The problem of Brinkmann-Benard-Magneto-Surface tension driven convection is investigated in an infinite horizontal composite layer enclosed by isothermal-adiabatic boundaries in the presence of invariable heat source/sink, which is subjected to linear, parabolic and inverted parabolic temperature gradients. The eigenvalue, thermal Marangoni number in the closed form is obtained for lower surface rigid, upper surface free from surface tension and with the continuity of normal and tangential stresses and continuity of normal, tangential velocity boundary conditions at the interface. The deviation of various parameters on the Marangoni number against thermal ratio is discussed. It is observed that the heat absorption in the fluid layer, viscosity ratio and the applied magnetic field play an important role in controlling Brinkmann-Benard-Magneto-Surface tension driven convection.

heat source (sink), thermal ratio, magnetic field, exact method, temperature gradients, isothermal-adiabatic boundaries.