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標題: Onset of stationary Benard-Marangoni convection in a fluid layer with variable surface tension and viscosity
作者: Char, M.I.
Chen, C.C.
關鍵字: thermal-convection;stability analysis;vertical slot;porous-medium;temperature
Project: Journal of Physics D-Applied Physics
期刊/報告no:: Journal of Physics D-Applied Physics, Volume 30, Issue 24, Page(s) 3286-3295.
The onset of stationary Benard-Marangoni convective instabilities in a fluid layer with thermally dependent surface tension and viscosity is studied by means of linear stability analysis. The dependence of viscosity and surface tension of the fluid on temperature is assumed to be exponential and linear respectively. The upper surface is free and is subject to a general thermal condition, while the lower boundary is rigid and is fixed at a constant temperature or a constant heat flux. For the latter case, the analytically asymptotic solution of long wavelength is obtained. For pure Benard convection, the system becomes more stable when the Biot number Bi increases. For both the upper and lower boundaries fixed at a constant heat flux, the critical Rayleigh number R-c decreases monotonically with the physical viscosity parameter B, and the corresponding critical wavenumber a(c) vanishes. The Blot number Bi, affecting the system, depends strongly on the parameter Gamma(=M/R). The critical Rayleigh number R-c decreases with Gamma and a jump in the critical wavenumber a(c) for large Gamma and B and small Bi exists. The critical conditions R-c and a(c), for various values of Gamma or Bi, approach constant values as the viscosity parameter B becomes large.
ISSN: 0022-3727
DOI: 10.1088/0022-3727/30/24/004
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