#immersol)
#declare
IMMERSOL Emitting and absorbing gray media
(1D, TEM1)
TEXT(IMMERSOL 1D Radiative equilibrium :202
TITLE
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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
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#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