UNIDIRECTIONAL ANALYSIS OF THE CONTINUOUS CASTING PROCESS Robert D, Pehlke Department of Chemical and Metallurgical Engineering The University of Michigan Ann Arbor, Michigan

THE UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLLEGE OF ENGINEERING UNIDIRECTIONAL ANALYSIS OF THE CONTINUOUS CASTING PROCESS Robert D. Pehlke August 1963 IP-628

TABLE OF CONTENTS Page LIST OF TABLES................................................. v LIST OF FIGURES............................................ vii INTRODUCTION................................................. i THE CONTINUOUS CASTING PROCESS................................ 1 HEAT TRANSFER ANALYSIS..................................... 3 A. Copper Mold, o....................................... 3 Bo The Water Spray oOO............o.......o............o.o 6 COMPUTER PROGRAM.........o......o.........................'7 DISCUSSION OF RESULTS o o................e....... o..........oo.. 7 CONCLUSIONS o.... o..........o........................... o.. BIBLIOGRAPHY......... o..................0................. 16 iii

LIST OF TABLES Table Page I Input Data for Computer Calculation.................... 11 II Calculated Results............................ 12 v

LIST OF FIGURES Figure Page 1 Schematic Diagram of Continuous Casting Process.,... 2 2 Flow Diagram for Computer Program.................... 8 3 Computer Program.................................... 4 Predicted Profile of Solidification Front in Mold and Spray Sections of a Continuous Casting Strand.................................... 13 vii

INTRODUCTI ON The continuous casting process has been known for some time, and practiced extensively in the non-ferrous metals industries. Its application in steelmaking has been proposed for a decade or more, but (1,2) has only recently been put into commercial practice. Considerable work remains to be done regarding modifications to the process and development of techniques for accomodating other shapes, sizes, and compositions of steel. With the specific purpose of simulating the process, a simplified approach to heat transfer during the continuous casting of a steel slab is proposed. The following analysis is based on unidirectional heat transfer, i.e., a one-directional analysis of heat flow during continuous casting. THE CONTINUOUS CASTING PROCESS A generalized sketch of the continuous casting process is presented in Figure 1o The process consists of two distinct heat transfer stages; 1o A water-cooled copper mold which oscillates to maintain its separation from the continuously downwardly moving slab. 2, A high-velocity water spray which is located immediately below the mold to promote rapid heat transfer from the surface of the hot slabo Two critical aspects of the process exist which are related to these heat transfer unitso First, the extent of solidification, io e,, the thickness of frozen skin, for the slab as it emerges from the water-1

-2BOTTOM POURING LADLE W: TUNDISH POURING BASIN WATER-COOLED COPPER MOLD,<^t| e ~ WATER SPRAY WITHDRAWING ROLLS a- OXYGEN CUT-OFF STATION VERTICAL TILTING f GEAR INCLINED CONVEYOR Figure 1. Schematic Diagram of Continuous Casting Process.

cooled copper mold must be great enough to support the head of liquid metal exte;.nding from the bottom of the mold up to the liquid metal surface. Secondly, the thickness of the solidified layer of metal leaving the water spray zone should be such that the solidification process is nearly complete,^ i.oeo the 1q1uid metal well which exists down through the ctnter of the sflab shouAld not ette nd far below the water spray, such thatu the slab is completely soil.dified, wher. i.t reaches the cutoff or bending station of the casting strando HEAT ITRANSFER ANALYSIS Ao Copper Mold Heat transfer in t.he copper mold canr be analyzed on. the basis of assumed heat transfer coefficients at each of the physical interfaces, and or. thermaL conduction, both through tthe slab as its solidified thickness builds cup, and through the wall of the copper moldo This path for heat transfer has beeni- chosen, neglecting aenocy heat transfer betwreen liquid and solid steel -ithin the slabo The ra te of energy trrasfer from the liqu.Ld-sollid Iterfac to the water stream at any point a'long the mold, assuming steady state con di i. ons is given'by Equation Lo (KS/) s (TF / l i + (KKS/X) tl/HMS + XWMKM + 1/HWM) where.q the rate of heat transfer in Btu/hr KS thermal conductivity of solid steel in Btu/ft-hr-~F X = thickness of the frozen layer in. ft TF = liquidus temperature of the steel in ~F 1TW average temperature of the water flowing in the mold

