The Coriolis Effect on Thermal Convection in a Rotating Sparsely Packed Porous Layer in Presence of Cross-Diffusion

Abstract

The effect of rotation and cross-diffusion on convection in a horizontal sparsely packed porous layer in a thermally conducting fluid is studied using linear stability theory. The normal mode method is employed to formulate the eigenvalue problem for the given model. One-term Galerkin weighted residual method solves the eigenvalue problem for free-free boundaries. The eigenvalue problem is solved for rigid-free and rigid-rigid boundaries using the BVP4c routine in MATLAB R2020b. The critical values of the Rayleigh number and corresponding wave number for different prescribed values of other physical parameters are analyzed. It is observed that the Taylor number and Solutal Rayleigh number significantly influence the stability characteristics of the system. In contrast, the Soret parameter, Darcy number, Dufour parameter, and Lewis number destabilize the system. The critical values of wave number for different prescribed values of other physical parameters are also analyzed. It is found that critical wave number does not depend on the Soret parameter, Lewis number, Dufour parameter, and solutal Rayleigh number; hence critical wave number has no impact on the size of convection cells. Further critical wave number acts as an increasing function of Taylor number, so the size of convection cells decreases, and the size of convection cells increases because of Darcy number.