Abstract: The effect of internal heat generation is applied to the Rayleigh-Benard convection in a horizontal micropolar fluid layer. The bounding surfaces of the liquids are considered to be rigid-free, rigid-rigid and free-free with the combination of isothermal on the spin-vanishing boundaries. A linear stability analysis is used and the Galerkin method is employed to find the critical stability parameters numerically. It is shown that the critical Rayleigh number decreases as the value of internal heat generation increase and hence destabilize the system.
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.