Temperature profiles due to continuous hot water injection into homogeneous fluid-saturated porous media through a line source

We report a theoretical study to determine the temperature proles due to the continuous and constant injection of hot water through a line source, into a homogeneous uid-saturated porous medium which has had initially a constant temperature T∞. In our treatment we have taken in to account the simultaneous injection of constant uxes of volume uid, q, and of heat, φ. By using a far-eld description, we found similarity solutions for the dimensionless temperature depending on the Peclet number, P e, as the single parameter of the problem.