aluminum tube, the bond resistance, rb is zero. Assuming no fouling on the inside and outside of the tube (ri = ro = 0), Equation 31 reduces to U1 = h- + rf + rm (A) + i( ) (2) Uo ho +i The outside coefficient ho is correlated by use of an equation of the following form: ho = c Vmax (11) 25

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN where c = a constant, and b = a constant. Equation 11 can be substituted into Equation 52 to give 1 1 A 1 A =cVb + rf + rm + O i3 U0oc max m(m) hi Ai Assuming that rf, rm, and hi are constant, this equation reduces to the following form: 1 1 0 cb +, (34) Uo c Vl- + max where M = a constant = rf + rm ( + L- m / hi Ai A plot of (l/Uo) vs (1/Vb) on rectangular coordinates should result in a straight line having a slope of (l/c) and an intercept value of M. DETERMINATION OF OUT'SIDE-AIR FILM COEFFICIENT The value of the exponent, b, was obtained using a least mean 22 square22 analysis of the all-aluminum-tube test data. Various exponents were assumed and the deviations of the data from Equation 34 were calculated. The sum of the square of' the deviations were plotted vs the assumed exponents as shown in Fig. 10. The best exponent was obtained from the minimum value of the sums of the square of the deviations. As given in Fig. 10, the exponent value obtained using this procedure is 0.4. Figure 11 presents a plot of (l/Jo) vs (l/Vm0'4) for the allaluminum-tube test data. The solid line given on this figure was obtained using a least mean square fit of the data and has the equation 1 =1 + o.00481 (35) Uo o.465 Vm04 By comparison of Equation 34 and 355 the values of c and M are obtained as c = 0.465 and M = 0.00481. 26

- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN 3.5C ) 3.40 e, z 0 o LL 0 cI, w U, 0 Un c: 4 3.30 cn UL I I I.L I to Vft I I I I W6 I I 0.30 0.35 0.40 0.45 EXPONENT ON VELOCITY Fig. 10 All-aluminum tubes; determination of exponent on velocity (ho = AVb). 27

- ENGINEERING RESEARCH INSTITUTE UNIVERSITY OF MICHIGAN — i v V 0.4 MAX Fig 11. Wilson plot for all-aluminum-tube data 28

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN The outside-air film coefficient obtained from the above analysis is expressed by the equation ho = 0.465 Vm 0.4 (36) A second least mean square analysis was made on the all-aluminumtube test data to determine the validity of the assumption of a constant fin resistance. The analysis employed a modified form of Equation 34, of the type 1 1 U - rf = c Vmb + m (37) where c' = a constant, b' = a constant, and m' = a constant = rm ( Am +- - *Am/ hi Ai The resistance of the fin was determined for each experimental point, using Fig. 4 and Equation 36. The constants obtained from this analysis were c' = 0.469, b' = 0.396, and m' = -ooo0036 The outside-air film coefficient obtained from this analysis is expressed by the equation h = 0.469 Vm396 (38) A comparison of Equations 56 and 38 indicates that for all practical purposes the outside-air film coefficients predicted by these equations are identical. Equation 36 is presented graphically in Fig. 12 and will be used throughout this report to predict the air film coefficient for 2-in.-OD finned tubes in the air-test apparatus. DETERMINATION OF INSIDE STEAM-CONDENSING COEFFICIENT The inside steam condensing can be calculated from the expression (see Equation 34) hi () M - (rf + rm A) (39) hi ~Aij mA 29

l 18 15 14 13 12 I I LL L 9 0 cr O D' 8 I6 6 5 4 -.O -.900 -10 000000000,00oeeo-oo'0000 00000,ooo'00-100 00000 - i II m z z m m 70 z 50 m -r m Tl m I z in C= - m C: z m 730 -I 0 r 500 1000 1500 2000 2500 3000 3500400045005000 VMAX(FT/MIN) Fig. 12. Air film coefficient as a function of air velocity.

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN The value of M is given in the previous section as 0.00481. The average fin resistance is obtained from Fig. 4 as rf = 0.0072. The metal resistance is computed as rm XA (40) K Am where X = average root-wall thickness = 0.078/12 ft, K = thermal conductivity of metal root wall = 121 Btu/hr/~F/ft, and - = ratio of outside to mean metal area = 13o2 Am (dimensionless). Substituting, (.078/12)(15.2) = 0.00071 hr/~F/ft2(outside) m 121 Btu Substituting the values of M, rf, and rw (Ao/Ai) into Equation 39, the inside resistance is obtained as 1 A i_ 4\ = 0.0048 - (0,0072 + 0.00071) = -0.00311 hi kAi The above indicates that the inside condensing coefficient, computed from the least mean square fit of the all-aluminum-tube test data, is a negative value. This is not physically possible. The reason for this apparent discrepancy can be seen from examination of Fig. 11. The solid line given on this figure represents Equation 36, obtained from the least mean square fit of the data. The numerical value of M is found from the value of (1/Uo) when (l/Vm04) is equal to zero. The data used in the analysis and plotted on this figure range from approximately (1/Vm~04) =.049 to (l/Vm~'4) =.07. Thus the line representing the data is extrapolated about two and one half times the range of trhe data in order to obtain the intercept value. A dashed line is also included in Fig. 11. The intercept of this line has a value of 0.01202 predicted by a steam-condensing coefficient calculated using Nusselt's theoretical equation. 3 As shown on Fig. 11, the dotted line reasonably represents the all-aluminum-tube air-test data. The sensitivity of the air test apparatus is such that the condensing coefficient cannot be experimentally determined. 31

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN XIIS ANALYSIS OF BIMETAL-TUBE DATA The overall coefficient of heat transfer with bimetal tubes can be computed using the data given in Appendix F and the modified long-form procedure illustrated in Appendix Go Assuming no fouling present on the tube, the overall coefficient is related to the individual resistances to heat transfer by the relationship 1 1 /A\ 1 _ - rf +m, + + rb (41) U0 ht mm r AL hi Ai( The outside-air film coefficient is a function of only the air mass velocity and the tube and apparatus geometry (for moderate temperature ranges) and is independent of the bond resistance of the tube. Since the exterior geometries of the bimetal and the all-aluminum tubes are essentially the same, the outside-air film coefficient for the bimetal tubes is obtained from the all-aluminum-tube data as ho = o0465 vmx4 o (36) Assuming constant fin, steam, and bond resistances and substituting Equation 36 into Equation 41, 1 1 - + M", (42) U0 0.465 VmOo4 + where M" = a constant for any one bimetal tube = rf + rm (A) + rb (fL + (i) Am )L hi Ai A comparison of Equations 42 and 34 indicates that they are of the same form and therefore a plot of (1/Uo) vs (l/Vm0O4) on rectangular coordinates should also result in a straight line for the bimetal-tube data. A comparison of Equations 42 and 355 further indicates that the data for a bimetal tube plotted in the above manner should result in a straight line which is parallel to that obtained for the all-aluminum tubes) but having a different intercept (M") value. Assuming that the steam condensing coefficient for a bimetal tube is the same as for an all-aluminum, the difference n intercepts is M" - M(aluminum) = rm bimetal m(- m )m m ). (43) — 2) bimetal - ( )alumin- A — 32.

- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN Figure 13 presents a plot of (1/Uo) vs (l/Vmax0'4) for five different bimetal tubes. Superimposed on this figure is the corresponding line obtained from the analysis of the all-aluminum-tube data (see Fig. 11). The bond resistances obtained using the intercept values given in this figure and Equation 43 are calculated in Appendix H and tabulated in Table VI. TABLE VI BOND-RESISTANCE VALUES FOR FIVE BIMETAL TUBES (Copper Liner Material) - -,AoBond Resistance Tube No. Bond Resistance x ( Bond Resisance Bond Resistae AL) (based on liner area) 3.09934.00725 4 less than 0.0068 less than 0.0005 36.01004.000733 54.01684.00123 38.06664 o00485 Bond-resistance values, such as given in Table VI, can be directly substituted into an overall coefficient equation such as Equation 41. Thus the designer can take into account the effect of the bond on the heat transfer performance of a unit in the design of equipment. A combined heat transfer coefficient which is a function of only the maximum air velocity (for a particular tube in the air test apparatus) can be computed by combining the bond and air film resistances. Figure 14 presents this type of a plot where + rb(f) is plotted vs the maximum air velocity in feet per minute on logarithmic coordinates. The line corresponding to the outside film coefficient (rb = 0) for this figure was obtained from Equation 36. This figure can be used to predict the effect of the bond resistance on the performance of a tube, as is illustrated in the following example. A bimetal tube, with no bond resistance, tested in the air-test apparatus at a maximum air velocity of 1500 ft/min would have an outside coefficient ho of 8.7. If this perfect tube were replaced by a second bimetal tube having a bond-resistance value of 0.001, the air velocity required to maintain the same overall coefficient would be 2120 ft/min for an increase of 41.4%. If the air velocity for the second tube were maintained 33 I

L - ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN - 1 -0 0.16 1 v0,4 Vm Fig. 135 Wilson plot for bimetallic tubes. 34

I L - ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN o 24 - 1l ] ll11 llIt 21 ___ __ 2 1 --- _ 12 13 -IT I Hill - i VIOX. Fig. 14. Combined heat transfer coefficient versus Vmax for various bond resistances. 55

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN at 1500 ft/min, the coefficient would drop to 7.7 for a decrease of 11.5%. Figure 15 presents the information given in Figo 44 with the coefficient based upon the tube-liner OD area and the air velocity based upon the face area of the tube. The average outside heat transfer area and minimum flow area used for these conversions were obtained from the nominal dimensions of the tubes tested. XIII. SENSITIVITY OF AIR-TEST APPARATUS The sensitivity of the air-test apparatus to bond-resistance differences between bimetal tubes is determined by (1) the degree to which the bond resistance controls the performance of the tubes and (2) the accuracy of the predicted air film, fouling, metal, and steam resistances to heat transfer. This can be illustrated by Fig. 16 where the percent of the heat transfer resistance due to the bond is plotted vs the bond-resistance with parameters of air film coefficients for a 16-gage admiralty tube having an inside coefficient of 1000. By use of this figure, the limits of the calculated bond-resistance value can be determined if the accuracy of the overall coefficient is also known. This is illustrated in the following two examples. EXAMPLE 1 It is assumed that an admiralty liner bimetal tube is installed in the air-test apparatus having a calculated bond-resistance value of 0.001 when the steam coefficient is 1000 and the air film coefficient, ho, is 10. Figure 16 indicates that the bond resistance is 10% of the overall resistance to heat transfer. (All other resistances constitute 90% of the total resistance.) In this range of maximum velocity, the overall coefficient is usually known within + 35% Since the bond resistance is obtained as the difference between the overall resistance and all individual resistances except the bond, the percent of resistance due to the bond is obtained for the limiting coefficients as: (a) true overall coefficient 35 higher than measured: resistance due to bond = (103 - 9 100 = 12.6% (of overall t or cf1053 ioresistance) (b) true overall coefficient 35 lower than measured: resistance due to bond = (97 90) 100 = 7.2%. (of overall 97 resistance) 36 —

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN - 400 Vfoce Fig. 15. Combined heat transfer coefficient versus Vface for various bond resistanceso 37

m z Z m m 7) m m 50 m I C m 70 z -n -- I: m m -) -< rb. BOND RESISTANCE Fig. 16. Percent of resistance due to bond resistance for hi = 1000. I

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN From Fig. 16, the corresponding bond-resistance values are 0.0013 and Oo00068, respectively. Thus, although the overall coefficient is known within ~ 3%, the bond resistance is known only within ~ 30%. Uncertainties in the air film and steam condensing coefficients tend to increase the uncertainty in the measured bond-resistance values. EXAMPLE 2 Assume the same admiralty liner tube is run at a lower air rate such that the outside-air film coefficient, ho, is 5. The bond-resistance value is again computed as 0.001 (with a steam condensing coefficient of 1000). From Fig. 16, the percent of the total resistance attributable to the bond is 5.5%. Again allowing 3% uncertainty in the overall coefficient, the percent of the resistance due to the bond for the limiting coefficients is: (a) true overall coefficient 5% higher than measured: resistance due to bond = (103 94.5 100 = 8.25 (b) true overall coefficient 3% lower than measured: resistance due to bond = ( 97 -945 100 258%. 97 0 From Fig-l 16, the corresponding bond-resistance values are 0.0015 and 0.00055, respectively. Thus, although the overall coefficient is known within ~ 5%, the bond resistance is known only within 0.001 - 0.0005 or + 50%. As shown in Fig. 16, the higher the bond resistance the more sensitive the air-test device because the bond resistance represents a higher percentage of the overall resistance for any fixed air film coefficient. Allowing a 3% indeterminacy in the overall coefficient, the smallest bond resistance measurable with confidence (ho = 10) would be about 0.00027. The tube in this particular case would have to perform as well as the average of the monometallic tubes (allowing for differences in metal resistance). Figure 17 presents the same information as Fig. 16 with an inside coefficient of 2000. As seen from a comparison of the two figures, a change in the inside coefficient shifts the position of the resulting curves. The measurable bond resistance is still in the order of 0.00027. 59

z 0 OD 0 w w I — O ~r Cn w 0 (/ m z r" z m m z m m m m 70 CI Z z --- m I< rn (A 7! oM o o IO D I -- oo o 0 0 0 o o 0 0 0 0000 - M r0 ) LO (D 0 0 0 0 00000 0 0 0 0 0 0 0 0 090 000 0 0 0 0 9 9900 rb,BOND RESISTANCE Fig. 17. Percent of resistance due to bond resistance for hi = 2000.

