Numerical Simulation of Transient Free Convection in a Rectangular Cavity Filled with Porous Material Using Finite Element Formulations

In this study, the finite element method is used to quantitatively explore transient free convection in porous cavities in order to understand the flow characteristics and heat conduction processes in the square cavities. In comparison to an uniform temperature gradient, the left wall is swiftly heated and the right wall is allowed to cool to a specific temperature. The horizontal walls are insulated on both sides. Dimensionless representations of the energy, Darcy and continuity equations are solved numerically. Equilibrium state between fluid and solid phases in porous material with a low Reynolds number and porosity was used to generate the results. To solve the dimensionless basic equations, a numerical finite element technique is applied. To solve a set of governing equations, a spatial discretization of triangular components with quadratic elements of 6 nodes and an implicit temporal integration approach are implemented. it can be concluded that the finite element formulation can be successfully implemented to analyze flow and heat transfer characteristics in porous medium with a relatively less computational time and coarse grid.