The effect of thermal expansion on porous media convection part 1: Thermalexpansion solution

The effect of thermal expansion on porous media convection is investigated by isolating first the solution of thermal expansion in the absence of conv ection which allows to evaluate the leading order effects that need to be i ncluded in the convection problem that is solved later. A relaxation of the Boussinesq approximation is applied and the relevant time scales for the f ormulated problem are identified from the equations as well as from the der ived analytical solutions. Particular attention is paid to the problem of w aves propagation in porous media and a significant conceptual difference be tween the isothermal compression problem in flows in porous media and its n on-isothermal counterpart is established. The contrast between these two di stinct problems, in terms of the different time scales involved, is evident from the results. While the thermal expansion is identified as a transient phenomenon, its impact on the post-transient solutions is found to be sens itive to the symmetry of the particular temperature initial conditions that are applied.