Onset of instability in internally heated non-Newtonian casson fluid flow in a hele-Shaw cell under magnetic and thermal edge effects

In this paper, we examine the effect of the magnetic field and the thermal boundary conditions on the onset of the convective instability in a non-Newtonian Casson fluid flow formed by purely internal heating in a Hele-Shaw cell. Two categories of thermal edges are employed; category (I) features both edge planes as isothermal, while category (II) has an insulated lower edge plane and an isothermal top plane. The modified Hele-Shaw cell model is taken to distinguish the rheology appearance of Casson fluid flow in a Hele-Shaw cell. The standard linear stability investigation is performed, and the consequential eigenvalue problem is resolved numerically taking an advanced Galerkin method, with the internal Rayleigh number serving as an eigenvalue. It is noted that the magnetic Chandrasekhar number has a stabilizing impact whereas the Casson factor and Hele-Shaw number show the destabilizing impact on the arrangement. The configuration exhibits greater stability when both edge plates are isothermal. The extent of the convection cells drops with cumulative the magnetic Chandrasekhar number, the Hele-Shaw number and the Casson factor. Additional, it is incredible to notice that without magnetic field, the Casson factor does not influence the extent of convective cells.