The onset of a Darcy–Brinkman convection using a thermal nonequilibrium model. Part II

A linearized analysis is performed in this paper in order to analyze the onset of Darcy–Brinkman convection in a fluid-saturated porous layer heated from below, by considering the case when the fluid and solid phases are not in local thermal equilibrium. The problem is transformed into an eigenvalue equation which is solved in a first step by using an one-term Galerkin approach: an explicit relationship between the Darcy–Rayleigh number based on the fluid properties R and the horizontal wave number k is obtained. Minimization of R over k is performed analytically and finally, critical values for R and k are obtained for various values of the three parameters of the problem, namely the Darcy number D, the porosity-scaled conductivity ratio γ and the scaled inter-phase heat transfer coefficient H. In a second step, a general N-terms Galerkin approach is used and finally comparisons are performed between the results given by these two approaches.