ONSET OF DARCY-BRINKMAN CONVECTION IN A ROTATING POROUS LAYER INDUCED BY PURELY INTERNAL HEATING

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Abstract
The influence of rotation and Darcy number on the criterion for the onset of convection induced by purely internal heating in a porous layer is investigated. The boundaries are considered to be free-free, rigid-rigid, lower-rigid, and upper-free boundaries and subjected to two sets of thermal boundary conditions, namely, case (i) both boundaries isothermal and case (ii) lower insulated and upper isothermal. The Darcy-Brinkman model, with fluid viscosity different from effective viscosity, is used to characterize the fluid motion in porous medium. The coupled governing partial differential equations are transformed into ordinary differential equations by use of linear stability analysis and solved numerically using the higher order Galerkin method with the internal Darcy-Rayleigh number as the eigenvalue. Results indicate that the nature of boundaries, Darcy number, and speed of rotation significantly influence the stability characteristics of the system. Convection, when it occurs for case (i) where both boundaries are isothermal, is concentrated in the upper portion of the layer; whereas for case (ii) with lower insulated and upper isothermal boundaries, it is concentrated in the whole layer. The effect of increasing rotation parameter inhibits the onset of convection, while Darcy number shows dual behavior on the criterion for the onset of convection in the presence of rotation. Some known results are also recovered as special cases of the present study.

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