The Effect of Strong Heterogeneity on the Onset of Convection Induced by Internal Heating in a Porous Medium: A Layered Model

An analytical investigation of the onset of convection, induced by internal heating, in a composite porous medium consisting of two horizontal layers has been made. The two-layer model that we adopted makes it possible to investigate and compare the effects of both weak and strong heterogeneity. Both cases of constant heat flux and constant wall temperature boundary conditions have been treated. In general, we established that anything that aids convection in the upper portion of the layer is destabilizing. In agreement with this rule, we found that conductivity increasing upward leads to a more stable situation, permeability increasing upward leads to a less stable situation, and source strength increasing upward generally leads to a less stable situation.