#immersol) #declare IMMERSOL Emitting and absorbing gray media (1D, TEM1) TEXT(IMMERSOL 1D Radiative equilibrium :202 TITLE ************************************************************** PHOTON USE AUTOPLOT FILE PHI 5 CL;DA 1 TEM1;DA 1 T3;COL3 1;BLB4 2;REDR MSG Temperature (curve) and T3 (crosses) profiles ENDUSE ************************************************************** #cls DISPLAY The problem is as for case 201; but now allowance is made for absorption and emission by the medium between the two plates. The gap between the plates is WG (default = 1.0), and the absorption/emission coefficient of the medium is EMISS. The exact solution for the heat flux is: QRAD = (EH - EC)/(0.75*ROSS*WGAP + 1/EMISH + 1/EMISC - 1) where EH and EC are the black-body emissive powers of the hot and cold surfaces, i.e. temperature**4 * Stefan-Boltzman constant; ROSS=(EMISS+SCATT) is the Rosseland coefficient. The ROSS*WG product gives optical thickness of the gas slab ENDDIS The case is set to exclude influence of the heat conduction in a gas. The user can activate heat conduction by substituting command TERMS(TEM1,N,N,N,P,P,P) by TERMS(TEM1,N,N,Y,P,P,P) . #direct #temps MESG( ENTER optical thickness Kr*Wg (default 1.): READVDU(OPTHI,REAL,1.0) settings of wall thicknesses and the gap between them WSL1 = 0.01; WSL2= 0.01; WGAP= 1.0; conductivity of medium swet to zero KGAS= 0.0 QRAD first used to store EH-EC (see above) QRAD= SIGMA*(THOT**4 - TCLD**4) KROSS deduced from above-set optical thickness; scattering coefficient set to zero; then medium emissivity deduced KROSS= OPTHI/WGAP; SCATT= 0.0; EMISS= KROSS-SCATT MESG( Expected radiative heat flux (W/m**2): QRAD now computed, based on above settings. Note that KGAS has been set to zero, so that NN1 and NN2 = 0 NN1 = KGAS*KROSS/4./SIGMA/THOT**3 NN2 = KGAS*KROSS/4./SIGMA/TCLD**3 QRAD= QRAD + KGAS/WGAP*(THOT-TCLD)*0.75*OPTHI AA1 = (1./EMISH-0.5)/(1.+0.75*NN1) AA2 = (1./EMISC-0.5)/(1.+0.75*NN2) QRAD= QRAD/(0.75*OPTHI + AA1 + AA2) QRAD MESG( Expected gas temperatures near walls are: TGCL = ((SIGMA*TCLD**4 + QRAD*AA2)/SIGMA)**0.25 TGHT = ((SIGMA*THOT**4 - QRAD*AA1)/SIGMA)**0.25 TGCL TGHT #pause SOLVE(TEM1) STORE(PRPS) #geom1 #radflux TERMS(TEM1,N,N,N,N,Y,N); PRNDTL(TEM1)=1.e10 INIADD= F; FIINIT(TEM1)= (THOT+TCLD)/2.; FIINIT(PRPS)= 0. FIINIT(T3)=FIINIT(TEM1) COVAL(HOT,TEM1,FIXVAL,THOT); COVAL(COLD,TEM1,FIXVAL,TCLD) INIT(SOL1,PRPS,0.0,111.); INIT(SOL2,PRPS,0.0,112.) LSWEEP= 500 IXMON=NX/2+1;IYMON=NY/2+1;IZMON=NZ/2+1 NXPRIN=1; NYPRIN=1; NZPRIN=1 OUTPUT(LTLS,N,N,N,N,N,N); OUTPUT(WDIS,N,N,N,N,N,N) load macro for storing and setting emissivity and scattering coefficient, using EMISS, SCATT, EMISH and EMISC load($r193) VARMAX(T3)=THOT;VARMIN(T3)=TCLD VARMAX(TEM1)=THOT;VARMIN(TEM1)=TCLD Activating the following In-Form statements (by moving them 2 spaces to the left) enables the coefficients in the equations for TEM1 and T3 to be inspected. inform7begin (stored var #3-1 is t3-tem1) (stored var #rs1 is resi(tem1)) (stored var #rs3 is resi(t3)) (stored var #ap1 is apco(tem1)) (stored var #ap3 is apco(t3)) if(idir.eq.1) then (stored var #ae1 is aeco(tem1)) (stored var #ae3 is aeco(t3)) endif if(idir.eq.2) then (stored var #an1 is anco(tem1)) (stored var #an3 is anco(t3)) endif if(idir.eq.3) then (stored var #ah1 is ahco(tem1)) (stored var #ah3 is ahco(t3)) endif inform7end