Linear and Weakly Nonlinear Stability of Thermo-Solutal Magnetoconvective Chemically Reacting Couple Stress Fluid in Porous Medium

Abstract

The aim of the current study is to investigate the stability analysis in case of the linear as well as nonlinear of a thermo-solutal chemically reactive couple stress fluid under uniform magnetic field convection. Investigations have been conducted on the impact of chemical reaction and external vertical magnetic field on the commencement of double diffusive convection in couple stress fluid between infinite horizontal parallel plates. Darcy's modified law governs the flow in porous media and the Oberbeck-Boussinesq approximation is accurate. For modelling the momentum equation, the modified Darcy equation with the time derivative and inertia terms is utilized. Expressions for the Rayleigh numbers with finite amplitude, oscillatory, and stationary states are found in accordance with the regulating factors. Graphics are used to illustrate how the couple-stress parameter, solute Rayleigh number, Vadasz number and diffusivity ratio affect stationary, oscillatory and finite-amplitude convection. Stationary, oscillatory and finite-amplitude convection are found to be stabilized by the couple-stress parameter and the solute Rayleigh number. The normal mode analysis method is utilized to look into the linear stability of flow dynamics after the nonlinear mathematical problem has been linearized. When stationary and finite-amplitude modes are present, the diffusivity ratio has a destabilizing effect; when oscillatory convection is present, it has a dual effect. Oscillatory convection develops earlier when the Vadasz number is higher. The couple-stress parameter and diffusivity ratio both increase with increasing solute Rayleigh number values, but the heat and mass transfer decreases as these values rise. Using double Fourier series, a generalized weakly nonlinear stability analysis is done. The research illustrates how various regulating parameters support and destabilize the flow dynamics. The influence of finite-amplitude convection on stability is also examined. Furthermore, the best conditions for stationary and oscillatory convection are based on altering the couple stress flow stability by controlling the applied magnetic field.

Keywords

• magnetoconvection
• thermo-solutal
• chemical reaction
• linear and nonlinear stability
• couple stress fluid
• porous medium