Natural Convection in a Vertical Cavity Partially Filled With Porous Medium: Effect of Aspect Ratio, Darcy and Fluid Rayleigh Numbers

Numerical investigation of natural convection in a rectangular cavity partially filled with fluid-saturated porous medium has been carried out. Rayleigh number (10⁴ to 10⁷) and Darcy Number (10⁻¹ to 10⁻¹⁰), Aspect Ratio (0.75, 1.0, and 1.25) are considered parameters. The governing equations have been solved numerically by SIMPLEC, a finite volume method on staggered grid arrangement. Power-law scheme has been used to approximate convective and diffusive fluxes. The results obtained are presented for the streamlines, isotherms and variation of Nusselt number at the walls. For values of Darcy Number above 10⁻⁴, a convective regime has been found to exist in which flow is nearly independent of Darcy Number, while at low values (below 10⁻⁶) the conduction dominated region occurs in the porous medium. Increase in Aspect Ratio increases intensity of circulation while maintaining the symmetry with respect to diagonals. Increase in aspect ratio increases the region of uniform temperature which covers most of the porous region.