#$r002 PHOTON USE AUTOPLOT file PHI 5 cl;d 1 h1;d 1 ha;col3 1;blb4 2;redr msg temperature profile; pressto continue ENDUSE TEXT(1D RADIATION+HEAT SOURCE IN A TUBE:123 TITLE DISPLAY The problem considered is similar to case 122 above, except that the radiative heat transfer takes place in a tube with a symmetry plane at r=0 and an isothermal wall at r=D/2. The problem is to solve for the temperature distribution given the wall temperature Tw, the optical thickness Kr*D; and the wall emissivity emw. Kr is the Rosseland mean absorption coefficient which is given by: Kr=(a+s). ENDDIS 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 = 0.25*D*Qv (Egc - Ew)/Qw = (3./16)*Kr*D+1./emw-0.5+9./(8.*Kr*D) (Egw - Ew)/Qw = (1./emw-0.5+9./(8.*Kr*D)) Eg = Egc - 0.75*Kr*Qw*r**2/D where Qw is the wall heat flux, and Egc and Egw are the gas emissive powers at the centre line and wall. REAL(EMWN,TWN,EWN,TA,GY,EG,EGC,EGW,ACON) REAL(QRAD,QVOL,KRAD,OTHICK,DIAM,QRADA,TWNA,QWNA,TGCA,TGWA) CHAR(CH1);INTEGER(JJM1) MESG( Enter optical thickness 0 < Kr*L << 10.0 (default 5) READVDU(OTHICK,REAL,5.0) DIAM=1.0;KRAD=OTHICK/DIAM SCATT=0.0;EMISS=KRAD-SCAT EMWN=1.0;TWN=1000.0;EWN=SIGMA*TWN**4;QRAD=EWN;QVOL=EWN/DIAM ** analytical solution QWNA=QVOL*0.25*DIAM EGC=EWN+QWNA*(3.*OTHICK/16.+1./EMWN-0.5+9./(8.*OTHICK)) EGW=EWN+QWNA*(1./EMWN-0.5+9./(8.*OTHICK)) TGCA=(EGC/SIGMA)**0.25;TGWA=(EGW/SIGMA)**0.25 ACON=QWNA/(EGC-EWN) GROUP 3,4,5. X,Y,Z-direction grid specification CARTES=F;GRDPWR(Y,50,0.5*DIAM,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) READVDU(CH1,CHAR,H1) IF(:CH1:.EQ.TEM1) THEN + MESG( TEM1 solution selected ELSE + MESG( H1 solution selected + TMP1=LINH;TMP1B=1.0/CP1 ENDIF RADIAT(RADI,EMISS,SCATT,: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 9. Properties of the medium (or media) GROUP 10. Inter-phase-transfer processes and properties GROUP 11. Initialization of variable or porosity fields FIINIT(:CH1:)=TWN;FIINIT(SRAD)=EWN ** analytical solution STORE(HA);ACON=0.75*KRAD*QWNA/DIAM 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=EGC-ACON*GY*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(WALLRB,NORTH,1,NX,NY,NY,1,NZ,1,1) COVAL(WALLRB,SRAD,2.*EMWN/(2.0-EMWN),EWN) ** uniformly-distributed volumetric heat source PATCH(QHEAT,VOLUME,1,NX,1,NY,1,NZ,1,1) COVAL(QHEAT,:CH1:,FIXFLU,QVOL) GROUP 15. Termination of sweeps LSWEEP=500;LITC=5 GROUP 16. Termination of iterations SELREF=F;RESREF(:CH1:)=1.E-4*QRAD;RESREF(SRAD)=RESREF(:CH1:) GROUP 17. Under-relaxation devices RELAX(:CH1:,LINRLX,0.3);RELAX(SRAD,LINRLX,0.6) GROUP 18. Limits on variables or increments to them VARMIN(:CH1:)=0.5*TWN GROUP 19. Data communicated by satellite to GROUND GROUP 20. Preliminary print-out GROUP 21. Print-out of variables GROUP 22. Spot-value print-out IYMON=1;NPLT=20;NYPRIN=1;ITABL=3 GROUP 23. Field print-out and plot control OUTPUT(:CH1:,Y,N,N,Y,Y,Y);PATCH(YWISE,PROFIL,1,1,1,NY,1,1,1,1) PLOT(YWISE,:CH1:,0.0,0.0);PLOT(YWISE,SRAD,0.0,0.0) GROUP 24. Dumps for restarts TSTSWP=-1