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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
************************************************************
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(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(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)
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.
ENUL =1.0E-05 ;ENUT =0.
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(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 )
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 )

PATCH(WALLRB ,NORTH , 1, 1, 50, 50, 1, 1, 1, 1)

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
************************************************************
Group 16. Terminate Iterations
************************************************************
Group 17. Relaxation
RELAX(H1,LINRLX,0.3)
RELAX(HA,LINRLX,1.)
RELAX(EMPO,LINRLX,1.)
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(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(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. )