Integral transform solution for natural convection in three-dimensional porous cavities: Aspect ratio effects

Three-dimensional natural convection in box-like cavities filled with a porous material is revisited, by considering a transient formulation for the energy balance and a quasi-steady formulation for the flow problem. The Generalized Integral Transform Technique (GITT) is employed in the hybrid numerical-analytical solution of the Darcy law based model for vertical cavities (insulated vertical walls with differentially prescribed horizontal wall temperatures), employing the vorticity-vector potential formulation. Comparisons with previously reported numerical solutions are performed and the transition between conductive and convective states is illustrated, centering on the aspect ratio influence on the flow and heat transfer phenomena. A set of reference results for the steady-state behavior under different aspect ratio is provided for covalidation purposes.