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This paper studied the problem of Benard-Marangoni convection in a horizontal fluid layer heated from below with non-uniform temperature gradient under magnetic field. A linear stability analysis is performed to undertake a detail investigation. The eigenvalues are obtained for both adiabatic boundaries. The influence of various parameters on the onset of convection has been analyzed. Six non-uniform basic temperature profiles are considered and some general conclusions about their destabilizing effects are presented.

Combined Effect of Non-Uniform Temperature Gradient and Magnetic Field on Bénard-Marangoni Convection with a Constant Heat Flux