Abstract: The onset of Marangoni convection in a horizontal
fluid layer with internal heat generation overlying a solid layer
heated from below is studied. The upper free surface of a fluid is
nondeformable and the bottom boundary are rigid and no-slip. The
resulting eigenvalue problem is solved exactly. The critical values of
the Marangoni numbers for the onset of Marangoni convection are
calculated and the latter is found to be critically dependent on the
internal heating, depth ratio and conductivity ratio. The effects of the
thermal conductivity and the thickness of the solid plate on the onset
of convective instability with internal heating are studied in detail.
Abstract: In this paper we use classical linear stability theory
to investigate the effects of uniform internal heat generation on the
onset of Marangoni convection in a horizontal layer of fluid heated
from below. We use a analytical technique to obtain the close form
analytical expression for the onset of Marangoni convection when
the lower boundary is conducting with free-slip condition. We show
that the effect of increasing the internal heat generation is always to
destabilize the layer.