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Stability of free-convection flows of variable-viscosity fluids in vertical and inclined slots. (English) Zbl 0662.76060

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.

MSC:

76E15 Absolute and convective instability and stability in hydrodynamic stability
76R10 Free convection
76E17 Interfacial stability and instability in hydrodynamic stability
76E99 Hydrodynamic stability
76M99 Basic methods in fluid mechanics
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