Thermal Convection of Power-Law Fluid in Bidispersive Porous Media with Throughflow

This study investigates the onset of thermal convection in a power-law fluid saturating a bidispersive porous medium using linear stability analysis. The eigenvalue problem is solved using the normal mode technique in conjunction with a numerical boundary value solver (bvp4c). The interaction parameter exhibits dual behavior depending on the rheology: it destabilizes the system in shear-thinning fluids while stabilizing it in Newtonian and shear-thickening regimes under certain conditions. The permeability ratio is found to have a consistently stabilizing effect, with higher values significantly delaying the onset of convection. Thermal transport parameters also play a crucial role, with increasing Peclet numbers generally enhancing stability, although non-monotonic behavior is observed in the shear-thinning regime due to competing effects of convective enhancement and thermal diffusion. For low values of the Peclet numbers, shear-thickening fluids exhibit the lowest critical Rayleigh number (least stable) and shear-thinning fluids the highest one (most stable). In contrast, for high Peclet numbers, shear-thickening fluids remain the least stable, while Newtonian fluids exhibit maximum stability.