The effect of Péclet number on the onset of Casson fluid convective motion in a porous layer: Analytical and numerical investigations

Abstract

In this article, we present analytical and numerical investigations of the influence of Péclet number on the arrival of Casson fluid convective motion in a horizontal porous layer utilizing the Galerkin technique. The flow in the porous matrix is modeled by an amended Casson-altered Darcy equation that considers the rheological behavior of Casson fluid. The outcomes indicate that the stability of the arrangement drops with growing the Casson parameter, while a reverse result is detected with Péclet number. We demonstrated that the oscillatory instability is not promising for the considered problem. It is also important to note that the extent of the convective cell declines with increasing the Péclet number on using the higher order Galerkin approximation while, on using the single term Galerkin approximation, the Péclet number has no impact on the magnitude of the convection cell. Further, the present results are equated with the available literature under the limiting situation of this study.