Finite Element Simulation with Heat lines and Entropy Generation Minimization during Natural Convection within Porous Tilted Square Cavities

A complete finite element analysis on the effect of the Darcy number for heat-flow visualization (via heatlines) and entropy generation due to heat transfer (S-theta) and fluid friction (S-psi) within inclined porous cavities is presented. Heat lines are obtained via solution of the Poisson equation using the finite element method. Strong features on conductive and convective heat fluxes were found for high Darcy number flows. Generalized formulations on finite element basis functions are used to calculate all derivatives (S-theta) and (S-psi) for entropy generation within tilted cavities for all tilted angles (phi). On the basis of the entropy generation minimization approach, it has been concluded that the cavities with inclination angles phi <= 30 degrees for lower Pr fluid (Pr = 0.025) and phi = 15 degrees for higher Pr (Pr = 998) may be an efficient strategy for optimal thermal processing.