The stability of the buoyancy-driven parallel shear flow of a variable-viscosity Newtonian fluid between vertical or inclined plates maintained at different temperatures is studied theoretically. The analysis is capable of dealing with arbitrary viscosity-temperature relations. Depending on the Prandtl number, angle of inclination, and form of the viscosity-temperature variation, the flow may become unstable with respect to two-dimensional longitudinal or transverse disturbances. Outstanding questions arising in previous investigations of the stability of parallel free-convection flows of constant-viscosity fluids in inclined slots and of variable-viscosity fluids in vertical slots are discussed. We find that, in a variable-viscosity fluid, non-monotonic dependence of the critical Rayleigh number on the inclination angle can occur at significantly higher Prandtl numbers than is possible in the constant-viscosity case. Results are also presented for the stability of the free-convection flow of several glycerol-water solutions in an inclined slot.
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