Stability of natural convection in superposed fluid and porous layers: Equivalence of the one- and two-domain approaches

Abstract

Stability analyses of thermal and/or solutal natural convection in a configuration composed by a fluid layer overlying a homogeneous porous medium have been performed using different modeling approaches, especially for the treatment of the interfacial region. Comparisons between the one-domain approach and the two-domain formulation have shown important discrepancies of the marginal stability curves. This note shows that, according to Kataoka [I. Kataoka, Local instant formulation of two-phase flow, Int. J. Multiphase Flow 12(5) (1986) 745–758.], the differentiation of the macroscopic properties of the porous layer at the interface (porosity, permeability, thermal effective diffusivity) must be considered in the meaning of distributions. In that case, the one- and the two-domain approaches are shown to be equivalent and very good agreement is indeed found when comparing the results obtained with both approaches.