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; press  to 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
 ************************************************************
  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