Linear instability of the vertical throughflow in a porous layer saturated by a power-law fluid with variable gravity effect

The present study investigates the thermal convection of a power-law fluid in a horizontal porous layer that is heated from below. The study of flow in a porous medium is important because of its applications in various fields such as agriculture, geothermal sciences, and engineering. Linear instability analysis is performed using the normal mode method to solve the governing equations after non-dimensionalization. The bvp4c routine in MATLAB R2020a has been used to solve the raised problem for linear instability. The impact of gravity parameter, Peclet number, and power-law index on linear instability has been investigated. Linear and quadratic variations of gravity field are considered. From the results, it is evident that the critical Rayleigh number exhibits a non-monotonic relationship with the Peclet number. Increasing the gravity variation parameter leads to a more stable system, particularly in the case of linear gravity variation.