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

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 [Formula: see text], the couple-stress parameter [Formula: see text], and the Darcy number [Formula: see text] on both stationary and oscillatory convections is investigated analytically and presented graphically in terms of the critical thermal Darcy–Rayleigh number [Formula: see text]. Below the critical value [Formula: see text], no convective motion arises in the considered system. It is recognized that the arrival of convective motion is oscillatory only if the rotation parameter [Formula: see text] 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 [Formula: see text], rotation parameter [Formula: see text], the Darcy number [Formula: see text], the Prandtl number ⪻, and the heat capacity ratio γ show stabilizing influences on the stability of arrangement.