Stability of Flow of a Variable-Viscosity Fluid Saturating a Differentially Heated Vertical Porous Layer

The effect of viscosity varying linearly with temperature and the Prandtl-Darcy number on the stability of buoyancy-driven convection in a vertical porous layer is investigated. The variation in viscosity causes a dramatic change in the base flow and thereby discards the analytical proof of stability even under the limit of an infinite Prandtl-Darcy number. The question about the stability/instability of the basic flow is thus examined by carrying out a numerical solution of the stability eigenvalue problem for infinite and finite values of the Prandtl-Darcy number. It is found that the linear temperature dependence of the viscosity does not activate the instability to small-amplitude disturbances.