The effect of viscosity and Darcy number on the start of convective motion in a rotating porous medium layer saturated by a couple-stress fluid

Abstract

In chemical process industry, food process industry, centrifugal filtration processes, and rotating machinery, convective flows are characterized by rotation, where couple-stress fluid (a type of non-Newtonian fluid) with variable viscosity in a porous medium can act as a working fluid. In the present work, the combined effect of the temperature-dependent viscosity, the Darcy number and the uniform rotation on the arrival of convective motion in a couple-stress fluid saturated porous layer is examined applying linear stability concept. The outcome of the viscosity variation parameter Q, the rotation parameter $T_D$ , the couple-stress parameter $C_s$ , and the Darcy number $\mathit{Da}$ on both stationary and oscillatory convections is investigated analytically and presented graphically in terms of the critical thermal Darcy–Rayleigh number $R_{t,c}$ . Below the critical value $R_{t,c}$ , no convective motion arises in the considered system. It is recognized that the arrival of convective motion is oscillatory only if the rotation parameter $T_D$ surpasses a threshold value which in turn depends on other physical parameters. The impact of the viscosity variation parameter Q has a destabilizing influence, while the couple-stress parameter $C_s$ , rotation parameter $T_D$ , the Darcy number $\mathit{Da}$ , the Prandtl number ⪻, and the heat capacity ratio γ show stabilizing influences on the stability of arrangement.