Thermal boundary conditions and rotation effects on the onset of casson fluid convection in a permeable layer produced by purely interior heating

Abstract

In this work, we inspect the effect of thermal boundary conditions and rotation on the coming of Casson fluid convective motion generated by purely internal warming in a flat porous layer. Two types of thermal boundaries are utilized, namely, type (I) both boundary planes are isothermal and type (II) bottom boundary plane is insulated and top plane is isothermal. The altered Darcy model is used to characterize the rheological performance of Casson fluid movement in porous medium. The classical Horton–Rogers Lapwood stability examination is accomplished and the resultant eigenvalue problem is resolved numerically with the help of advanced-term Galerkin technique with the internal Rayleigh Darcy number as the eigenvalue. It is observed that the Taylor Darcy number has a stabilizing weight while the Casson parameter shows the dual influence on the system. The structure is more stable when both boundary planes are isothermal. The magnitude of the convection cells falls with increasing both the Taylor Darcy number and the Casson parameter. In the absence of Taylor Darcy number, the system’s stability decreases with the Casson parameter. Further, it is remarkable to observe that without rotation, the Casson parameter has no impression on the magnitude of convection cells.