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 [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.

Influence of anisotropy on the Jeffrey fluid convection in a horizontal rotary porous layer

“…To get an analytical result of Equations (19)–(21), the general Galerkin practice is used. Thus, we consider the following 35,50–60 : …”

Chemical Reaction and Internal Heating Effects on the Double Diffusive Convection in Porous Membrane Enclosures Soaked with Maxwell Fluid

“…It is known that fluids that take place in the majority of the above-mentioned applications and in nature exhibit non-Newtonian fluid features [ 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 ]. The problem of double-diffusive instability in a porous medium layer drenched by non-Newtonian fluid taking an Oldroyd model was explored by Malashetty and Swamy [ 39 ].…”

Couple stress effects on the stability of three‐component convection‐diffusion in a porous layer

“…The combined influence of temperature‐dependent viscosity and internal heat source on the onset of convection in porous enclosures saturated by a viscoelastic fluid is studied by Yadav and Maqhusi 8 . Besides, double‐diffusive convection in a layer of couple stress fluid saturating a porous medium has also been investigated 9‐17 . Yadav et al 18 discussed the thermal instability in a rotating porous layer saturated by a non‐Newtonian nanofluid with thermal conductivity and viscosity variation.…”

“…8 Besides, double-diffusive convection in a layer of couple stress fluid saturating a porous medium has also been investigated. [9][10][11][12][13][14][15][16][17] Yadav et al 18 discussed the thermal instability in a rotating porous layer saturated by a non-Newtonian nanofluid with thermal conductivity and viscosity variation. Chand et al 19 analyzed the thermal instability of a couple stress nanofluid with vertical rotation in a porous medium.…”