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The effect of uniform distribution of internal heat generation on the stability of the Benard-Marangoni convection in a horizontal fluid layer with a deformable upper free surface is investigated. The stability analysis in this study is based on the linear stability theory. The eigenvalue equations obtained from the analysis are solved by using the fourth-order Runge-Kutta-Gill method with the shooting technique. The results indicate that the stability of Benard-Marangoni convection is significantly affected by internal heat generation in the fluid layer and by surface tension at the upper free surface. There are two different kinds of instability mode: the thermal mode and the surface tensile mode. At lower values of the Crispation number C, the instability is dominated by the thermal mode. At higher values of C, the system becomes more unstable and creates the surface tensile mode, which is induced by the surface tensile effect. The Crispation number C at the transition between the thermal and the surface tensile modes decreases as the value of internal heat generation increases and that of thermal buoyance decreases. The bond number Bo at the mode transition increases due to the existence of the internal heat generation. In addition, the system becomes more stable when the Biot number Bi of the upper free surface increases.

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