Free Convection in a Porous Wavy Cavity Based on the Darcy-Brinkman-Forchheimer Extended Model

Abstract

A numerical investigation is carried out for steady, free convection inside a cavity filled with a porous medium. The cavity has vertical wavy walls which are isothermal. The top and bottom horizontal straight walls are kept adiabatic. The numerical method is based on the finite-volume method with body-fitted and nonorthogonal grids. A generalized model, which includes a Brinkman term, a Forcheimmer term, and a nonlinear convective term, is used. Studies are carried out for a range of wave ratio λ = 0 − 1.8, aspect ratio A = 1–5, Darcy number Da = 10⁻¹–10⁻⁶, and Darcy-Rayleigh number Ra∗ = 10–10⁵. Results are presented in the form of streamlines, isotherms, and local and average Nusselt numbers. The generalized model which considers viscous, inertia, and convective effects enables results to be obtained for a wider range of Darcy and Rayleigh numbers.