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.
Highlights
Rotating convection in a sparsely packed porous layer, which is heated from below, has important applications in geophysics and geophysical fluid dynamics
Eigenvalue problems with rigid–rigid and free–rigid boundaries are solved with the help of bvp4c in MATLAB R2020b
The linear instability threshold parameters consisting of Rayleigh number, Ra. and corresponding wave number, a, depend on Soret parameter, Sr., Dufour parameter, Du., Solutal Rayleigh number, Rs., Taylor number, Ta., Lewis number, Le. and Darcy number, Da. are shown in Figures 2–11, and Tables 3–7
Summary
Rotating convection in a sparsely packed porous layer, which is heated from below, has important applications in geophysics and geophysical fluid dynamics. Gaikwad and Kamble [18] studied the effects of cross-diffusion on rotating anisotropic porous layer and deduced that the Dufour parameter could stabilize the system. It has been deduced that heat and mass transfer of the system can be suppressed if the value of the Soret parameter increases It is quite clear from the above discussion that we should not neglect the Soret and Dufour effects in doublediffusive convection. The study of the Soret and Dufour effect on rotating convection in a sparsely packed porous layer for the realistic boundary conditions is of tremendous importance because it may be used as a fundamental mechanism for contaminant transport in groundwater, biochemical engineering, petroleum industry, oceanography, chemical engineering or oceans experience geothermal heating from below.
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