Numerical analysis of natural convection in a rectangular porous enclosure with partially active thermal walls

Abstract

The current study deals with a two-dimensional natural convection heat transfer in a rectangular porous enclosure with partially active thermal walls. Within the enclosure, the middle position of two sidewalls are partially cooled at constant temperature θc and the middle section of the bottom wall is kept at constant temperature θh (θh > θc), where the top and the rest part of the bottom wall and the side walls of the enclosure are assumed to be insulated. The physical problems are presented mathematically by different sets of governing equations (such as the mass, momentum and energy balance equations) along with the corresponding initial and boundary conditions by using Brinkman-Forchheimer-extended Darcy flow model and the Boussinesq approximation. In the non-dimensional form, the governing equations along with the transformed initial and boundary condition are then solved by employing a finite-element scheme based on the Galerkin method of weighted residuals. Results are presented in terms of isotherms, streamlines, average Nusselt number along the partially active thermal wall for different combinations of the governing parameters, namely Darcy number (Da), Porosity (ε), and the physical parameters namely cavity aspect ratio (Ar) and the three positions of heating source (Lp, Mp, Rp) and the three positions of cooling source (Tc, Mc, Bc) with various heater length for two values of Grashof number (Gr = 105, 106) with respect to time (τ). Which have been shown graphically by using Post-processing software. Comparisons with previously published work are made and the results are found to be in excellent agreement. The results indicate that both the flow and the thermal fields strongly depend on the aforesaid parameters. The computational results also indicate that the average Nusselt number at the heated part of active wall with respect to time are depending on the aforementioned parameters. The results in terms of average Nusselt number are shown in tabular form. The heater location and the cooling source location has also significant effect on the average Nusselt number.