Effect of Vadasz term on the onset of convection in a Darcy-Brinkman anisotropic rotating porous medium in LTNE

TL;DR

This paper investigates how the Vadasz inertia term influences the onset of convection in a rotating anisotropic porous medium, revealing it promotes oscillatory convection without affecting steady convection onset.

Contribution

It analytically and numerically demonstrates the Vadasz term's role in favoring oscillatory convection and examines the effects of rotation and anisotropies on instability onset.

Findings

Vadasz term promotes oscillatory convection.

Steady convection onset remains unaffected by the Vadasz term.

Rotation and anisotropies influence the instability conditions.

Abstract

In the present paper, the effect of the Vadasz inertia term on the onset of convective motions for a Darcy-Brinkman model is investigated. It is proved that this term leads to the possibility for oscillatory convection to occur. Hence, convection can occur via either oscillatory or steady motions. It is proved analytically that the onset of steady convection is not affected by the Vadasz term, while oscillatory convection is favoured by it. Moreover, conditions to rule out the occurrence of oscillatory convection are determined numerically. The influence of rotation, interaction coefficient and mechanical and thermal anisotropies on the onset of instability is investigated, both analytically and numerically.