THE EFFECT OF A WEAK HETEROGENEITY OF A POROUS-MEDIUM ON NATURAL-CONVECTION

The results of an investigation on the effect of a weak heterogeneity of a porous medium on natural convection are presented. A medium heter ogeneity is represented by spatial variations of the permeability and of the effective thermal conductivity. As a general rule the existence of horizontal thermal gradients in heterogeneous porous media provide s a sufficient condition for the occurrence of natural convection. The implications of this condition are investigated for horizontal layers or rectangular domains subject to isothermal top and bottom boundary conditions. Results lead to a restriction on the classes of thermal co nductivity functions which allow a motionless solution. Analytical sol utions for rectangular weak heterogeneous porous domains heated from b elow, consistent with a basic motionless solution, are obtained by app lying the weak nonlinear theory. The amplitude of the convection is ob tained from an ordinary non-homogeneous differential equation, with a forcing term representative of the medium heterogeneity with respect t o the effective thermal conductivity. A smooth transition through the critical Rayleigh number is obtained, thus removing a bifurcation whic h usually appears in homogeneous domains with perfect boundaries, at t he critical value of the Rayleigh number. Within a certain range of sl ightly supercritical Rayleigh numbers, a symmetric thermal conductivit y function is shown to reinforce a symmetrical flow while antisymmetri c functions favour an antisymmetric flow. Except for the higher-order solutions, the weak heterogeneity with respect to permeability plays a relatively passive role and does not affect the solutions at the lead ing order. In contrast, the weak heterogeneity with respect to the eff ective thermal conductivity does have a significant effect on the resu lting flow pattern.