TALK=T;RUN(1,1) PHOTON USE AUTOPLOT file PHI 5 cl;d 1 h1;d 1 ha;col3 1;blb4 2;redr msg temperature profile; pressto continue ENDUSE DISPLAY The problem considered is that of radiative heat transfer in a stationary emitting and absorbing gray medium containing a uniformly-distributed volumetric heat source. The medium is bounded by two infinite, plane parallel walls at y=0 and y=L, which are kept at the same uniform temperatures. Thus, symmetry is exploited in the calculations. The energy transfer is by pure radiation, so that the energy equation is simply: -d/dy (Qr) + Qv = 0 where Qr is the radiative heat flux and Qv is the uniform volumetric heat generation rate in the medium. Thermal radiation is modelled by solving the equation for the radiosity R, as follows: d/dy ( 1/(a+s) dR/dy ) + 4*a*(E - R) = 0 where a is the absorption coefficient, s is the scattering coefficient, and E is the black-body emissive power. The problem is to solve for the temperature distribution given the wall temperature Tw, the optical thickness Kr*L; and the wall emissivity emw. Kr is the Rosseland mean absorption coefficient which is given by: Kr=(a+s). This problem has been solved by Deissler [ASME J.Heat Transfer P241-246, (1964)] who used the Diffusion approximation with jump boundary conditions to obtain the following solutions: Qw = 0.5*L*Qv (Egc - Ew)/Qw = (3./16)*Kr*L+1./emw-0.5+3./(4.*Kr*L) (Egw - Ew)/Qw = (1./emw-0.5+3.0/(4.*Kr*L)) Eg = Egc - (3./8)*Kr*Qv*y**2 where Qw is the wall heat flux, and Egc and Egw are the gas emissive powers at the centre line and wall. ENDDIS ************************************************************ Group 1. Run Title and Number ************************************************************ ************************************************************ TEXT(1D RADIATION+HEAT SOURCE IN A SLAB:122 ) ************************************************************ ************************************************************ IRUNN = 1 ;LIBREF = 2 ************************************************************ Group 2. Time dependence STEADY = T ************************************************************ Group 3. X-Direction Grid Spacing CARTES = T NX = 1 XULAST =1. XFRAC(1)=1. ************************************************************ Group 4. Y-Direction Grid Spacing NY = 50 YVLAST =0.5 YFRAC(1)=0.02 ;YFRAC(2)=0.04 YFRAC(3)=0.06 ;YFRAC(4)=0.08 YFRAC(5)=0.1 ;YFRAC(6)=0.12 YFRAC(7)=0.14 ;YFRAC(8)=0.16 YFRAC(9)=0.18 ;YFRAC(10)=0.2 YFRAC(11)=0.22 ;YFRAC(12)=0.24 YFRAC(13)=0.26 ;YFRAC(14)=0.28 YFRAC(15)=0.3 ;YFRAC(16)=0.32 YFRAC(17)=0.34 ;YFRAC(18)=0.36 YFRAC(19)=0.38 ;YFRAC(20)=0.4 YFRAC(21)=0.42 ;YFRAC(22)=0.44 YFRAC(23)=0.46 ;YFRAC(24)=0.48 YFRAC(25)=0.5 ;YFRAC(26)=0.52 YFRAC(27)=0.54 ;YFRAC(28)=0.56 YFRAC(29)=0.58 ;YFRAC(30)=0.6 YFRAC(31)=0.62 ;YFRAC(32)=0.64 YFRAC(33)=0.66 ;YFRAC(34)=0.68 YFRAC(35)=0.7 ;YFRAC(36)=0.72 YFRAC(37)=0.74 ;YFRAC(38)=0.76 YFRAC(39)=0.78 ;YFRAC(40)=0.8 YFRAC(41)=0.82 ;YFRAC(42)=0.84 YFRAC(43)=0.86 ;YFRAC(44)=0.88 YFRAC(45)=0.9 ;YFRAC(46)=0.92 YFRAC(47)=0.94 ;YFRAC(48)=0.96 YFRAC(49)=0.98 ;YFRAC(50)=1. ************************************************************ Group 5. Z-Direction Grid Spacing PARAB = F NZ = 1 ZWLAST =1. ZFRAC(1)=1. ************************************************************ Group 6. Body-Fitted Coordinates ************************************************************ Group 7. Variables: STOREd,SOLVEd,NAMEd ONEPHS = T NAME(14)=H1 ;NAME(146)=HA NAME(147)=EMPO ;NAME(148)=SRAD NAME(149)=SCAT ;NAME(150)=EMIS * Y in SOLUTN argument list denotes: * 1-stored 2-solved 3-whole-field * 4-point-by-point 5-explicit 6-harmonic averaging SOLUTN(H1,Y,Y,N,N,N,Y) SOLUTN(HA,Y,N,N,N,N,Y) SOLUTN(EMPO,Y,N,N,N,N,Y) SOLUTN(SRAD,Y,Y,N,N,N,Y) SOLUTN(SCAT,Y,N,N,N,N,Y) SOLUTN(EMIS,Y,N,N,N,N,Y) ************************************************************ Group 8. Terms & Devices * Y in TERMS argument list denotes: * 1-built-in source 2-convection 3-diffusion 4-transient * 5-first phase variable 6-interphase transport TERMS(H1,N,N,N,N,Y,Y) TERMS(SRAD,N,N,Y,N,Y,N) DIFCUT =0.5 ;ZDIFAC =1. GALA = F ;ADDDIF = F ISOLX = -1 ;ISOLY = -1 ;ISOLZ = -1 ************************************************************ Group 9. Properties used if PRPS is not stored, and where PRPS = -1.0 if it is! RHO1 =1. ;TMP1 = GRND2 ;EL1 =0. TSURR =0. ;TEMP0 =0. ;PRESS0 =0. DVO1DT =0. ;DRH1DP =0. TMP1A =0. ;TMP1B =1. ;TMP1C =0. TMP2A =0. ;TMP2B =0. ;TMP2C =0. EMISS =5. ;SCATT =0. RADIA =5. ;RADIB =0. ENUL =1.0E-05 ;ENUT =0. PRNDTL(SRAD)=-GRND1 PRT(SRAD)=1.0E+10 CP1 =1. ;CP2 =1. ************************************************************ Group 10.Inter-Phase Transfer Processes ************************************************************ Group 11.Initial field variables (PHIs) FIINIT(H1)=1000. ;FIINIT(HA)=1.0E-10 FIINIT(EMPO)=1.0E-10 ;FIINIT(SRAD)=5.6697E+04 FIINIT(SCAT)=0. ;FIINIT(EMIS)=0. PATCH(IN1 ,INIVAL, 1, 1, 1, 1, 1, 1, 1, 1) INIT(IN1 ,HA ,0. ,1157.277832 ) PATCH(IN2 ,INIVAL, 1, 1, 2, 2, 1, 1, 1, 1) INIT(IN2 ,HA ,0. ,1157.217285 ) PATCH(IN3 ,INIVAL, 1, 1, 3, 3, 1, 1, 1, 1) INIT(IN3 ,HA ,0. ,1157.096313 ) PATCH(IN4 ,INIVAL, 1, 1, 4, 4, 1, 1, 1, 1) INIT(IN4 ,HA ,0. ,1156.914795 ) PATCH(IN5 ,INIVAL, 1, 1, 5, 5, 1, 1, 1, 1) INIT(IN5 ,HA ,0. ,1156.672485 ) PATCH(IN6 ,INIVAL, 1, 1, 6, 6, 1, 1, 1, 1) INIT(IN6 ,HA ,0. ,1156.369507 ) PATCH(IN7 ,INIVAL, 1, 1, 7, 7, 1, 1, 1, 1) INIT(IN7 ,HA ,0. ,1156.005493 ) PATCH(IN8 ,INIVAL, 1, 1, 8, 8, 1, 1, 1, 1) INIT(IN8 ,HA ,0. ,1155.580444 ) PATCH(IN9 ,INIVAL, 1, 1, 9, 9, 1, 1, 1, 1) INIT(IN9 ,HA ,0. ,1155.094116 ) PATCH(IN10 ,INIVAL, 1, 1, 10, 10, 1, 1, 1, 1) INIT(IN10 ,HA ,0. ,1154.546265 ) PATCH(IN11 ,INIVAL, 1, 1, 11, 11, 1, 1, 1, 1) INIT(IN11 ,HA ,0. ,1153.936646 ) PATCH(IN12 ,INIVAL, 1, 1, 12, 12, 1, 1, 1, 1) INIT(IN12 ,HA ,0. ,1153.264893 ) PATCH(IN13 ,INIVAL, 1, 1, 13, 13, 1, 1, 1, 1) INIT(IN13 ,HA ,0. ,1152.530762 ) PATCH(IN14 ,INIVAL, 1, 1, 14, 14, 1, 1, 1, 1) INIT(IN14 ,HA ,0. ,1151.733887 ) PATCH(IN15 ,INIVAL, 1, 1, 15, 15, 1, 1, 1, 1) INIT(IN15 ,HA ,0. ,1150.873779 ) PATCH(IN16 ,INIVAL, 1, 1, 16, 16, 1, 1, 1, 1) INIT(IN16 ,HA ,0. ,1149.950195 ) PATCH(IN17 ,INIVAL, 1, 1, 17, 17, 1, 1, 1, 1) INIT(IN17 ,HA ,0. ,1148.962524 ) PATCH(IN18 ,INIVAL, 1, 1, 18, 18, 1, 1, 1, 1) INIT(IN18 ,HA ,0. ,1147.910278 ) PATCH(IN19 ,INIVAL, 1, 1, 19, 19, 1, 1, 1, 1) INIT(IN19 ,HA ,0. ,1146.793091 ) PATCH(IN20 ,INIVAL, 1, 1, 20, 20, 1, 1, 1, 1) INIT(IN20 ,HA ,0. ,1145.610107 ) PATCH(IN21 ,INIVAL, 1, 1, 21, 21, 1, 1, 1, 1) INIT(IN21 ,HA ,0. ,1144.361084 ) PATCH(IN22 ,INIVAL, 1, 1, 22, 22, 1, 1, 1, 1) INIT(IN22 ,HA ,0. ,1143.045044 ) PATCH(IN23 ,INIVAL, 1, 1, 23, 23, 1, 1, 1, 1) INIT(IN23 ,HA ,0. ,1141.661499 ) PATCH(IN24 ,INIVAL, 1, 1, 24, 24, 1, 1, 1, 1) INIT(IN24 ,HA ,0. ,1140.209717 ) PATCH(IN25 ,INIVAL, 1, 1, 25, 25, 1, 1, 1, 1) INIT(IN25 ,HA ,0. ,1138.688843 ) PATCH(IN26 ,INIVAL, 1, 1, 26, 26, 1, 1, 1, 1) INIT(IN26 ,HA ,0. ,1137.098022 ) PATCH(IN27 ,INIVAL, 1, 1, 27, 27, 1, 1, 1, 1) INIT(IN27 ,HA ,0. ,1135.436523 ) PATCH(IN28 ,INIVAL, 1, 1, 28, 28, 1, 1, 1, 1) INIT(IN28 ,HA ,0. ,1133.703369 ) PATCH(IN29 ,INIVAL, 1, 1, 29, 29, 1, 1, 1, 1) INIT(IN29 ,HA ,0. ,1131.897583 ) PATCH(IN30 ,INIVAL, 1, 1, 30, 30, 1, 1, 1, 1) INIT(IN30 ,HA ,0. ,1130.018066 ) PATCH(IN31 ,INIVAL, 1, 1, 31, 31, 1, 1, 1, 1) INIT(IN31 ,HA ,0. ,1128.063965 ) PATCH(IN32 ,INIVAL, 1, 1, 32, 32, 1, 1, 1, 1) INIT(IN32 ,HA ,0. ,1126.033936 ) PATCH(IN33 ,INIVAL, 1, 1, 33, 33, 1, 1, 1, 1) INIT(IN33 ,HA ,0. ,1123.926758 ) PATCH(IN34 ,INIVAL, 1, 1, 34, 34, 1, 1, 1, 1) INIT(IN34 ,HA ,0. ,1121.741333 ) PATCH(IN35 ,INIVAL, 1, 1, 35, 35, 1, 1, 1, 1) INIT(IN35 ,HA ,0. ,1119.476196 ) PATCH(IN36 ,INIVAL, 1, 1, 36, 36, 1, 1, 1, 1) INIT(IN36 ,HA ,0. ,1117.130005 ) PATCH(IN37 ,INIVAL, 1, 1, 37, 37, 1, 1, 1, 1) INIT(IN37 ,HA ,0. ,1114.701294 ) PATCH(IN38 ,INIVAL, 1, 1, 38, 38, 1, 1, 1, 1) INIT(IN38 ,HA ,0. ,1112.188477 ) PATCH(IN39 ,INIVAL, 1, 1, 39, 39, 1, 1, 1, 1) INIT(IN39 ,HA ,0. ,1109.589844 ) PATCH(IN40 ,INIVAL, 1, 1, 40, 40, 1, 1, 1, 1) INIT(IN40 ,HA ,0. ,1106.903687 ) PATCH(IN41 ,INIVAL, 1, 1, 41, 41, 1, 1, 1, 1) INIT(IN41 ,HA ,0. ,1104.128296 ) PATCH(IN42 ,INIVAL, 1, 1, 42, 42, 1, 1, 1, 1) INIT(IN42 ,HA ,0. ,1101.261597 ) PATCH(IN43 ,INIVAL, 1, 1, 43, 43, 1, 1, 1, 1) INIT(IN43 ,HA ,0. ,1098.301514 ) PATCH(IN44 ,INIVAL, 1, 1, 44, 44, 1, 1, 1, 1) INIT(IN44 ,HA ,0. ,1095.245972 ) PATCH(IN45 ,INIVAL, 1, 1, 45, 45, 1, 1, 1, 1) INIT(IN45 ,HA ,0. ,1092.092651 ) PATCH(IN46 ,INIVAL, 1, 1, 46, 46, 1, 1, 1, 1) INIT(IN46 ,HA ,0. ,1088.839233 ) PATCH(IN47 ,INIVAL, 1, 1, 47, 47, 1, 1, 1, 1) INIT(IN47 ,HA ,0. ,1085.483032 ) PATCH(IN48 ,INIVAL, 1, 1, 48, 48, 1, 1, 1, 1) INIT(IN48 ,HA ,0. ,1082.021362 ) PATCH(IN49 ,INIVAL, 1, 1, 49, 49, 1, 1, 1, 1) INIT(IN49 ,HA ,0. ,1078.451538 ) PATCH(IN50 ,INIVAL, 1, 1, 50, 50, 1, 1, 1, 1) INIT(IN50 ,HA ,0. ,1074.770264 ) INIADD = F FSWEEP = 1 NAMFI =CHAM ************************************************************ Group 12. Patchwise adjustment of terms Patches for this group are printed with those for Group 13. Their names begin either with GP12 or & ************************************************************ Group 13. Boundary & Special Sources PATCH(RADISO ,FREEVL, 0, 0, 0, 0, 0, 0, 1, 1) COVAL(RADISO ,H1 , GRND1 , GRND1 ) COVAL(RADISO ,SRAD, GRND1 , GRND1 ) PATCH(WALLRB ,NORTH , 1, 1, 50, 50, 1, 1, 1, 1) COVAL(WALLRB ,SRAD,2. ,5.6697E+04 ) PATCH(QHEAT ,VOLUME, 1, 1, 1, 50, 1, 1, 1, 1) COVAL(QHEAT ,H1 , FIXFLU ,5.6697E+04 ) XCYCLE = F EGWF = T WALLCO = GRND2 ************************************************************ Group 