PHOTON USE AUTOPLOT file PHI 5 cl;d 1 h1;d 1 ha;col3 1;blb4 2;redr msg temperature profile; pressto continue pause cl;d 1 radx;d 1 ra;col3 1;blb4 2;redr msg radiation-flux profile; press e to end pause;end ENDUSE GROUP 1. Run title and other preliminaries TEXT(X-D Radiative Equilibrium In Slab TITLE DISPLAY The problem considered is that of radiative heat transfer in a 1d plane-parallel slab in radiative equilibrium. The slab is of thickness L and the gray medium may absorb, emit and scatter radiation. At x=L the wall is a diffuse emitter and reflecter kept at a fixed temperature. At the x=0 the net radiative heat flux Qrad is specified at the wall. ENDDIS Since the energy transfer is by pure radiation, the energy equation is given by: -d/dx (Qrad) = 0 The equation for the composite radiative heat flux is given by: d/dx ( 1/(a+s) d/dx (Rx) ) + a (E - Rx) = 0 where a is the absorption coefficient, s is the scattering coefficient, Rx is the composite radiation flux defined as the average of the +ve and -ve radiation fluxes, and E is the black-body emissive power. It may be noted that the radiative heat flux is given by: d/dx (Qrad) = 2a (E - Rx) The black-body emissive power E=sig*T**4 where sig is the Stefan-Boltzmann constant and T is the temperature of the medium. The problem is the determination of the temperature and composite radiative-flux distributions, as given by the following analytical solutions: Rx = E ( radiative equilibrium ) E = Ew + Qrad*[ 1./emw - 0.5 + 0.5*(a+s)*L*(1 - x/L) ] where Ew is the emissive power at the wall and emw is the emissivity of the wall. For the case considered below, Qrad is taken to be Qrad = 2.*Ew. The locally-defined parameters are as follows: GSIGMA Stefan-Boltzmann constant {W/m**2/K**4} SCAT Scattering coefficient { 1/m } ABSORB Absorption coefficient { 1/m } EMIW emissivity of the wall TWAL wall temperature at x=L { K } QRAD net radiative heat flux at x=0 {W/m**2} CHAR(CH1);REAL(GSIGMA,SCAT,ABSORB,EMIW,TWAL,QRAD) GSIGMA=5.6697E-8;SCAT=0.5;ABSORB=0.5;EMIW=1.0;TWAL=1000.0 QRAD=2.*GSIGMA*TWAL**4 GROUP 3,4,5. X,Y,Z-direction grid specification GRDPWR(X,50,1.0,1.0) GROUP 7. Variables stored, solved & named CP1=1.0 MESG( Enter required energy variable ? (TEM1 or H1) IF(:CH1:.EQ.) THEN + READVDU(CH1,CHAR,H1) ENDIF IF(:CH1:.EQ.TEM1) THEN + MESG( TEM1 solution selected ELSE + MESG( H1 solution selected + TMP1=LINH;TMP1B=1.0/CP1 ENDIF RADIAT(FLUX,ABSORB,SCAT,:CH1:);STORE(EMPO) GROUP 8. Terms (in differential equations) & devices ** Deactive conduction & any built-in sources TERMS(:CH1:,N,N,N,N,P,P) GROUP 11. Initialization of variable or porosity fields FIINIT(RADX)=0.5*QRAD;FIINIT(:CH1:)=TWAL ** analytical solution REAL(EW,EG,QRADA,ALF,BET,TA,RAN,GX);STORE(HA,RA);INTEGER(JJM1) EW=GSIGMA*TWAL**4;QRADA=2.*EW;ALF=1./EMIW-0.5 BET=0.5*(ABSORB+SCAT)*XULAST DO JJ=1,NX +PATCH(IN:JJ:,INIVAL,JJ,JJ,1,NY,1,NZ,1,1) +GX=0.5*XFRAC(JJ) IF(JJ.NE.1) THEN +JJM1=JJ-1;GX=XFRAC(JJM1)+0.5*(XFRAC(JJ)-XFRAC(JJM1)) ENDIF +GX=GX*XULAST;EG=EW+QRADA*(ALF+BET*(1.-(GX/XULAST))) +RAN=EG;TA=(EG/GSIGMA)**0.25 +INIT(IN:JJ:,RA,ZERO,RAN);INIT(IN:JJ:,HA,ZERO,TA) ENDDO GROUP 13. Boundary conditions and special sources ** Net radiation flux from wall PATCH(WALLRA,WEST,1,1,1,NY,1,NZ,1,1) COVAL(WALLRA,RADX,FIXFLU,0.5*QRAD) PATCH(WALLRB,EAST,NX,NX,1,NY,1,NZ,1,1) COVAL(WALLRB,RADX,EMIW/(2.0-EMIW),GSIGMA*TWAL**4) GROUP 15. Termination of sweeps LSWEEP=50 GROUP 16. Termination of iterations RESREF(:CH1:)=1.E-12*QRAD;RESREF(RADX)=0.5*RESREF(:CH1:) GROUP 17. Under-relaxation devices RELAX(:CH1:,FALSDT,100./QRAD) GROUP 22. Spot-value print-out IXMON=NX/2;NPLT=5;NXPRIN=NX/10 GROUP 23. Field print-out and plot control OUTPUT(:CH1:,Y,N,N,Y,Y,Y) PATCH(XWISE,PROFIL,1,NX,1,1,1,1,1,1) PLOT(XWISE,:CH1:,0.0,0.0);PLOT(XWISE,RADX,0.0,0.0) GROUP 24. Dumps for restarts TSTSWP=-1