Thermodynamically Constrained Averaging Theory Approach for Heat Transport in Single-Fluid-Phase Porous Medium Systems

The recently developed thermodynamically constrained averaging theory is briefly summarized as a tool for the building of rigorous macroscale models of transport phenomena in complex systems. The specific case of thermal transport in a single-fluid-phase porous medium system is considered. Key results from the application of this theory are used to develop a simplified entropy inequality, which is in turn used to guide the development of closure relations. The decomposition of exchange terms is considered, and closed models for internal energy are derived for the case of nonequilibrium and local thermal equilibrium conditions. Since all variables are expressed in terms of precisely defined averages of microscale quantities, the resultant models can be compared with highly resolved microscale simulations to determine the range of validity of the upscaled models.