The dual effect of Ellis model and Biot number on the Darcy-Benard instability: A numerical study

The study examines the dual behavior of the Biot number and the Ellis number on the Darcy-Benard convective instability problem saturated with a shear-thinning fluid whose behavior appertains to the Ellis model. The dimensionless process is carried out, which leads to the appearance of various governing parameters among them the Biot number and the Ellis number. Asymmetric thermal conditions are assumed by considering the Robin condition at the lower impermeable layer and the Dirichlet condition at the upper one. A numerical technique is employed in Mathematica 10 to handle the eigenvalues problem developed by the linear stability analysis. Based on the results, the transverse modes exhibit the highest level of instability. Furthermore, compared to the Newtonian fluid, the shear-thinning fluid illustrates unstable behavior for the same flow configuration.