A thermo-mechanical model for flows in superposed porous and fluid layers with interphasial heat and mass exchange

作者：Papalexandris M V^*; Antoniadis P D

来源：International Journal of Heat and Mass Transfer, 2015, 88: 42-54.

DOI：10.1016/j.ijheatmasstransfer.2015.04.049

• Porous media flows
• Porous medium - pure fluid interface
• Thermal convection
• One-domain approach
• Thermal non-equilibrium
• Continuum theories
• Mixture-theoretic formalism

In this paper, we develop a thermo-mechanical model for flows in superposed porous and fluid layers with interphasial heat and mass exchange. This model is based on a mixture-theoretic formalism, according to which, the fluid and the solid phases are treated as two coexisting but open thermodynamic continua that interact with each other. As such, each phase is endowed with its own set of thermodynamic variables and conservation laws. In particular, each phase is assigned with its own tempera ture field, thereby allowing for thermal non-equilibrium between the two phases. Constitutive equations for all dissipative and relaxation phenomena occurring in both phases are derived by exploiting the constraints imposed by the entropy axiom when applied to the entire mixture. This model is valid for both compressible and incompressible flows. Herein we also derive its low-Mach number approximation, which is substantially simpler and, therefore, more convenient for flows where compressibility effects are negligible. The efficacy of the proposed model and the effect of thermal non-equilibrium between the two phases are examined via direct numerical simulations of natural convection in a horizontal channel consisting of a porous layer and a superposed pure-fluid domain.

• 出版日期2015-9