-4HMS = heat transfer coefficient between the mold and the slab in Btu/hr-~F XM = mold thickness in feet KM = thermal conductivity of the mold material HWM = heat transfer coefficient between the cooling water and the mold in Btu/hr-~F Assuming steady-state heat transfer, the temperatures at each interface can be computed from thermal resistances and are given by the expressions: TWM = q/HWM + TW (2) TMS = q * (XM/KM) + TWM (3) TSM = q/HMS + TMS (4) where TWM = temperature of the mold on the water side in ~F TMS = temperature of the mold on the slab side in ~F TSM = temperature of the slab on the mold side in ~F The slab moves downwardly through the mold. By considering each discrete point along the vertical dimension of the mold as being a point where unidirectional steady-state heat transfer takes place, the heat extracted can be equated to the solidification of a given amount of steel. As solidification progresses, the heat extracted is equal to that to: a. Remove the liquid super-heat, i.e., cool the steel from the pouring temperature to the liquidus temperature. b. Remove the heat of fusion, assuming that this heat is extracted at a specific temperature. c. Remove the heat from the already frozen steel in order to provide a linear temperature gradient through the slab.

-5In the present analysis a specific thickness of metal to be frozen per iteration was chosen, and the heat which must be removed to accomplish this can be computed from Equation (); QREQD = (TS-TF) * (CPL) * (DX) * (RHO) + (HF) * (DX ) (RHO) + ((TF + TSM)/2) * (X) ( (CPS) * (RHO) + (TF)*(DX)*(CPS)*(RHO) ((TF + TSM)/2) * (X + DX) * (CPS) * (RHO) (5) where QREQD = heat in Btu required to freeze a steel increment of thickness DX in fto CPS = specific heat of the solid steel in Btu/lb-~F RHO density of solid steel in lb/ft3 TS =temperature of the liquid steel in the well in ~F HF = heat of fusion of the steel in Btu/lb The time required to remove the quantity of heat computed in Equation (5) is determined by the rate of heat transfer q under the physical conditions assumed to exist at any point along the vertical surface of the moldo The time required to remove this quantitvy of heat is given by the relationship; t = QREQD/q (6) where t = time in hours to freeze a increment of thickness DXo The vertical movement of the slab can then be computed from the expression~ DIST = (t) (VTEL)/(60) (7)

where DIST = vertical distance in feet which the slab moves downward during the freezing on the layer of thickness DX VEL = average downward velocity of the slab in ft/min. In actual operating practice, the mold is usually given a vertical oscillating movement in order to prevent sticking of the slab to the mold wallso This movement has been ignored in the present analysis, assuming that its effect is of secondary importance Also, an average heat transfer coefficient between mold and slab has been assumedo Bo The Water Spray Heat transfer in the spray section of the strand can be computed in a manner parallel to that employeI for calculating heat transfer in the copper mold. A heat transfer coeIfficient between the water spray and the slab is assumed. This surface resis%;-ance tno heat transfer is added to that related to thermal conductivity in the solid portion of the slab, thus permitting a calculation of the rate of heat transfer q by the relationship q~ = [(KS/X) * (TFT'I (8) (8) [1 + (KS/X) - (l/HSPS where HSPS = heat transfer coefficient between the water spray and the slab surface in Btu/hr-~F and, in a manner parallel to Equations (2), (3), and (4), the surface temperature of the slab can be estimated to be: TSSP = (q/HSPS) + TW (9)

l7The heat which must be removed in order to effect the freezing of a layer of thickness DX during passage through the water spray can be calculated by considering the same heat terms as in the case of the copper moldo The heat which must be removed by the spray is: QREQD = ('TS-TF) * {CPL) * (DX") RHO + () (X) F (DX) RHO) + ((TFF4rtSSP)/2 (X') (CPS) (RHO)+ (TF) (DX)*(CPS)*(RHO)' (TF+TSSP) /2) -(XDx () fC(RHO) (o0) Equations (6) and (7) can then be employed to compute the vertical movement of the slab during the time period required to freeze an increment of thickness DX COMPUJTER PROGRAM Employing an iterative procedure in which the transfer at each successive point along the mold surface is computed based on the heat flow at the previously computed point,'the thickness of shell as a function of position. in the mold and spray system was estimated~ The flow diagram for this iterative procedure is presented in Figure 2, and the computer program itself presented in Figure 3A summary of the input data used in the calculation is presented in Table I. The computer output is presented in Table IIo DISCUSSION OF RESULTS The resu!lts of the computer calculation employing the data presented in Table I are shown graphically in Figure 4o The estimated thickness at the exit of the copper mold is approximately 155 inches and

