GROUP 1. Run title and other preliminaries TEXT(2D Laminar Duct Flow And Heat Trans TITLE DISPLAY The case considered is three-dimensional fully-developed, laminar flow and heat transfer of an incompressible, constant- property fluid in a rectangular duct of aspect ratio alfa=0.5, where alfa=height/width. The calculations are performed for a Reynolds number of 100, a Prandtl number of 1.0 and a constant temperature boundary condition is applied on all four sides of the duct. The solution exploits symmetry by performing the calculation over one quadrant of the duct cross section only. The flow Reynolds number is based on the hydraulic diameter of the duct. ENDDIS Data on the friction factor, pressure drop and Nusselt number may be found in 'Handbook of Heat Transfer Fundamentals', Ed. W.M.Rohsenow, J.P.Hartnett & E.N.Ganic', Chapter 7, McGraw Hill, 2nd Edition, (1985). The friction factor ( and hence pressure drop ) is taken from the correlation of Shah and London, which is given in the reference just cited. The Nusselt number is based on the hydraulic diameter and the difference between the wall and the bulk temperature. For the Reynolds number, thermal boundary condition, and duct aspect ratio considered here, the data are friction factor f=0.1556, pressure drop dp/dz=0.233 and Nu=3.383. The PHOENICS predictions are in excellent agreement with the data, yielding f=0.1556, dp/dz=0.233 and Nu=3.41. It should be noted that, as predicted by PHOENICS, no secondary flows are expected for fully-developed laminar flow. Finally, one may BFC=T with NONORT=T or F to verify that the same results are obtained with the body-fitted-coordinates facility. BOOLEAN(HEAT);HEAT=T REAL(HEIGHT,WIDTH,ALF,HD2,WD2,WIN,DPDZ,REY,FRIC) REAL(AIN,DHYD,FLOWIN) REAL(QIN,DTDZ,CP,COND,AWAL,TW) ** ALFA = HEIGHT/WIDTH WIDTH=2.0;ALF=0.5;HEIGHT=ALF*WIDTH HD2=0.5*HEIGHT;WD2=0.5*WIDTH WIN=1.0 REY=100.;DHYD=4.*WIDTH*HEIGHT/(2.*HEIGHT+2.*WIDTH) GROUP 3. X-direction grid specification AIN=HD2*WD2 XULAST=WD2;NX=15;GRDPWR(X,NX,XULAST,1.0) GROUP 4. Y-direction grid specification YVLAST=HD2;NY=15;GRDPWR(Y,NY,YVLAST,1.0) GROUP 7. Variables stored, solved & named SOLVE(P1,U1,V1,W1) GROUP 8. Terms (in differential equations) & devices TERMS(W1,N,P,P,P,P,P) IF(HEAT) THEN + SOLVE(H1);TERMS(H1,N,P,P,P,P,P);PRNDTL(H1)=1.0 ENDIF GROUP 9. Properties of the medium (or media) RHO1=1.0;ENUT=0.0 FLOWIN=RHO1*WIN*AIN;ENUL=WIN*DHYD/REY ** compute expected pressure drop from Shah-London correlation REAL(ALF2,ALF3,ALF4,ALF5,TERM1);ALF2=ALF*ALF;ALF3=ALF2*ALF ALF4=ALF3*ALF;ALF5=ALF4*ALF;TERM1=1.-1.3553*ALF+1.9467*ALF2 FRIC=24.*(TERM1-1.7012*ALF3+0.9564*ALF4-0.2537*ALF5)/REY FRIC DPDZ=4.*RHO1*FRIC*WIN*WIN/(2.*DHYD) DHYD DPDZ IF(HEAT) THEN + QIN=0.1;CP=1.0 + AWAL=(WD2+HD2)*ZWLAST + DTDZ=QIN*AWAL/(CP*FLOWIN) + TW=10. ENDIF GROUP 11. Initialization of variable or porosity fields FIINIT(W1)=WIN IF(HEAT) THEN + FIINIT(H1)=0.5*TW ENDIF GROUP 12. Convection and diffusion adjustments PATCH(GP12CONH,CELL,1,NX,1,NY,1,NZ,1,1) COVAL(GP12CONH,U1,0.0,0.0);COVAL(GP12CONH,V1,0.0,0.0) COVAL(GP12CONH,W1,0.0,0.0) GROUP 13. Boundary conditions and special sources PATCH(WALLT,NWALL,1,NX,NY,NY,1,NZ,1,1) COVAL(WALLT,W1,1.0,0.0);COVAL(WALLT,U1,1.0,0.0) PATCH(WALLS,EWALL,NX,NX,1,NY,1,NZ,1,1) COVAL(WALLS,W1,1.0,0.0);COVAL(WALLS,V1,1.0,0.0) PATCH(RELIEF,CELL,NX/2,NX/2,NY/2,NY/2,1,NZ,1,1) COVAL(RELIEF,P1,FIXP,0.0);COVAL(RELIEF,H1,ONLYMS,SAME) FDFSOL=T;USOURC=T PATCH(FDFW1DP,VOLUME,1,NX,1,NY,1,NZ,1,1) COVAL(FDFW1DP,W1,FLOWIN,GRND1) IF(HEAT) THEN ** constant wall-temperature boundary condition + PATCH(FDFCWT,PHASEM,1,NX,1,NY,1,NZ,1,1) + COVAL(FDFCWT,H1,DTDZ,TW) + COVAL(WALLS,H1,1.0/PRNDTL(H1),TW) + COVAL(WALLT,H1,1.0/PRNDTL(H1),TW) + COVAL(GP12CONH,H1,0.0,0.0) ENDIF GROUP 15. Termination of sweeps LSWEEP=20;LITHYD=2;LITER(W1)=15 GROUP 16. Termination of iterations RESREF(P1)=1.E-12*WIN*AIN RESREF(W1)=1.E-12*DPDZ*ZWLAST*AIN RESREF(U1)=RESREF(W1);RESREF(V1)=RESREF(W1) IF(HEAT) THEN + RESREF(H1)=1.E-12*QIN*ZWLAST*AWAL + ISWC1=5 + QIN + COND=RHO1*CP*ENUL/PRNDTL(H1) + COND ENDIF GROUP 17. Under-relaxation devices REAL(DTF);DTF=5.*(YVLAST/NY)**2/ENUL RELAX(U1,FALSDT,DTF);RELAX(V1,FALSDT,DTF) RELAX(W1,FALSDT,DTF) GROUP 22. Spot-value print-out IXMON=NX-2;IYMON=NY-2;TSTSWP=-1 GROUP 23. Field print-out and plot control NPLT=1;NYPRIN=3;NXPRIN=3 GROUP 24. Dumps for restarts