The onset of convection in a tridisperse porous medium

This paper develops a theory of mass, momentum, and heat transfer in a tridisperse porous medium. Coupling between three different scales present in this medium is accounted for by introducing momentum and interphase heat transfer coupling coefficients. The developed theory is then applied to solve the classical Rayleigh–Bénard problem, for the onset of convection in a horizontal layer uniformly heated from below, for this new type of a porous medium. The formulation uses the Darcy law, which now results in three different filtration velocities in three porosity scales present in this medium. The linear stability analysis leads to an expression for the critical Rayleigh number as a function of three volume fractions, two permeability ratios, two thermal capacity ratios, two thermal conductivity ratios, two inter-phase heat transfer parameters and two inter-phase momentum transfer parameters. The dependence of the critical Rayleigh number on these parameters is investigated.