Thermal convection in an inclined porous layer with Brinkman law

Abstract

A model for thermal convection of a fluid saturating an inclined layer of porous medium with a Brinkman law and stress-free boundary conditions is studied. When the Darcy number $$\tilde{D}a$$ is zero, this problem has been studied by Rees and Bassom (Acta Mech 144(1–2):103–118, 2000). When the Brinkman term is present in the model ( $$\tilde{D}a\not =0$$ ) the basic motion is a combination of hyperbolic and polynomial functions. With the Chebyshev collocation method we study the linear instability of the basic motion for three-dimensional perturbations. We also give nonlinear stability conditions and, for longitudinal perturbations, we prove the coincidence of linear and nonlinear critical Rayleigh numbers.