## Abstract

In this chapter we focus on the equation that expresses the first law of thermodynamics in a porous medium. We start with a simple situation in which the medium is isotropic, and where radiative effects, viscous dissipation, and the work done by pressure changes are negligible. Very shortly we shall assume that there is local thermal equilibrium so that *T* _{ s } = *T* _{ f } = *T*, where *T* _{ s } and *T* _{ f } are the temperatures of the solid and fluid phases, respectively. More complex situations will be considered in Section 6.5. Here we also assume that heat conduction in the solid and fluid phases takes place in parallel so that there is no net heat transfer from one phase to the other.

## Keywords

Porous Medium Direct Numerical Simulation Viscous Dissipation Thermal Boundary Condition Darcy Number
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