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Rayleigh-Marangoni thermoconvective instability with non-Boussinesq corrections. (English) Zbl 0930.76030

Summary: We present a linear analysis of coupled surface tension and gravity driven instabilities in fluids with variable thermophysical properties. The fluid layer is initially at rest, of infinite horizontal extent, bounded by two flat boundaries and subject to a vertical temperature gradient. Viscosity is supposed to vary exponentially with respect to temperature, while linear laws are assumed for heat capacity and thermal conductivity. The relative departure from the Boussinesq model, where fluid properties are constant, is derived by selecting reference properties at the bottom temperature. We give a physical interpretation of non-Boussinesq effects on the critical threshold. Computations for glycerol and liquid potassium show that the temperature dependence of thermophysical properties may have a significant influence on the onset of convection.

MSC:

76E06 Convection in hydrodynamic stability
76D45 Capillarity (surface tension) for incompressible viscous fluids
80A20 Heat and mass transfer, heat flow (MSC2010)
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