Anisotropic thermal conductivity and Péclet number in the stability analysis of Casson fluid flow in a porous medium channel

In this study, analyses of linear and nonlinear stability of Casson fluid movement underneath a saturated porous medium characterized by the Péclet number and anisotropy thermal conductivity effects are carried out. The Darcy–Brinkman model under the Oberbeck–Boussinesq assumption is used. This study has various applications in environmental engineering, petroleum engineering, polymer processing, and biomedical engineering. Utilizing the Chebyshev tau method, the linear stability issue is resolved. Nonlinear stability is investigated using the energy method. Here, marginal stability plots illustrate the stable and unstable regions and the variation of the critical Darcy–Rayleigh number with variations in other parameters such as the porous medium parameter, the Peclet number, the anisotropic thermal conductivity, and the Casson parameter. Growth rate plots are presented to indicate the growth or decay of the disturbance, and contour plots are presented and analyzed to determine the flow patterns of both the streamlines and the isotherms. The results obtained in the study are validated with existing literature for some special cases. Furthermore, the subcritical region is shown in marginal stability plots. The system is stabilized as a result of the increased permeability, which delays convection, as indicated by an increasing Darcy number. It demonstrates the stabilizing effect, and the anisotropic thermal conductivity parameter also stabilizes as a result of an increase in horizontal thermal conductivity in the horizontal direction.