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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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