Linear Stability of Double Diffusive Convection of Hadley-prats Flow with Viscous Dissipation in a Porous Media

Abstract

Linear stability analysis of double diffusive convection in a horizontal fluid saturated porous layer has been carried out. Effects of viscous dissipation, horizontal mass flow are taken into account. Combined effects of horizontal mass flow, viscous dissipation may cause instability in the fluid system. To carry out linear stability analysis, disturbances are the form of longitudinal rolls, transverse rolls have been considered. In order to solve eigenvalue problem numerically, Runge-Kutta and shooting methods have been employed for the case of longitudinal rolls. Chebyshev-Tau method has been used for the case of transverse rolls. Critical wave number aC , critical vertical thermal Rayleigh number RaC are evaluated for assigned values of flow governing parameters. For the onset of convection, physical explanation is given.