On the Stability of Hadley-Flow in a Horizontal Porous Layer with Non-Uniform Thermal Gradient and Internal Heat Source

Abstract

The present study deals with the effects of non-uniform inclined thermal gradient and internal heat source effect on the stability of buoyant flows in a fluid-saturated horizontal porous layer. Both linear and non-linear stability analyses have been performed. The non-linear stability analysis has been carried out by using the energy functional. The eigenvalue problems in both cases are solved numerically by shooting and Runga-Kutta methods. It is observed that the preferred mode at the onset of convection is longitudinal stationary mode. Comparison between linear and energy thresholds is given and found that the flow is stabilized at higher horizontal Rayleigh number for linear and non-linear cases irrespective of heat source. For fixed horizontal thermal Rayleigh number, increasing the value of internal heat source parameter destabilizes the system and favors the convection to commence.