Influence of viscosity variation on the stationary Bénard-Marangoni instability with a boundary slab of finite conductivity. (English) Zbl 0936.76020
Summary: We study the onset of stationary Bénard-Marangoni instability in a variable-viscosity fluid layer overlying a boundary slab of finite conductivity. The relations between the viscosity and surface tension of the fluid and the temperature are exponential and linear, respectively. We derive asymptotic solutions for the long wavelength, and for small values of conductivity and thickness of the solid. These solutions compare well with numerical results. As the viscosity ratio increases, the validity of the asymptotic solutions is extended to larger values of thermal conductivity and thickness ratio.
MSC:
| 76E06 | Convection in hydrodynamic stability |
| 76D45 | Capillarity (surface tension) for incompressible viscous fluids |
| 80A20 | Heat and mass transfer, heat flow (MSC2010) |
Keywords:
Bénard-Marangoni instability; variable-viscosity fluid layer; surface tension; asymptotic solutions; viscosity ratio; thermal conductivityReferences:
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