-8TH - 0.0 DXr ODX/12 PRINT XOO D LPHA INPUT DATA T-TLE, I. a XO, DX TSM =77. LM.OR. TH ( DATA -XM =XM/12 LMO.T>X CALC k~J —-' —I' TWM. La L+DIST CALC CCALC tDS,_! — TMS,TSM, - DIST TH-(X+DX'WI:2.,. --.s.sOREQD -: f PV( SMF- T | PRINT 1=0 - ALPHA PRINT TSSP TSM IZ0 < RESULTS RESULTS CALC. - F' DELT,TH, - LLM ^\ / BETA \ -I CALC. C777 CALC LL+DIST Y~X, DX = I:+ 1 CQTSSP. CALC - YsX, DX, TSSP, T IT TH a(Y+DX) 1K12'~(LM+LSP).OR/ QREOD ST.TH (XS/2)/ ( L>(LM+LS F iN PRINT 1=0 L ETA PRINT RESULTS RESULTS TH CALC DELTTH iL=LM+LSP Figure 2. Flow Diagram for Computer Program.

-9$COMPILE MAD,EXECUTEDUMP,PRINT OBJECT,PUNCH OBJECT MAD ( 6 JUN 1963 VERSION) PROGRAM LISTING...... GAMMA READ FORMAT TRANSHWM, KM, HMS, HSPS, KS- *001 VECTOR VALUES TRANS = $5F10.0*$ _ 002 READ FORMAT GEOM, LM, XM, XS, LSP, VEL, RHO *003 VECTOR VALUES GEOM = $6F10.4*$ *004 READ FORMAT TEM, TW, TF, TS *005 VECTOR VALUES TEM = $3F10.0*$ *006 READ FORMAT THERMO, HF, CPL, CPS *007 VECTOR VALUES THERMO =$ F10.0,2F10.4*$ _ 008 READ FORMAT CALC, DX,N *009 VECTOR VALUES CALC= $ F10.5, I5*$ *010 PRINT FORMAT TITLE *011 VECTOR VALUES TITLE = $1H1,40HSIMULATION OF CONTINUOUS CASTI *012 1NG PROCESS///*$ *012 PRINT FORMAT DATA HM K,, HSPM, KM, HM S, HSPS, KS, LM, XM, XS, LSP, __ 013 1VEL *013 VECTOR VALUES DATA = $1H,59HWATER-MOLD HEAT TRANSFER COEFFIC *014 lIENT, BTU/HR-SQ FT- DEG F = F10.0/S1, 47HTHERMAL CONDUCTIVITY *014 2 OF MOLD, BTU/HR-FT DEG F = F1O.O/S1,58HMOLD-SLAB HEAT TRANSF *014 3ER COEFFICIENT, hTU/HR-SQ FT- DEG F = F10.4/ SI, 59HSPRAY-SLA *014 4E HEAT TRANSFER COEFFICIENT, BTU/HR-SQ FT- DEG F = F10.0/S1, *014 548HTHERMAL CONDUCTIVITY OF STEEL, BTU/HR-FT-DEG F = FO1.0/S1, *014 617HMOLD LENGTH, FT =F6.2/S1, 20HMOLD THICKNESS, IN F6.2/S1, *014 720HSLAB THICKNESS, IN = F6.2/S1,18HSPRAY LENGTH, FT = F6.2/S1 *014 8,23HSLAB VELOCITY, FT/MIN = F6.2*$ *014 PRINT FORMAT DATAl,RHO,TW,TF, TS, HF, CPL, CPS, DX,N *015 VECTOR VALUESDATA1 = $1H, 28HDENSITY OF STEEL, LB/CU FT = F _ _ 016 16.0/S1, 27HWATER TEMPERATURE, DEG F = F4.0/S1, 38HLIQUIDUS TE *016 2MPERATURE OF STEEL, DEG F = F6.0/S1, 37HTAPPING TEMPERATURE 0 *016 4F STEEL, DEG F = F6.0/S1, 33HHEAT OF FUSION OF STEEL, BTU/LB *016 5=F6.0/S1, 44HSPECIF IC HEAT OF LIQUID STEEL, _TU/LB-DEG F= F6 *016 6.4/S1, 44HSPECIFIC HEAT OF SOLID STEEL, BTU/LB-DEG F = F6.4/S *016 61, 37HINCREMENT OF FREEZING THICKNESS, IN = F6.4/S1,25HITERAT __ __ 016 7IONS FOR PRINTOUT = I3*$ *016 PRINT FORMAT HEAL *017 VECTOR VALUES HEAD $////,S44,20H CALCULATED RESULTS ///, *018 2S 10,16H TEMPERATURE_ F //S3,9H T MOLD-W,S3,9H T MOLD-SS3, __ _ __ _ _ 018 39H T SLAb-M,S5,7H Q, BTUS2,12H Q REQD, BTU,S1,1OH TIME, SEC, *018 4S2,13H DISTANCEt__FTSLllH LENGTHFT,S14H THICKNESS, IN// *018 5*- *018 INTEGER I, N *019 TH= 0. *020 DX = DX/12. *021 L= 0.0 *022 I = C *023 TSM = 77. *024 XM = XM/12. *025 THROUGH ALPHA, FOR X= 0,DX,L.E. LM.OR. TH.GE. (XS/2.) *026 I = I+ 1 *027 Q= KS/(X+DX)* (TF-TW)/ (1. +KS/(X+DX)*(1./HMS+XM/KM+1./HWM)) *028 TWM = Q/HWM + TW _ _ 029 TMS = Q*XM/KM+ TWM *030 TSM = Q/HMS+IMS *031 CREQL = ((TF+ TSM )/2.)*(X) *CPS*RHO +TF* DX*CPS*RHO - (T *032 Figure 3. Computer Program.

