The effect of a horizontal pressure gradient on the onset of a Darcy–Bénard convection in thermal non-equilibrium conditions

In this paper there is studied the effect of a horizontal pressure gradient on the onset of Darcy–Bénard convection in a fluid-saturated porous layer heated from below, when the fluid and solid phases are not in local equilibrium. In the context of a linearized stability analysis, the problem is transformed into an eigenvalue equation. The problem, when cast in dimensionless form, contains three parameters (the pressure gradient, the porosity-scaled conductivity ratio and the scaled inter-phase heat transfer coefficient). This problem is solved numerically by using two methods: Galerkin approach and the numerical solver dsolve from Maple and comparisons between these methods are performed. Critical values of Rayleigh number, wave number and frequency are obtained for various values of the problem parameters.