A Local Model for the Energy Transfer in a Saturated Static Mixture

In the present work the transient energy transfer in a nonsaturated porous medium is studied, using a mixture theory viewpoint. The porous matrix is assumed homogeneous, rigid and isotropic, while the fluid is a Newtonian incompressible one and both are assumed static. Since the homogeneous matrix is not saturated, gradients of concentration are present. The porous medium and the fluid (a liquid) will be regarded as continuous constituents of a mixture that will have also a third constituent, an inert gas, assumed with zero mass density and thermal conductivity. The problem is described by a set of two partial differential equations which represent the energy balances for the fluid and the solid constituents. Isovalues for these two constituents are plotted, considering representative time instants and selected values for the energy equations coefficients and for the saturation.