Non-linear thermohaline instability of a Jeffrey fluid in a porous layer with chemical reaction

Abstract

Porous materials have various applications in solar energy systems, including adsorption, insulation, and evaporation. This study examines the use of porous materials in solar energy systems and focuses on the thermohaline convection of a Jeffrey fluid in a horizontal porous layer. The analysis includes both linear and non-linear approaches and employs the method of normal modes to solve the governing equations. It demonstrates that there is a coincidence between the linear and non-linear stability thresholds and shows that linear stability alone captures all the physics of the system. The linear instability is solved using the one-term Galerkin approach, while the non-linear instability is solved numerically using the bvp4c routine in MATLAB. The study highlights the destabilising effect of the Jeffrey parameter on the fluid layer, while the solute Rayleigh number is found to stabilise the flow. The Damkholer number shows no impact on the stationary convection when the thermal and solutal diffusivities are equal; however, it exhibits a stabilising influence on the oscillatory convection. Additionally, the Vadasz number does not affect the stationary instability but contributes to the destabilisation of the oscillatory instability.