-101F+TSM)/2.)* (X+DX) *CPS*RHO +(TS-TF)* CPL*DX*RHO+ HF*RHO*DX *032 T = (QREQD/Q)*3600. *033 DIST = (r*VEL)/60. *034 L = L + DIST *035 TH = (X+DX)*12. *036 WHENEVER L.GE. LM *037 DELT = (LM -L)* DX/DIST *038 X = X+DX+DELT *039 TH = X*12. *040 L = LM *041 OTHERWISE *042 CONTINUE *043 END OF CONDITIONAL *044 WHENEVER I.E. N *045 PRINT FORMAT OUTI, TWM,TMS, TSM, Q, QREQD, T, DIST, L,TH *046 I = 0 *047 OTHERWISE *048 TRANSFER TO ALPHA *049 END OF CONDITIONAL *050 ALPHA CONTINUE *051 PRINT FORMAT OUTI, TWM,TMS, TSM, Q, QREQD, T, DIST, L,TH *052 VECTOR VALUES OUT1= $1H, 3F12.4, F12.0, F12.2, 4F12.5*$ *C53 TSSP = TSM *054 I = *055 THROUGH BETA, FOR Y=X, DX, L.GE. (LM+LSP).OR. TH.GE. (XS *056 2/2.) *056 i = I + 1 *057 Q= KS/(Y+DX)* (TF-TW)/(1.+ KS/(Y+DX)*(1./HSPS)) *058 TSSP = Q/HSPS + TW *059 QREQD = ((TF+TSSP )/2.)*Y*CPS*RHO+TF*DX*CPS*RHO-(ITF+TSSP)/2. *060 2)*(Y+DX)*CPS*RHO+ (TS-TF)*CPL*DX*RHO+HF*DX*RHO *060 T = (QREQD/Q)*3600. *061 LIST = (1*VEL)/6C. *062 L= L+ DIST *063 TH = (Y+OX)*12. *064 WHENEVER L.GE. (LM+LSP) *065 LELT = ((LM+LSP)-L)*DX/DIST *066 Y = Y+DX+DELT *067 TH = Y*12. *068 L = LM + LSP *069 OTHERWISE *C70 CONTINUE *071 END OF CONDITIONAL *072 WHENEVER I.E. N *073 PRINT FORMAT OUT2, TSSP, Q, QREQD, T, DIST, L, TH *074 1 =0 *075 OTHERWISE *076 TRANSFER TO BETA *077 ENC OF CONDIIIONAL *078 BETA CONTINUE *079 PRINT FORMAT OUT2, TSSP, Q, QREQD, T, DIST, L, TH *080 VECTOR VALUES OUF2 = $1H, F36.4, 12 F12.2, 4F12.5*$ *081 IRANSFER TO GAMMA *082 END OF PROGRAM *083 Figure 3. (Continued)

