This study considers an open trapezoidal cavity beneath a porous medium-filled channel. The unsteady free convective flow through porous material is investigated under Darcy's law. The fluid and porous medium properties are assumed to be in thermal equilibrium. The non-dimensionalized governing equations for heat transport and fluid flow were calculated using the weighted residual Galerkin finite element method. Steady-state solutions, a comparison with previously published results, and a grid independence test are used to illustrate the numerical technique's algorithm's accuracy. Results for the iso-thermal lines and fluid streamlines are displayed graphically, and the average Nusselt numbers for the fluctuation of the inverse Darcy's number and Rayleigh's number are tabulated.