Chemically driven Rayleigh-Benard convection in a sparsely distributed porous medium saturated with a couple-stress fluid

Chemically driven Rayleigh-Benard convection in a sparsely distributed porous medium saturated with a couple-stress fluid

Mathematics

The problem of Rayleigh-Benard convection in a couple-stress fluid saturated sparsely distributed porous medium with chemical reaction is studied within the framework of linear stability analysis. Only infinitesimal disturbances are considered. The linear stability analysis is based on the normal mode technique. The Darcy-Brinkman law is used to model the momentum equation. Closed form solution for the basic quiescent state is first obtained. The principle of exchange of stabilities is valid and the existence of oscillatory instability is ruled out. The expression for the stationary media-Rayleigh number is obtained as a function of the governing parameters, viz., the wave number, the couple-stress parameter, the Frank-Kamenetskii number, the porous parameter and the Brinkman number. The Galerkin method is used to determine the eigenvalues. The effect of various parameters on the stability of the fluid layer is discussed through figures.

B.N DEEPIKA

CHRIST (Deemed to be University)

2010

English

M Phil