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In this dissertation, both stationary and oscillatory modes of the Benard-Marangoni instabilities in a variable-viscosity fluid layer with andwithout rotation are studied by means of linear stability analysis.We consider a layer of a liquid of mean thickness d, standing upon a heatinghorizontal plate of infinite extent. The dependency of viscosity and surfacetension of the fluid on temperature are assumed exponential and linearrespectively.The upper deformable surface of the liquid is open to the atmosphere, whilethe lower boundary is in contact with a solid wall. The linearized perturbation equations are solved by using the shooting method to obtain theeigenvalues that governs the onset of Benard-Marangoni convection.The asymptotic solutions of long wavelength are achieved and very well comparedwith the numerical ones and might be reduced to the case with constant viscosity.In present study, for C=0 and Ta=0, the possibility of existence of oscillatorymode is not found, whether the viscosity varies or not. The regions forexistence of overstability and the dependence of the critical Rayleigh numberRc and Marangoni number Mc on the various physical parameters are investigated.The numerical results show that the onset of both stationary and oscillatoryconvection in a variable-viscosity fluid layer with rotation will possiblyexhibit the formation of a sublayer.
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