  In this article, a finite element model is implemented to analyze
hydro-thermal convective flow in a porous medium. The mathematical model
encompasses Darcy's law for incompressible fluid behavior, which is coupled
with a convection-diffusion-type energy equation to characterize the
temperature in the porous medium. The current investigation presents an
efficient, stable, and accurate finite element discretization for the
hydro-thermal convective flow model. The well-posedness of the proposed
discrete Galerkin finite element formulation is guaranteed due to the
decoupling property and the linearity of the numerical method. Computational
experiments confirm the optimal convergence rates for a manufactured solution.
Several numerical results are obtained for the variations of the hydraulic
resistivity and thermal diffusivity. In the present study, the bottom wall is
maintained at a constant higher hot temperature while side vertical walls are
thermally insulated and the top wall is maintained at a constant cold
temperature. Heat transfer rates at the heated bottom wall are presented in
terms of local Nusselt number. A linear variation in hydraulic resistivity and
a quadratic variation in thermal diffusivity show an increase in the heat
transfer rate.
