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#\$r002
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
TEXT(1D RADIATIVE EQUILIBRIUM IN SLAB : 121
#cls
TITLE
DISPLAY
The problem considered is radiative heat transfer in a stationary
emitting and absorbing gray medium bounded by two infinite, plane
parallel walls. The boundary surfaces at y=0 and y=L are kept at
fixed temperatures Ts and Tn. The energy transfer is by pure
radiation, so that the energy equation is simply:

-d/dy (Qr) = 0

where Qr is the radiative heat transfer per unit area. Thermal
radiation is modelled by solving an the equation for the

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, and
hence Qr, given Ts, Tn, the optical thickness Kr*L; and the wall
emissivities emws and emwn. Kr is the Rosseland mean absorption
coefficient which is given by: Kr=(a+s).
#pause
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:

Qr = (Ews - Ewn)/(0.75*Kr*L + 1./emws + 1./emwn - 1.0)

(Ews - Egs)/Qrad = 1./emws - 0.5

(Egn - Ewn)/Qrad = 1./emwn - 0.5

E  = Egs - 0.75*Kr*Qr*y

where Ews and Ewn are the emissive powers at the wall, and Egs
and Egn are the emissive powers in the gas at the wall. The
results of the radiosity model show excellent agreement with
Deissler's results for the whole range of optical thickness
considered by Deissler, i.e. 0 < Kr*L < 10.0.
ENDDIS
#pause
REAL(EMWS,EMWN,TWS,TWN,EWS,EWN,ACON,GY)
CHAR(CH1);INTEGER(JJM1)
MESG( Enter optical thickness  0 < Kr*L << 10.0 (default 5)
EMWS=1.0;EMWN=1.0;TWS=1500.0;TWN=1000.0
** analytical solution
GROUP 3,4,5. X,Y,Z-direction grid specification
GRDPWR(Y,50,LENGTH,1.0)
GROUP 6. Body-fitted coordinates or grid distortion
GROUP 7. Variables stored, solved & named
CP1=1.0
MESG( Enter required energy variable ? (TEM1 or H1)
IF(:CH1:.EQ.TEM1) THEN
+ MESG( TEM1 solution selected
ELSE
+ MESG( H1 solution selected
+ TMP1=LINH;TMP1B=1.0/CP1
ENDIF
GROUP 8. Terms (in differential equations) & devices
** Deactive conduction & any built-in sources
TERMS(:CH1:,N,N,N,N,P,P)
GROUP 9. Properties of the medium (or media)
GROUP 10. Inter-phase-transfer processes and properties
GROUP 11. Initialization of variable or porosity fields
** analytical solution
DO JJ=1,NY
+PATCH(IN:JJ:,INIVAL,1,NX,JJ,JJ,1,NZ,1,1)
+GY=0.5*YFRAC(JJ)
IF(JJ.NE.1) THEN
+JJM1=JJ-1;GY=YFRAC(JJM1)+0.5*(YFRAC(JJ)-YFRAC(JJM1))
ENDIF
+GY=GY*YVLAST;EG=EGS-ACON*GY
+TA=(EG/SIGMA)**0.25;INIT(IN:JJ:,HA,ZERO,TA)
ENDDO
GROUP 13. Boundary conditions and special sources
** Net radiation flux from wall
PATCH(WALLRA,SOUTH,1,NX,1,1,1,NZ,1,1)
PATCH(WALLRB,NORTH,1,NX,NY,NY,1,NZ,1,1)
GROUP 15. Termination of sweeps
LSWEEP=500;LITC=5
GROUP 16. Termination of iterations