14. Downstream Pressure For PARAB ************************************************************ Group 15. Terminate Sweeps LSWEEP = 500 ;ISWC1 = 1 LITHYD = 1 ;LITFLX = 1 ;LITC = 5 ;ITHC1 = 1 SELREF = F RESREF(H1)=5.6697 ;RESREF(SRAD)=5.6697 ************************************************************ Group 16. Terminate Iterations LITER(H1)=20 ;LITER(SRAD)=20 ENDIT(H1)=1.0E-03 ;ENDIT(SRAD)=1.0E-03 ************************************************************ Group 17. Relaxation RELAX(H1,LINRLX,0.3) RELAX(HA,LINRLX,1.) RELAX(EMPO,LINRLX,1.) RELAX(SRAD,LINRLX,0.6) RELAX(SCAT,LINRLX,1.) RELAX(EMIS,LINRLX,1.) OVRRLX =0. EXPERT = F ;NNORSL = F ************************************************************ Group 18. Limits VARMAX(H1)=1.0E+10 ;VARMIN(H1)=500. VARMAX(HA)=1.0E+10 ;VARMIN(HA)=-1.0E+10 VARMAX(EMPO)=1.0E+10 ;VARMIN(EMPO)=-1.0E+10 VARMAX(SRAD)=1.0E+10 ;VARMIN(SRAD)=-1.0E+10 VARMAX(SCAT)=1.0E+10 ;VARMIN(SCAT)=-1.0E+10 VARMAX(EMIS)=1.0E+10 ;VARMIN(EMIS)=-1.0E+10 ************************************************************ Group 19. Data transmitted to GROUND PARSOL = F ISG62 = 1 SPEDAT(SET,GXMONI,PLOTALL,L,T) ************************************************************ Group 20. Preliminary Printout ************************************************************ Group 21. Print-out of Variables INIFLD = F ;SUBWGR = F * Y in OUTPUT argument list denotes: * 1-field 2-correction-eq. monitor 3-selective dumping * 4-whole-field residual 5-spot-value table 6-residual table OUTPUT(H1,Y,N,N,Y,Y,Y) OUTPUT(HA,Y,N,Y,N,N,N) OUTPUT(EMPO,Y,N,Y,N,N,N) OUTPUT(SRAD,Y,N,Y,Y,Y,Y) OUTPUT(SCAT,Y,N,Y,N,N,N) OUTPUT(EMIS,Y,N,Y,N,N,N) ************************************************************ Group 22. Monitor Print-Out IXMON = 1 ;IYMON = 1 ;IZMON = 1 NPRMON = 100000 ;NPRMNT = 1 ;TSTSWP = -1 UWATCH = T ;USTEER = T HIGHLO = F ************************************************************ Group 23.Field Print-Out & Plot Control NPRINT = 100000 ;NUMCLS = 5 NYPRIN = 1 ;IYPRF = 1 ;IYPRL = 10000 IPLTF = 1 ;IPLTL = -1 ;NPLT = 20 ISWPRF = 1 ;ISWPRL = 100000 ITABL = 3 ;IPROF = 1 ABSIZ =0.5 ;ORSIZ =0.4 NTZPRF = 1 ;NCOLPF = 50 ICHR = 2 ;NCOLCO = 45 ;NROWCO = 20 PATCH(YWISE ,PROFIL, 1, 1, 1, 50, 1, 1, 1, 1) PLOT(YWISE ,H1 ,0. ,0. ) PLOT(YWISE ,SRAD,0. ,0. ) ************************************************************ Group 24. Dumps For Restarts SAVE = T ;NOWIPE = F NSAVE =CHAM STOP