-11TABLE I INPUT DATA FOR COMPUTER CALCULATION SIMULATICN OF CONTINUCUS CASTING PROCESS WATER-MOLD HEAT TRANSFER COEFFICIENT, BTU/HtR-SQ FT- DEG F = 300C THERMAL CONDUCTIVITY OF MOLD, BTU/HR-FT DEG F = 200 MOLD-SLAB FEAT TRANSFER COEFFICIENT, BTU/HR-SC FT- DEG F = 300.0000 SPRAY-SLAB HEAT TRANSFER CCEFFICIENT, BTU/HR-SQ FF- DEG F = 150C TkERMAL CCNDUCTIVITY OF STEEL, BTU/HR-FT-DEG F = 25 M1OLD LENGTH, FT = 5.CO MiOLD TFICKNESS, IN =.50 SLAB THICKNESS, IN = 7.00 SPRAY LENGTH, FT = 4.50 SLAB VELOCITY, FF/MIN = 2.5U DENSITY CF STEEL, LB/CU FT = 49C WATER [EMIPERATURE, DEG F = 1CC LIQUIDUS TEMPERAlURE OF STEEL, DEC F = 2760 TAPPING TEMPERATLJRtE OF SrEEL, DEU F = 2840 HEAT OF FUSION OF STEEL, BTU/LB - 118 SPECIFIC HEAT OF LIQUID STEEL, BTU/Lb-DEG F=.1840 SPECIFIC HEAT CF SCLID STEEL, BTU/LB-DEG F =.1550 INCREMENT OF FREEZING THICKNESS, IN =.0100 ITERATIONS FOR PRINTOUT = 5

-12TABLE II CALCULATED RESULTS TEMPERATLRE, F r MCLC-W T MCLL-S 1 SLAB-M Q, BTU Q KEQD, bTU TIME, SEC DISTANCE, FT LENGTH, FT THICKNESS, 319.3814 456.4948 265C.3C92 658144 57.67.31542.01314.06311.05C00 31C.6931 442.3762 2549.3C69 632079 60.86.34664.01444.13273.10O00 302.6667 429.3333 2456.0000 608000 63.81.37785.01574.20884.15000 295.2294 417.2477 2369.5413 585688 66.55.40906.01704.29146.20C00 288.3186 4C6.0177 2289.2035 564956 69.09.44027.01834.38059.25000 281.8803 395.5556 2214.3590 545641 71.46.47148.01965.47621.30000 275.8678 385.7851 2144.4629 527603 73.67.50269.02095.57834.35000 270.24CO 376.64CO 2U79.04C0 510720 75.74.53391.02225.68697.40C00 264.9612 368.C620 2C17.6745 494884 77.69.56512.02355.80210.45000 26C.C0CO 36C.0CO0 1960.0001 480000 79.51.59633.02485.92373.50000 255.3285 352.4C88 1905.6935 465985 81.23.62754.02615 1.05187.55000 250.9220 345.2482 1854.4682 452766 82.85.65875.02745 1.18651.60000 246.7586 338.4828 18C6.0691 440276 84.38.68996.02875 1.32765.65000 242.8188 332.0806 1760.2686 428456 85.83.72118.03005 1.47530.70000 23S.0850 326.C131 1716.8629 417255 87.20.75239.03135 1.62944.75000 235.5414 320.2548 1675.6690 406624 88.51.78360.03265 1.79009.80000 232.1739 314.7826 1636.5219 396522 89.75.81481.03395 1.95724.85000 228.9697 309.5758 1599.2729 386909 90.93.84602.03525 2.13090.90000 225.9172 304.6154 1563.7872 377752 92.05.87723.03655 2.31105.95000 223.0058 299.8844 1529.9424 369017 93.12.90845.03785 2.49771 1.00C00 220.2260 295.3673 1497.6274 360678 94.14.93966.03915 2.69087 1.05000 217.5691 291.0498 1466.74C6 352707 95.12.97087.04045 2.89054 1.10000 215.0271 286.9190 1437.1895 345081 96.06 1.00208.04175 3.09670 1.15000 212.5926 282.9630 1408.8892 337778 96.95 1.03330.04305 3.30937 1.20000 210.2591 279.1710 1381.7620 330777 97.81 1.06450.04435 3.52854 1.25000 208.C2C3 275.5330 1355.7364 324061 98.63 1.09572.04565 3.75422 1.3000 205.3707 272.0398 1330.7466 317612 99.42 1.12693.04696 3.98639 1.35000 203.8049 268.6830 13C6.7321 311415 100.18 1.15814.04826 4.22507 1.4CC00 201.8182 265.4546 1283.6367 305455 100.91 1.18935.04956 4.47025 1.45000 199.9061 262.3475 1261.4088 299718 101.62 1.22056.05086 4.72193 1.50000 198.0646 259.3549 1240.0004 294194 102.30 1.25177.05216 4.98012 1.55000 197.7043 258.7696 1235.8130 293113 102.43 1.25802.05242 5.00000 1.55379 393.3082 439962 129.09 1.05628.04401 5.21746 1.61379 385.4396 428159 129.34 1.08749.04531 5.44142 1.66379 377.9822 416973 129.57 1.11870.04661 5.67188 1.71379 37C.9045 406357 129.80 1.14991.04791 5.90884 1.76379 364.1782 396267 130.01 1.18113.04921 6.15231 1.81379 357.7779 386667 13C.21 1.21234.05051 6.40228 1.86379 351.6804 377521 130.41 1.24355.05181 6.65875 1.91379 345.8647 368797 130.59 1.27476.05312 6.92173 1.96379 340.3117 360468 130.77 1.30598.05442 7.19120 2.01379 335.0040 352506 130.93 1.33718.05572 7.46718 2.06379 329.9256 344888 131.10 1.36839.05702 7.74966 2.11379 325.0621 337593 131.25 1.39961.05832 8.03865 2.16379 320.4002 330600 131.40 1.43082.05962 8.33413 2.21379 315.9274 323891 131.54 1.46203.06092 8.63612 2.26379 311.6325 317449 131.67 1.49324.06222 8.94461 2.31379 307.5052 311258 131.81 1.52446.06352 9.25961 2.36379 304.3175 306476 131.91 1.54942.06456 9.50000 2.40127