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN XIV. CONCLUSIONS AND RECOMMENDATIONS The following conclusions and recommendations are made: A, The single-tube test data (i.e., Equation 36 for air film coefficient) cannot be used for the design of tube banks. B. The effect of the bond resistance (interfacial contact resistance) should be included in the design calculations as an added resistance to heat transfer for design purposes. C, The bond resistance with steam condensing inside bimetal tubes and with average air temperatures of 110~F is about 0,001 (based on liner area) for an acceptable bimetal tube, D. The equipment can be used for production control if the accuracy indicated is acceptable (0.001 +.0003 at ho = 10). E, The equipment cannot be used to obtain sufficiently accurate bond-resistance values in the cyclic testing of bimetal tubes. F. The air-test apparatus when used for production control should be operated at the highest air throughput with screens in order to obtain the greatest sensitivity to bond resistance. G. A bond-resistance testing apparatus that can accurately measure bond resistance of the order of 0,0004 ~ 0.0001 or less is seriously needed. We believe that bimetal tubes can be consistently fabricated without serious losses for shipment with bond resistance not exceeding 0.0005 if a sensitive productioncontrol device is available, H. The bond resistance value of 0.001 as given in C and D above amounts to approximately 10% of the total resistance to heat transfer in normal applications. It is recommended that the control value be reduced to at least 5% (or to 0,0005). i 41

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN REFERENCES 1. W. H. McAdams. Heat Transmission, Third Edition. New York: McGraw-Hill Book Co., 1954, ppo 17-18. 2. N. D. Weills and E. A. Ryder, "Thermal Resistance Measurements of Joints Formed Between Stationary Metal Surfaces," Trans. ASME, 71:259 (1949). 3. F. Kesselring. Elements of Switchgear Design. New York: Pitman Pub. Corp., 1932. 4. R. Jacobs and C. Starr, "Thermal Conductance of Metallic Contacts," Rev. Sci. Inst., 10:140 (1939). 5. F. P. Bowden and Do Tabor, "The Area of Contact Between Stationary and Between Moving Surfaces," Proc. Roy. Soc. London, A, 169:391-413 (1939). 6. T. N. Centinkale and M. Fishenden, "Thermal Conductance of Metal Surfaces in Contact," Proceedings of the General Discussion on Heat Transfer, Section II, Institute of Mechanical Engineering and ASME, London, 1951. 7. R. Holm. Electrical Contacts. Stockholm: Hugo Gebers Forlag, 1946. 8. A. E. H. Love, A Treatise on the Mathematical Theory of Elasticity. New York: Dover Publications, 1944, p. 196. 9. W. B. Kouwenhoven and J. H. Potter, "Thermal Resistance of Metal Contacts' The Welding Journal (Research Supplement), 27:515-S (1948). 10. A. W. Brunot and Fo F. Buckland, "Thermal Contact Resistance of Laminated and Machined Joints," Trans. ASME, 71:253 (1949). 11. W. H. Carrier and S. W. Anderson, "The Resistance to Heat Flow Through Finned Tubing," Heating, Piping, and Air Conditioning, May, 1944, pp. 304-318. 12. Air Conditioning Refrigerating Data Book, Design, American Society of Refrigerating Engineers, 9th Ed., 1955.

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN REFERENCES (Concl.) 13. K. A. Gorden, "The Efficiency of Extended Surface," Trans. ASME, 65: 621-623 (1945), 14. R. H. Norris and W. A. Spofford, "High Performance Fins for Heat Transfer," Trans. ASME, 64:489-496 (1942). 15. A. W. Lemmon, Jr,, A. P. Colburn, and H. B. Nottage, "Heat Transfer from a Baffled-Finned Cylinder to Air," Trans. ASME, 67:601 (1945). 16. S. L. Jameson, "Tube Spacing in Finned Tube Banks," Trans. ASME, 67:633 (1945). 17. W. M. Kays and A. C. London, Compact Heat Exchange Surfaces. Palo Alto, California: The National Press, 1955. 18. D. L. Katz, K. 0, Beatty, Jr., and A. S. Foust, "Heat Transfer Through Tubes with Integral Spiral Fins," Trans. ASME, 67:665 (1945). 19. T. E. Schmidt, "Heat Transmission and Pressure Drop in Banks of Finned Tubes and in Laminated Coolers," Proceedings of the General Discussion on Heat Transfer, Section II, Institute of Mechanical Engineering and ASME, London, 1951, p. 186. 20. D. L. Katz, E. H. Young, et al, "Correlation of Heat Transfer and Pressure Drop for Air Flowing Across Banks of Finned Tubes,"Report 50, Project 1592, Eng. Res, Inst., Univ. of Mich., 1954. 21. E. H. Young, et al., "Investigation of the Performance of Vane-Type Anemometers in a Four-Inch Duct,"Report 37, Project 1592, Eng. Res. Inst., Univo of Mich., 1955. 22. W. J. Youden. Statistical Methods for Chemists. New York: John Wiley and Sons, 1951, pp. 40-49o 23. W. H. McAdams. Op. cit., p. 338, Equation (13-12). j i 43

- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN APPENDIX A DERIVATION OF FIN RESISTANCE METHOD FOR A FOULED TUBE Nomenclature tbs / (I) ci) 94 0);-q~ E-4 / 1/f tmff / tmrf J / _, I tmif ti Position Let the coefficient be constant for both root and fin area and equal let the outside fouling resistance be constant and equal to ro. to ho and Ignoring the outside area difference due to fouling, the heat transfer to the root portion of the tube is

