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This paper studied the problem of Bénard-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.