Variable property effects on the onset of convection in an elastic porous matrix

Equations for steady convection in a porous linear elastic matrix are formulated. When porosity changes are of the order of the pressure induced compressions in matrix and fluid, and these in turn can be neglected in comparison with thermal expansions in the fluid, the fluid balance laws uncouple from the equilibrium balance of the matrix. Plane flow in a horizontal layer is considered for temperature increases with depth up to 250°K, and the significant variations of viscosity and thermal expansion coefficients with temperature are included. The critical Rayleigh number for small disturbances harmonic in the horizontal direction is found to be substantially reduced from the constant expansion coefficient value, but the associated wavenumber and incipient flow patterns are little changed. However, if a Rayleigh number based on an appropriate mean value of the expansion coefficient is used, the critical values for constant and variable expansion coefficient solutions are in close agreement.