Onset of Darcy–Benard Penetrative Convection in Porous Media

Abstract

The onset of Darcy–Benard penetrative convection in a liquid saturated porous layer of high permeability of practical importance is investigated by employing the Brinkman–Forchheimer– Lapwood extended Darcy flow model with fluid viscosity different from effective viscosity. The lower boundary is taken to be rigid and isothermal and the upper surface is free and subject to the general thermal condition. The critical eigen values are obtained numerically, in general, using Galerkin method. The stability of the system is found to be dependent on the dimensionless internal heat source strength , permeability parameter and the ratio of effective viscosity to fluid viscosity . It is observed that the increase in the value of permeability parameter is to delay while increase in the value of internal heat source strength is to hasten the onset of convection in a fluid saturated porous layer.

Keywords

• Penetrative convection; Volumetric heat source; Darcy–Benard convection.