-130 H \2 w 6 LiJ CL 6) LL )D 3 I rW HI 9 THIKNESO I — I'W 0 I3 3 4 2 3 4_ THICKNESS OF THICKNESS OF SOLIDIFIED LAYER, INCHES SOLIDIFIED LAYER, INCHES 2_ w O I Z 3 1 0 1 — _2 3 4 SOLIDIFIED LAYER. INCHES SOLIDIFIED LAYER, INCHES SOLIDIFICATION IN MOLD SOLIDIFICATION IN SPRAY Figure 4. Predicted Profile of Solidification Front in Mold and Spray Sections of a Continuous Casting Strand.

-14the thickness at the bottom of the water spray is approximately 2o4 incheso This result is in. reasonable agreement with the calculations and experi(3) mental data of Korotkov, et alo Several assumptions were made in deriving this unidirectional pseudo steady-state heat transfer simulation. One particular aspect which should be considered is heat transfer between the liquid metal contained in the well and the solidifying shell. This heat transfer was neglected in the present calculation and the temperature in the metal liquid well was assumed to remain constant. This is, of course, not the case in practice, and furthermore, there is some liquid circulation in the well which would promote heat transfer and delay the initial buildup of the shell, at the expense of a decreasing temperature in the metal well. It was not possible in the present case to estimate the influence of this error, Another rough assumption was that the temperature gradient through the solidified layer of the slab was linear. Although this assumption is known to be in error, the first order correction, ioeo, correcting the heat removal term for the energy removed from the solidified layer as it becomes thicker and the temperature gradient levels out, was sufficient to give the liquid-solid interface a nearly parabolic shape in the mold and spray heat transfer zones, A parabolic interface is predicted theoretically if no superheat is present in, the liquid by the relationship. X k cat (11) where k constant = - thermal diffusivity, KS/((RHO) * (CPS))

-15% This agreement between the assumed simulation and conditions amenable to theoretical analysis is a good indication that this error did not have a marked influence on the results of the continuous casting simulationo CONCLUSIONS lo A unidirectional heat transfer analysis of the continuous casting process has been carried out with reasonable agreement between predicted behavior of the cast slab and that attained in practice. 2o The use of the computer in solving this problem should permit easy extension to modifications in a given casting operation in order to estimate the influences of changes in operating variableso

-16BIBLI OGRAPHY 1o Journal of Metals August and September, 1957o 2. Continuous Casting, Do L. McBride, and To E Dancy, Editors, AIME, 1962, New York 35 Ko Po Korotkov, Ho Po Mayorov, A A Skvortsov, and A Do Akimenko, The Continuous Casting of Steel in Commercial Use Published in Translation, Pergamon Press, 1960, Londono

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