Dissolution-driven convection of a power-law fluid in a porous medium in the presence of chemical reaction

Abstract

The flow through porous medium accounts for numerous applications in various fields namely, agriculture, geothermal sciences, and engineering. Furthermore, dissolution-driven convection in porous media has grabbed great attention in recent years due to its practical applications in long-term geological storage of carbon dioxide, in the production of mineral deposits, and other industrial applications. In this regard, the current numerical analysis focuses on addressing the thermal instability of dissolution-driven convective phenomena of a power-law fluid through a porous horizontal domain with a first-order chemical reaction. For linear stability analysis, the method of normal modes has been employed to solve governing dimensionless equations which give rise to an eigenvalue problem. The bvp4c routine in MATLAB R2020a has been used to solve the raised problem for the onset of convection. The impact of Damkohler number, Peclet number, and power-law index on the onset of convection has been investigated. The role of these critical parameters is found to be highly significant in stabilizing the system. An increase in the power-law index causes stabilization or destabilization in the system, depending on the Peclet number. An enhancement in the magnitude of Damkohler number makes the system stable for all values of the Peclet number. Also, Damkohler and critical Rayleigh number are inter-related, that is, an increment in Damkohler number results in the enhancement of critical Rayleigh numbers, which in turn leads to stabilization of the system. The critical wave number is observed to have a remarkable influence on Damkohler number as well as power-law index.