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN qr = ho Ar (tbs - tmrf) (A) It necessarily follows that qr = (A) Ar (trf - tr) (2A) Solving Equation 2A for tmrf gives tmrf = + tmr (3A) Ar Substituting Equation 3A into Equation 1A gives qr = hAr (tbs - r - tmr ) (4A) A^r Rearranging Equation 4A gives r = Ar (tbs - tmr) (5A):1 -7 + ro hJ o Now, again ignoring the area difference due to fouling, the heat transfer to the fin is given by qf = ho Af (tbs - tmff), (6A) and it also follows that qf = Af (tmff - tmf), (7A) ro where tmff and tmf are the integrated average fouled-fin interface and finmetal interface temperatures, respectively. Solving Equation 7A for tmff tmff = rl qf + tmf (8A) Af Substituting Equation 8A into Equation 6A gives qf = h Af (tbs - A tmf)A (9A)

- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN Rearranging Equation 9A gives qf = Af (tbs - tmf) 1 I ho + rT o 0 (10A) Equation 10A for the fin is analogous to Equation 5A for the root. Now, the total heat transfer through the tube must equal the sum of that occurring across the root wall and that occurring across the finned section, or qT = r + qf' (mLA) where qT = total heat transfer rate. Substituting Equations 5A and 10A into Equation 11A gives Ar (1 + ro) (tbs Af - tmr) + A (tbs (t + ro) - tmf). (12A) Now, defining a factor equal to the bulk stream to the fin and the drop fin efficiency, ratio of the temperature drop from the from the bulk stream to the root, i.e., Ef = tbs - tmf tbs - tmr Substituting Equation 13A into Equation 12A gives (13A) = _Ar (tbs 1 + rO) - tmr) Af + - r- (tbs <I + r - tmr) Ef. (14A) Rearranging Equation 14A gives q (tbs - tm) T(% + r ) 0 [Ar + Ef Af]. (15A) Defining an equivalent area as Aeq = Ar + Ef Af, (16A) substituting Equation 16A into Equation 15A gives

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN qT = - Aeq (tb - tmr) (17A) (.k + ro) Now, the remainder of the heat transfer coefficients, involved have the relationship T = Am (tr tmi) = i (tmi - tmif) = Ai hi (tmif - ti), (18A) rm ri where Am = the mean metal heat transfer area, Ai = the inside heat transfer area, - = r = the metal resistance to heat transfer, ri = the inside fouling resistance to heat transfer, hi = the inside film coefficient for heat transfer, tmi = the inside tube-metal temperature, tmif = the inside fouling-film interface temperature, and ti = the bulk stream inside temperature. Upon solving Equation 18A for the interface temperature as in the outer films, the following can be obtained: qrT r= Ai Ai (tr - ti). (19A) q T + ri + Am J Am Solving Equation 17A for tr, qT (ho ~) (20A) tmr = tbs - q- (20A) Substituting Equation 20A into Equation 19A gives qT 1= I Ai tb. - Ae t\ (2LA) Ai Aeq + ri + rm j -4 47

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN Rearranging Equation 21A gives Aeq [tbs - ti] qT (22A) (Aeq) 1 /Aeq\ Aeq 1, i )ri + A rm + h + ro 1 0i A, ho Now, defining qT Ueq ( Aeq (tbs - ti) (23A) solving Equation 23A for qT and substituting into Equation 22A gives 1 Ueq (24A) Aeq 1 Aeq Aeq Aei h + - ri + Ai hi Ai Am 1 t rm +-h ro o Now, defining Uo = Ueq (A, (25A) substituting Equation 25A into Equation 24A and solving for U0 gives Aeq Ao U = (26A) /Aeq\ 1 Ae) + (Aeq) 1, (A — i +\- 4- / ri + — m) rm + -- 4- r~ \A hi ^Ai Aml ( ~h i h~~~~~~~~~ Solving Equation 26A for 1/Uo gives 1 Uo = a 1 Ao AO AmAo - Ai) hi (AiA~ ri l Aeq Ah qeq( r' (27A) Defining an overall resistance containing a fin-metal resistance, rf, 1 Uo 1-10 - + L2 r i + "O r ~r+ rf+ t-ro O Ai hiA mM h (28A) Setting the right-hand sides of Equation 28A equal to Equation 27A and canceling terms gives rf + 1 ho + ro Aeq ht, + Ao r Aeq ~ (29A) Solving Equation 29A for rf and simplifying gives rf = h + r A [- Aeeq I o ~] L Ae I (30A)

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN but A = Ar + Af (31A) and Aeq = Ar + Ef Af. (32A) Substituting Equations 31A and 32A into Equation 30A and rearranging gives rf r= [ + -r. (33A) +.1

-- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN - APPENDIX B ANEMOMETER CORRECTION FACTOR OBTAINED FROM THE AIR-TEST APPARATUS 50

DATA AND CALCULATED RESULTS FOR ANEMOMETER CORRECTION FACTOR I\1 Ambient Steam Anemometer Inlet-Air Outlet-Air Condensate Heat Actual Air Run Press Temp Press Temp Reading Temp Temp Collected me Transferred Velocity Remarks No. (mm Bg) (~C) (psig) (~C) (std ft/min) (~C) (~C) (grams) (mn) (Btu/hr) (std ft/min) actual 391 737.5 21.0 10.0 114.5 -- -- -- 53 15 461 -- - Calibration of equipment for heat losses. 392 737.5 21.0 10.0 114.5 -- -- -- 49 15 424 - 393 737.5 21.0 10.0 114.5 -- -- 51 15 441 394 737.5 21.0 10.0 114.4 -- -- — 49 15 424 395 737.5 21.0 10.0 114.5 -- -- 52 15 450 396 737.5 21.0 10.0 114.3 -- -- -- 55 15 476 - 397 737.5 21.0 10.0 114.4 1980 25.84 45.60 543 15 4690 1263 1.515 398 737.5 21.0 10.0 114.3 1919 25.75 45.65 548 15 4730 1283 1.493 399 731.8 21.5 10.0 114.2 2004 25.65 45.16 556 15 4750 1313 1.528 400 731.8 21.5 10.0 114.2 2004 25.67 45.26 555 15 4800 1320 1.520 401 731.8 21.5 10.0 114.5 1643 25.63 47.53 511 15 4410 1071 1.533 402 731.8 21.5 10.0 114.5 1637 25.64 47.52 513 15 4435 1070 1.528 403 731.8 21.5 10.0 114.1 1284 26.04 51.11 463 15 4000 840 1.540 404 731.8 21.5 10.0 114.0 1285 26.14 51.07 466 15 4020 850 1.510 405 731.8 21.5 10.0 114.1 926 26.06 57.04 400 15 3450 570 1.625 406 731.8 21.5 10.0 114.2 928 26.04 57.35 398 15 3440 571 1.622 m z m m w C3 m m 70 z lI I zm -< -n m Z (A) zy

- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN APPENDIX C DATA FOR THERMOMETER CORRECTION FACTORS 52

- ENGINEERING RESEARCH INSTITUTE UNIVERSITY OF MICHIGAN - TEMPERATURE RISE OF INLET AIR DUE TO BLOWER, RADIATION, AND OTHER EFFECTS Ambient-Air Inlet-Air TinletRun No. Temperature*,~C Temperature~C TambientC max emarks 437 438 439 440 441 442 443 444 445 450 451 452 453 407 408 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 23.42 23507 23.07 23.04 26.35 26.46 26.48 26.08 26.71 26.87 26.92 28.57 Temperature 27.40 27.36 25.67 25.72 25.51 25.68 25.82 25,80 25,94 25.95 27 83 r-7,73 28.06 28.00 27.97 28001 28.18 28.06 Temperature Rise Due 24.08 23.67 24,02 24.01 24.13 26.51 26.49 26.67 26,44 26.90 27.12 27.24 28.93 to Blower 0,66 0.60 0,95 1.03 0.75. 16 0.03 0.19 0.36 0.19 0.25 0.32 0.36 750 1079 1362 1352 1352 1344 1641 1045 700 1788 1451 1345 960 Rise Due to Blower, Radiation, 29.55 2.15 29.62 2.26 27.14 1.47 27.24 1.52 26.91 1.40 26.97 1.29 26.95 1.13 26.94 1.14 26.91 0.97 26.95 1.00 28.88 1.05 28.80 1.07 29.88 1.82 29.92 1.92 29.52 1.55 29.52 1.51 29.45 1.27 29.42 1.36 and Other 748 793 1170 1178 1510 1505 1743 1743 18533 1833 1882 1882 810 810 1213 1213 1215 1213 No steam No steam No steam No steam No steam No steam No steam No steam No steam No steam No steam No steam No steam Effects Steam in tube Steam in tube Steam in tube Steam in tube Steam in tube Steam in tube Steam in tube Steam in tube Steam in tube Steam Steam Steam in tube in tube in tube Steam in tube Steam in tube Steam in tube Steam in tube Steam in tube Steam in tube L 427 428 429 430 431 432 433 434 435 436 28.19 28.32 28.23 28.15 27.55 27.63 27.91 27 87 28.17 28.18 29.92 29.95 28.92 28.91 28.65 28.54 29.30 29.28 30,11 30017 1.73 1.63 0.69.76 1.10 0.91 1.39 1.41 1.94 1.99 807 807 1855 1855 1886 1886 1220 1225 813 813 Steam in tube Steam in tube Steam Steam Steam Steam Steam Steam Steam Steam in tube in tube in tube in tube in tube in tube in tube in tube *The ambient-air temperature was measured inlet of the blower. with a thermometer located at the 53

- ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN - APPENDIX D DATA ON EFFECT OF SCREENS J 54

DATA ON EFFECT OF SCREENS Steam Air-Inlet Air-Outlet Orifice Run Tube Tube Steam Pressure Temperature Temperature Temperature Q ATLM Vx U Size Remarks No. Designation Characteristics (Corrected, psia) (F) (Corrected "F) (Corrected'F) (Btu/hr) (in.) First Tests 407 17 408 17 411 17 412 17 413 17 414 17 415 17 416 17 417 17 418 17 419 17 420 17 421 17 422 17 423 17 424 17 425 17 426 17 427 17 428 17 429 17 430 17 431 17 432 17 433 17 434 17 435 17 436 17 Ao = 3.63 ft2 Aflow = 0.063 ft2 All-aluminum tube 24.58 24.58 24.50 24.50 24.50 24.50 24.50 24.50 24.50 24.50 24.50 24.50 24.50 24.50 24.50 24.50 24.50 24.50 24.50 24.50 24.50 24.50 24.50 24.50 24.50 24.50 24.50 24.50 239.25 239.25 239.05 239.05 239.05 239.05 239.05 239.05 239.05 239.05 239.05 239.05 239.05 239.05 239.05 239.05 239.05 239.05 239.05 239.05 239.05 239.05 239.05 239.05 239.05 239.05 239.05 239.05 83.40 83.50 79.05 79.22 78.65 78.75 78.70 78.68 78.65 78.70 82.18 82.05 84.00 84.05 83.35 83.35 835.20 83.15 84.05 84.10 82.25 82.25 81.75 81.56 82.95 82.90 84.40 84.50 137.10 137.38 124.65 124.90 119.47 119.55 117.00 116.98 116.22 116.25 119.12 119.10 141.10 141.30 129.58 129.53 131.70 131.85 141.92 142.45 121.00 121.07 118.95 118.97 129.38 129.65 141.80 142.30 2690 2870 3570 3570 4150 4130 4475 4475 4610 4610 4660 4660 3100 3105 3760 3760 3950 3960 3130 3150 4820 4830 4710 4730 3790 3840 3130 3170 127.30 748 5.60 127.30 793 6.21 135.70 1170 7.24 136.60 1178 7.20 138.60 1510 8.24 138.60 1505 8.19 139.80 1743 8.83 139.60 1743 8.83 140.60 1833 9.02 139.60 1833 9.02 137.30 1882 9.34 137.20 1882 9.34 124.10 810 6.88 123.80 810 6.91 131.50 1215 7.87 131.50 1213 7.89 130.30 1215 8.35 130.10 1213 8.37 123.70 807 6.98 123.40 807 7.02 137.50 1855 9.65 137.50 1855 9.68 136.90 1886 9.46 140.50 1886 9.28 131.20 1220 7.96 131.20 1225 8.07 123.50 813 7.18 123.00 813 7.12 2 2 2-1/2 2-1/2 3 3 3-1/2 3-1/2 4 4 4 4 2 2 2-1/2 2-1/2 2-1/2 2-1/2 2 2 4 4 4 4 2-1/2 2-1/2 2 2 two screens two screens two screens two screens two screens two screens two screens two screens two screens two screens one screen one screen one screen one screen one screen one screen no screen no screen no screen no screen no screen no screen one screen one screen one screen one screen one screen one screen m z z m m 70 z mA m m 7n -4 C: r m \J1 VJl n n z rm 07 -n I T1 z Second Tests 521 16 522 16 523 16 524 16 525 16 526 16 527 16 528 16 Ao = 3.52 ft2 Aflow = 0.0642 ft2 All-aluminum tube 24.31 24.31 24.31 24.31 24.31 24.31 24.31 24.31 238.55 238.55 238.55 238.55 238.55 238.55 238.55 238.55 77.00 81.85 83.00 83.75 84.20 84.85 83.27 82.40 113.90 118.10 122.95 129.25 140.25 145.00 131.07 124.67 4570 4420 3990 3620 2950 3210 3805 4480 142.00 1820 9.15 138.00 1783 9.10 134.50 1460 8.42 131.20 1165 7.85 124.20 780 6.70 121.50 782 7.50 129.80 1168 8.34 133.70 1551 9.52 4 4 3 2-1/2 2 2 2-1/2 3 two screens one screen one screen one screen one screen no screen no screen no screen -- _

- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN - APPENDIX E SUMMARY OF ALL-ALUMINUM TUBE DATA 56

- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN SUMMARY OF ALL-ALUMINUM-TUBE DATA Run Tube Tube Steam Pressure Steam Air-Inlet Air-Outlet Orifice No. Designation Characteristics (Corrected, psia) Temperature Temperature Temperature (B~u/hr) TM Vm UO Size ('F) (Corrected ~F) (Corrected ~F) ( (in.) 486 21 487 21 488 21 489 21 490 22 491 22 492 22 493 22 446 16 447 16 448 16 449 16 454 16 455 16 456 16 457 16 458 16 459 16 460 16 461 16 462 16 463 16 464 16 465 16 478 16 479 16 480 16 481 16 482 16 483 16 484 16 485 16 521 16 466 32 467 32 468 32 469 32 470 32 471 33 472 33 473 33 474 33 407 17 408 17 411 17 412 17 413 17 414 17 415 17 416 17 417 17 418 17 Ao = 3.28 ft2 Aflow = 0.0669 ft2 Ao = 3.57 ft2 Aflow = 0.0638 ft2 Ao = 3.52 ft2 Aflow = 0.0642 ft2 Ao = 3.365 ft2 Aflow = 0.0616 ft2 Ao = 3.43 ft2 Aflow = 0.0604 ft2 Ao = 3.63 ft2 Aflow = 0.063 ft2 24.17 24.17 24.17 24.17 24.32 24.32 24.32 24.32 24.43 24.43 24.43 24.43 24.35 24.35 24.35 24.35 24.12 24.12 24.12 24.12 23.94 23.94 23.94 23.94 24.11 24.11 24.11 24.11 24.25 24.25 24.25 24.25 24.31 23.94 23.94 23.94 23.94 23.94 23.94 23.94 23.94 23.94 24.58 24.58 24.50 24.50 24.50 24.50 24.50 24.50 24.50 24.50 238.35 238.35 238.35 238.35 238.60 238.60 238.60 238.60 238.88 238.88 238.88 238.88 238.68 238.68 238.68 238.68 238.10 238.10 238.10 238.10 237.65 237.65 237.65 237.65 238.10 238.10 238.10 238.10 238.42 238.42 238.42 238.42 238.55 237.65 237.65 237.65 237.65 237.65 237.65 237.65 237.65 237.65 239.25 239.25 239.05 239.05 239.05 239.05 239.05 239.05 239.05 239.05 87.45 86.75 86.37 85.50 84.55 84.90 85.07 85.55 81.55 81.78 80.36 80.37 84.05 83.70 82.03 82.09 81.80 81.23 79.56 81.95 80.30 79.50 79.07 79.35 83.15 84.20 82.80 82.50 85.47 85.20 85.75 86.75 77.00 80.15 80.43 81.20 82.65 82.48 82.05 82.38 83.17 84.51 83.40 83.50 79.05 79.22 78.65 78.75 78.70 78.68 78.65 78.70 143.55 3040 121.00 762 6.65 131.98 3420 127.80 1130 7.27 126.10 4010 132.00 1415 8.05 121.15 4380 134.50 1730 8.60 120.00 124.35 129.57 140.00 136.19 136.36 117.67 117.40 138.37 138.66 118.60 118.60 118.42 121.88 125.90 137.40 136.40 126.45 120.75 117.05 128.85 139.73 123.68 119.65 121.80 125.70 131.35 141.52 113.90 4275 135.00 1775 8.88 3930 133.30 1468 8.25 3490 130.80 1157 7.47 2870 124.00 775 6.48 2945 128.20 781 6.26 2900 127.50 779 6.12 4530 139.80 1785 8.85 4510 139.70 1785 8.81 2950 125.20 792 6.43 2962 125.30 792 6.45 4430 138.00 1780 8.75 4410 138.30 1772 8.71 4430 136.00 1775 8.89 4100 136.10 1480 8.22 3675 134.90 1165 7.46 2980 126.70 787 6.43 2980 127.20 792 6.42 3580 133.50 1132 7.38 4100 135.50 1465 8.31 4510 137.50 1172 9.01 3590 131.10 1176 7.64 2950 124.0o 796 6.64 4030 133.30 1479 8.43 4430 135.50 1790 9.13 4260 133.80 1710 8.90 4020 130.20 1480 8.60 3540 129.50 1160 7.64 2895 121.70 792 6.84 4570 142.00 1820 9.15 2 2-1/2 3 4 4 3 2-1/2 2 2 2 4 4 2 2 4 4 4 3 2-1/2 2 2 2-1/2 3 4 2-1/2 2 3 4 4 3 2-1/2 2 4 4 3 2-1/2 2 4 4 3 2-1/2 2 2 2 2-1/2 2-1/2 3 3 3-1/2 3-1/2 4 4 114.55 4150 139.90 1835 8.83 118.60 3795 137.50 1513 8.20 124.45 3365 134.30 1185 7.44 135.56 2825 127.00 814 6.60 116.62 4100 137.50 1825 8.85 118.16 4200 137.50 1810 8.90 121.99 3860 134.20 1512 8.38 127.63 3445 130.70 1210 7.70 138.65 2840 124.30 818 6.65 i 137.10 137.38 124.65 124.90 119.47 119.55 117.00 116.98 116.22 116.25 2690 2870 3570 3570 4150 4130 4475 4475 4610 4610 127.30 748 5.60 127.30 793 6.21 135.70 1170 7.24 136.60 1178 7.20 138.60 1510 8.24 138.60 1505 8.19 139.80 1743 8.83 139.60 1743 8.83 140.60 1833 9.02 139.60 1833 9.02 57

- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN APPENDIX F SUMMARY OF BIMETAL-TUBE DATA 58

~1 BIMETALLIC TUBE DATA Steam Air-Inlet Air-Outlet Orifice Run Tube Tube DSeteam iPtressure Temperature Temperature Temperature Q ATL V UO Size No. Designation Characteristics (Corrected, psia) (F) (Corrected F) (Corrected F) /(in.) ("F (Corrected ~F) (Corrected ~F) (Btu/kr (in.) 494 3 495 3 496 3 497 3 498 3 499 3 500 4 501 4 502 4 503 4 504 4 Ao = 3.48 Aflow = 0.0614 Ao = 3.51 ft" Aflow = 0.0657 ft2 24.35 24.35 24.35 24.35 24.35 24.35 24.05 24.05 24.05 24.05 24.05 238.70 238.70 238.70 238.70 238.70 238.70 237.92 237.92 237.92 237.92 237.92 82.80 80.50 80.45 80.25 80.70 81.05 84.40 82.86 83.33 84.07 84.95 118.30 108.95 116.25 107.70 104.35 101.95 116.08 116.27 120.74 126.94 137.57 1885 2220 1880 2170 2360 2525 4110 4360 3915 3440 2860 139.00 143.00 140.00 143.70 147.00 149.00 136.30 136.80 155.80 128.90 125.90 811 1205 825 1210 1529 1860 1860 1861 1495 1148 775 3.89 4.47 3.86 4.35 4.61 4.86 8.59 9.09 8.22 7.61 6.48 2 2-1/2 2 2-1/2 3 4 4 4 3 2-1/2 2 m z m m z m m 70 50 m m I nZ - c I m \10 505 356 A = 3.665 ft2 23.89 237.55 506 36 Aflow = 0.0659 ft2 23.89 237.53 507 36 25.89 237.53 508 36 23.89 237.53 510 54 Ao = 3.69 ft2 24.15 238.20 511 54 Aflow = 0.064 ft2 24.15 238.20 512 54 24.15 28.20 513 54 24.15 238.20 514 54 24.10 238.05 515 54 24.10 238.05 517 38 Ao = 3.64 ft2 24.00 237.80 518 38 Aflow = 0.0642 ft2 24.00 237.80 519 38 24.00 237.80 520 38 24.00 237.80 86.07 137.50 2755 123.90 763 6.06 2 85.55 127.25 3320 131.00 1137 6.90 2-1/2 86.65 122.10 3710 134.00 1450 7.55 3 85.80 118.10 4010 135.20 1770 8.09 4 z 81.45 117.33 3610 138.50 1480 7.27 3 82.25 122.00 3180 135.80 1172 6.34 2-1/2 m 83.00 134.43 2750 126.90 786 5.88 2 o 81.00 114.10 4190 141.00 1800 8.05 4 4 83.75 116.60 4040 133.50 1800 8.20 4 _ 84.15 120.65 3670 135.00 1475 7.36 3 84.27 125.40 2180 132.30 775 4.55 2 83.30 116.30 2565 137.50 1140 5.13 2-1/2 83.15 111.70 2860 140.50 1465 5.60 3 83.03 108.25 3065 144.30 1772 5.83 4 a a 0 0 i I I i I I i I z Z

- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN - APP EIXX G CALCULATION OF RUN NO. 481, USING SHORT-FORM, MODIFIED SHORT-FORM, LONG-FORM, AND MODIFIED LONG-FORM CALCULATION PROCEDURES 6o

-ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN - SHORT FORM CONTROL UNIT DATA SHEET Run No. 481 Date: 2/11/56 Tube Designation: All aluminum No. 16 Tube Characteristics: Liner Material: BWG Fin O.D. Root O.D. Fins/inch None 2.021 1.143 9.017 Ao/Ai: 13.8 (assumed) Air Vel. 9400 ft / 4 min 21.8 se: ir Out 48.7 ~C = 119.73~F Air In 28.98~C = 84.20~0 AT 19.7 C = 35.53~F team 10 + 4.11 = 24.11 psi, T = 238.1~F Avg. Slot Width: 2.021 Calculations: Anemometer Reading: 2158 ft/min -81 Correction: Corr. Anemometer Rdg: 2077 Heat Load = 2077 0.0872 ( 530 579.73 Orifice Size: 4 in. Combined Steam, Metal and Fouling Resistance: 0.00085 (assumed) = 165.5 0.06 35.53 = = 6230 Btu/hr r = 153.90 1.298 118.37 Lnr = 0.2602 ATL 35.23 = 136.2~F -30 SFM 1 - 1. h 174.58 =.00488 LMTD: 238.1 238.1 U(Liner O.D.) = h(Air-Liner O.D.) 84.20 = 153.90~F - 119.73 = 118.37~F 6230 = 174.5 0.262 0 136.2 = 205 at 9E

- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN - MODIFIED SHORT FORM CONTROL UNIT DATA SHEET I I I L Run No. 481 Date: 2/11/56 Tube Designation: All aluminum No. 16 Tube Characteristics: Liner Material: BWG Fin O.D. Root O.D. Fins/inch None 2.021 1.143 9.017 Ao/Ai: 13.8 (assumed) Air Vel. 9400 ft / 4 min 2L.8 se Air Out 48.73 - O.04 = 48.69 C = 119.6 )F Air In 28.98 + 0.07 - 1.)0 = 28.05 = 82.50~F AT _ 20.64 C = 37.1'~F ____ _ Steam 10 + 14.11 = 24 11 ps a T = 238.10)~F_ Avg. Slot Width: 2.021 Orifice Size: 4 in. Calculations: Anemometer Reading: 2158 ft/min Correction -81 Corr. Anemometer Rdg: 2077 Heat Load = 2077 _ 0.0872 ( 530 1.52 579.65 I I I I i Combined Steam, Metal and Fouling Resistance: 0.00085 (assume) = 109.0 o 1.06 37.15 = 4290 Btu/hr r 155.60 1315 118.45 Ln 1.315 = 0.274 ATLM = 37.15 = 135.5F 0.274 6 SFM LMTD: 238.1 _ 82.50 = 155.60 238.1 _ 119.65 = 118.45 U(Liner O.D.) = 4290 = 120.5 0.2620 135.5 h(Air-Liner O.D. ) = 134 at 64 - 1 1 o0.000 ooo85 ho 120.5 = 0.00745 62

-- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN LONG FORM AIR TEST CALCULATION SHEET II Date of run:_ Tube Designation: 2/11/56 Run No. 481 All aluminum No. 16 Test section: A 3.58 ft2 o A:0.0626 ft2 flow Tube Characteristics: Orifice size 4 in. "dia Anemometer reading 9,400 ft Anemometer time4 min21.8sec Barometer: 732.2 Temperature: 20.2 Liner Material N Rootwall Thickness Fin O.D.__ Root O.D. _ Fins/inch _ mm H ~C 0.06 2.021 in. in. in. L.143 9.017 T. reading. in Corr: T: in 28.98 +0.07 ~C ~C ~C out reading: Corr: T: out - T out - -0.04 oC oC oC ~F 29.05 48.69 84.30 119.65 p steam= 10 psig + [( 729.7 steam ) mm Hg x 0.019355 = T = steam 24.11 238.1 psia ~F (steam tables) AT = 238.1 - 84.30 = 153.80 ~F 1 AT = 238.1 - 119.65 = 118.45 ~F 2 AT1 AT2 T Ln = T2 1.298 0.2605 AT = 135.4 OF LM At = 35.35 ~F p Po 729.7 mm 6975= 0.878 OR 0.6975 = * n 579.65 I I I Anemometer reading: 9400 ft x 60 sec/min = 2020 ft/min ( 261.8 )sec PO Taylor correction: -b9 ft/min 1951 1285 1 nwi n' = x - Std~r. f t of air f I.... 1 U Vi C -.. 1L -L1.52v - 1.52 W = 1285 x 0.587 = 497 lbs/hr Q = 498 x 35.35 x 0.24 = 4210 Btu/hr Uo(liner O.D.) = Uo(outside area) 4210 1 = 118.5 0.262 x (135.4 1 = 0.00845 (on liner area) Uo.00085 118.5 0.262 (5.58) 8.68 = 1285 x 0.0872 x.0626) max (0.0626) 1 ho.00760 1790 672 Vface = ft/min and ho(liner O.D.) assuming all resistances except air film = 0.00085 (based on liner area). 63

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN - MODIFIED LONG FORM AIR TEST CALCULATION SHEET Date of run: 2/11/56 Tube Designation: All aluminum No. 16 Test section: A: 3.58 ft2 A. 0.0626 ft2 flow - Tube Characteristics: Orifice size 4 in. "dia Anemometer reading400 ft Anemometer time 4 min2L8sec Run No. Barometer: 732.2 Temperature: 20.2 Liner Material N Rootwall Thickness Fin O.D. 2.021 Root O.D. 1.143 Fins/inch 9.017 481 mm Hg - o o.o6 in. in. in. T. reading: in Corr: T.: inT.: in - 28.98 -0.95 ~C oC 0C ~F out reading: Corr: Tout: t: out 48.73 -0.04 oC oC oC oF 48.69 82.50 119.65 steam 10 psig + [( 729.7 steam AT = 258.1 - 82.50 = 1 --------------- ) mm Hg x 0.019355 = 24.11 T = 238.1 steam psia ~F (steam tables) 155.6 ~F AT1 AT2 1.315 AT = 238.1 119.65 2 118.45 ~F 37.15 ~F ATLM - 135.5 ~F p -/ 729.7 At = Ln T2 / __ 7 P 0.274 mm ) 0.6975 = 0.878 0.937 579.65 Anemometer reading: 9400 ft x 60 sec/min 2020___ ft/min (261.8 )sec Taylor correction: -69 ft/min Std. ft of air flowing = 1951 x 1.52 1285 W = 1285 x 0.587 = 497 lbs/hr Q = 497 x 37.15 x 0.24 = 4430 Btu/hr Uo(iner 0D) ( 4430 Uo(liner O.D.) = n - / ) = 124.8 f1 7 E; I u.-UD X / kJ. ) Uo(outside area) = 124.8 0.262 0.58) _~~~~~i 9.13 1 U0 _ ho 0.00802 0.00085 (on liner area) V max 1285 0.0872 (0.0626) 0.00717 1790 672'-6ce ft/min and ho(liner O.D.) __c e -=o l ne.. 139.5 assuming all resistances except air film = 0.00085 (based on liner area). 64

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN - APPENDIX H CALCULATION OF BOND RESISTANCE VALUES FROM THE DATA FOR THE FIVE BIMETAL TUBES PRESENTED IN FIG. 13 Equation 43 can be arranged in the form L rb FM" A AL AO L - Mall al. bimetal + m (+m) a (1-H) aluminum where rb = bond resistance of the tube, AL = heat transfer area of liner/ft length, Ao = outside heat transfer area/ft length, M" = intercept value of line representing the bimetal (from Fig. 13), Mall al. = intercept value of all-aluminum tubes, J m ()bimetal rm (A)aluminum = metal resistance of bimetal tube, equals root wall plus liner resistance, and = metal resistance of aluminun tube, equals root-wall resistance Assuming equivalent thickness in the average aluminum-tube root-wall thickness and the bimetal-tube root-wall thickness, Equation I-H reduces to A _r rb = M "t - Ao Mall al. - A (2-H) - 65

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN All of the five tubes have copper liners, therefore the liner resistance is computed for a 16 gage tube as XL A (0.065)(35.59) K Am (220)(12)(0.25) =.000353. The area ratio AL 0.262 1 Ao 3 59 13.7 Substituting into Equation 2-Ho 1 rb EM" - Mall al. - 0.000353] (3-H) 13 7 Tube No. 3: The intercept value M" = 0.1045 (from Fig. 13). The value of Mall aluminum = 0.00481. Substituting the intercept values into Equation 3-H rb = [0.1045 - 0o00481 0.000353] 1357 — 09_34 = 0.00725 13.7 Tube No. 38: The intercept value M" = 0.0718 (from Fig. 13)o As before, Mall alo = 0.00481 Substituting in Equation 3-H: rb = [0.0718 - 0.00481 - 0,000353] 1357,06664.7 =.oo0004850 Tube No. 54: The intercept value M" = 0.0220 (from Fig. 13). 66

- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN - Mall al. = o.oo481. Substituting in Equation 3-H: rb = 1 [0.0220.48 - 048 0.000353] 13.7.01684 13.7 0.00123. Tube No. 36: The intercept values M? = 0.0152 Mall al. o.oo00481. Substituting in Equation 3-H: rb = _ 1 [0.0152 13.7 - 0.00481 - 0.0003535 o,oloo4 01004 1-.7 0.000733 Tube No. 4: The intercept value for tube No. 4 is very close to that for the all-aluminum tubes and therefore the bond-resistance value is too small to be measured using the air-test apparatus. 67