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

We report a theoretical study aimed at determining the temperature distribution of a homogeneous, fluid-saturated porous medium initially at a low temperature, into which a constant flow rate of hot water is injected. The size of the heated region is assumed to be large compared to the radius of the injection pipe, which is idealized as a line source of mass and heat. The temperature distribution is found to be self-similar and to depend on a single dimensionless parameter which is a Peclet number.