A Finite Element Model for Hydro-thermal Convective Flow in a Porous Medium: Effects of Hydraulic Resistivity and Thermal Diffusivity

TL;DR

This paper develops a finite element model to analyze hydro-thermal convective flow in porous media, examining how hydraulic resistivity and thermal diffusivity influence heat transfer, with validated numerical results demonstrating optimal convergence.

Contribution

It introduces an efficient, stable finite element discretization for coupled hydro-thermal flow, ensuring well-posedness and demonstrating accuracy through computational experiments.

Findings

Heat transfer rate increases with hydraulic resistivity and thermal diffusivity variations.

The finite element method achieves optimal convergence rates.

Numerical results validate the model's effectiveness in simulating heat transfer in porous media.

Abstract

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.