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The effect of thermal expansion on porous media convection is investigated by isolating first the solution of thermal expansion in the absence of convection which allows to evaluate the leading order effects that need to be included in the convection problem that is solved later. A relaxation of the Boussinesq approximation is applied and the relevant time scales for the formulated problem are identified from the equations as well as from the derived analytical solutions. Particular attention is paid to the problem of waves propagation in porous media and a significant conceptual difference between the isothermal compression problem in flows in porous media and its non-isothermal counterpart is established. The contrast between these two distinct 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 sensitive to the symmetry of the particular temperature initial conditions that are applied.