Study of the natural convection flow induced by injecting a hot fluid in a porous medium

In this work, we present the study of a steady flow driven by the injection of a hot fluid of temperature T$_{i}$, from a horizontal line source of mass embedded in an unbounded porous medium of constant permeability K and porosity $\phi$, the medium is saturated with the same fluid. The fluid far from the source is stagnant with a uniform temperature T$_{\infty}$, where T$_{\infty}$$<$T$_{i}$. The density changes of the fluid are considered to be small enough so that the Boussinesq approximation is applicable and we shall also assume that the fluid and solid in the porous medium have the same temperature locally. This configuration conforms interesting flow and temperature patterns in the surrounding medium near the line source as demonstrated numerically and experimentally.