Convection instability in a vertical porous Brinkman fluid layer with uniform horizontal throughflow

Abstract

The present paper examines the effect of a uniform horizontal throughflow on the linear stability of buoyancy-driven convection in an infinite vertical fluid layer saturating a Brinkman porous medium. Two different constant temperature distributions are assigned on the rigid-permeable boundaries, so that there exists a horizontal temperature gradient. The resulting eigenvalue problem is solved numerically using the Chebyshev collocation method. The neutral stability curves are presented, and the critical values of the Rayleigh number are calculated for various prescribed values of the governing parameters. The onset of convection relies on several dimensionless parameter values of Darcy number Da, Péclet number Pe (it determines the strength of the horizontal throughflow), and Darcy-Prandtl number Pr_D. It is shown that there exists a critical value of the throughflow parameter Pe, which will increase with Da. Below the critical value of Pe, critical Rayleigh number Ra_c becomes smaller with the increase of Pe, which means the horizontal throughflow has a destabilizing effect. However, when Pe is larger than the critical value, an opposite conclusion can be drawn and the horizontal throughflow has a stabilizing effect. Moreover, the influence of the Pr_D on convection instability exhibits a dual behavior depending on Pe. The Pr_D stabilizes the system when Pe is small, and it destabilizes the system when Pe is large.