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The problem of Bènard-Magneto-Marangoni convection in a composite layer which is horizontally infinite, is investigated for the Darcian case in the presence of constant heat source/sink in both the layers. This composite layer is enclosed by adiabatic boundaries and subjected to linear, parabolic and inverted parabolic temperature gradients. The eigenvalue, thermal Marangoni number is obtained in the closed form for lower rigid and upper free with surface tension velocity boundary combinations. The influence of various parameters on the eigenvalue against depth ratio is discussed. It is observed that the effect of heat source/sink is dominant in the fluid layer. The parameters which manipulate (advance or delay) the convection are determined.

malaya journal of matematik

Effects of Heat Source/ Sink and non uniform temperature gradients on Darcian-B\`{e}nard-Magneto-Marangoni convection in composite layer horizontally enclosed by adiabatic boundaries