Further thoughts on buoyancy-induced instability of a variable viscosity fluid saturating a porous slab

The stability of buoyant flow in a vertical porous layer bounded by impermeable-isothermal boundaries is studied insofar as the variability fluid viscosity with temperature concerned. governed modified Darcy's law two different forms viscosity–temperature relationships namely, quadratic and exponential. modal analysis carried out velocity–temperature formulation governing equations for perturbations. temperature-dependence forbids energy Gill [“A proof that convection slab stable,” J. Fluid Mech. 35, 545–547 (1969)] embarking upon any definite conclusion on even under limit an infinite Prandtl–Darcy number, consequently, eigenvalue problem solved numerically. Types temperature-dependent laws are found to demonstrate conflicting behavior characteristics base flow. results show linearly stable if varies quadratically. On contrary, instability emerges exponential type variation beyond certain range values corresponding parameter depending number. It established increase value decrease critical Darcy–Rayleigh number markedly thereby destabilizes