Bi-disperse convection under the action of an internal heat source

The aim of this paper is the investigation on hydrodynamic stability of an incompressible fluid saturating a horizontal layer of bi-disperse porous medium, heated from below and internally, in order to analyse the effect of the internal heat source on the onset of convective instabilities. The principle of exchange of stabilities is proved, so convection can arise only via stationary motions. Via linear instability and nonlinear stability analyses of the conduction solution, the linear threshold and the nonlinear threshold in the L^2- norm for the onset of convective motions are determined and compared.