ONSET OF STATIONARY BENARD-MARANGONI CONVECTION IN A FLUID LAYER WITHVARIABLE SURFACE-TENSION AND VISCOSITY

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 visc osity 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 r igid and is fixed at a constant temperature or a constant heat flux. F or the latter case, the analytically asymptotic solution of long wavel ength is obtained. For pure Benard convection, the system becomes more stable when the Biot number Bi increases. For both the upper and lowe r boundaries fixed at a constant heat flux, the critical Rayleigh numb er R-c decreases monotonically with the physical viscosity parameter B , and the corresponding critical wavenumber a(c) vanishes. The Blot nu mber Bi, affecting the system, depends strongly on the parameter Gamma (=M/R). The critical Rayleigh number R-c decreases with Gamma and a ju mp 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 Ga mma or Bi, approach constant values as the viscosity parameter B becom es large.