Effect of Prandtl Number on Linear Stability of Mixed Convective Flow in a Vertical Porous Annulus: A LTNE Approach

Abstract

A comprehensive numerical study on linear stability of fully developed mixed convective flow in a vertical annulus filled with saturated porous medium is investigated. A local thermal non-equilibrium (LTNE) approach is considered. The flow is induced by external pressure gradient and buoyancy force. The non-Darcy Brinkman-Forchheimer extended model is considered. The governing equations are solved by spectral collocation method. Special attention is given to understand the effect of thermal non-equilibrium parameters: inter phase heat transfer coefficient (H) and porosity scaled thermal conductivity ratio (?) on instability boundary of basic flow in (Pr, Ra) -plane. Stability results indicate that for high permeable porous media depending on Prandtl number, the flow is least stable under either first azimuthal mode or zero azimuthal modes. The stability criteria of basic flow decreases on increasing the Prandtl number. Increasing of H stabilizes the basic flow, whereas, increasing of ? destabilizes it. Keywords: Porous media, mixed convection, linear stability, thermal non-equilibrium, non-Darcy model.