GROUP 1. Run title and other preliminaries TEXT(Trans Heat Conduction-Uniform Fin TITLE DISPLAY Cases 110 to 114 illustrate how "porosity" values may be used to introduce not only geometrical data, but also variations in thermal conductivity, specific heat and heat-transfer coeff. In case 110, the cross-section and other properties are uniform. Subsequent cases introduce non-uniformities, by way of porosity, one by one. A sketch of the geometry for case 110 follows: /--/| /**/ | /**/ | /**/ | /**/ <------- surface in contact with |--| | ^ surrounding fluid |**| | | at temperature = 0.0 |**| | |x |**| | | ///// |**| ////////////////////////////////// ////// |**| ////////////////////////////////// /////// |**| ////// base at temperature = 1.0 / //////// |**| ////////////////////////////////// ///////// |--|////////////////////////////////// y----> l(pause That it is possible to act in this way does not mean that it is necessary or even recommended. These cases were very early entries to the library, and have been retained for historical interest. However, the treatment of H1 as though it represented temperature is valid only for a constant specific heat; and, in the final case of the series, the specific heat is supposed to vary. Nowadays, use of TEM1 is recommended rather than H1; and In-Form provides a much more convenient way of introducing variations of properties and boundary conditions. ENDDIS ** The locally-defined variables are as follows: COEF Surface heat-transfer coefficient COND1 Thermal conductivity SPHT1 Specific heat REAL(COEF,COND1,SPHT1) COND1=400.0; COEF=1.0E01; SPHT1=500.0 GROUP 2. Transience; time-step specification ** The transient lasts for 20 seconds STEADY=F; GRDPWR(T,100,20.0,1.0) GROUP 3. X-direction grid specification ** The fin length is 0.1 meters GRDPWR(X,20,0.1,1.0) GROUP 4. Y-direction grid specification ** The fin thickness is twice YVLAST YVLAST=0.001 GROUP 7. Variables stored, solved & named SOLVE(TEMP) GROUP 8. Terms (in differential equations) & devices ** Built-in source and convection terms are cut out TERMS(TEMP,N,N,Y,Y,P,P) GROUP 9. Properties of the medium (or media) ENUL=1.0; RHO1=1.E4; PRNDTL(TEMP)=SPHT1*ENUL*RHO1/COND1 GROUP 11. Initialization of variable or porosity fields FIINIT(TEMP)=1.0 GROUP 13. Boundary conditions and special sources ** Uniform zero temperature at the fin surface PATCH(SURFACE,FREEN,1,NX,1,1,1,1,1,LSTEP) COVAL(SURFACE,TEMP,COEF,0.0) ** Fixed temperature at the fin root WALL(ROOT,WEST,1,1,1,1,1,1,1,LSTEP) COVAL(ROOT,TEMP,1.0/PRNDTL(TEMP),1.0) GROUP 15. Termination of sweeps ** One sweep suffices to yield the exact solution LSWEEP=1 SPEDAT(SET,GXMONI,TRANSIENT,L,F) GROUP 21. Print-out of variables NPRMNT=LSTEP GROUP 23. Field print-out and plot control OUTPUT(TEMP,Y,Y,N,N,N,N) NXPRIN=NX/10; NTPRIN=LSTEP/2; ORSIZ=0.2 PATCH(FIXEDT,PROFIL,1,NX,1,1,1,1,1,LSTEP) PLOT(FIXEDT,TEMP,0.0,1.0) PATCH(FINTIP,PROFIL,NX,NX,1,1,1,1,1,LSTEP) PLOT(FINTIP,TEMP,0.0,0.0) GROUP 24. Dumps for restarts