Author(s): S Huq, MM Rahman, MF Karim and MR Amin

Abstract: Natural convection heat transfer and fluid flow through a two-dimensional rectangular porous enclosure with partially active thermal walls are investigated numerically in this study. A small part of two sidewalls are partially cooled at a constant temperature θ_c and a small part of the bottom wall is kept at constant temperature θ_h (θ_h > θ_c), where the top and the remaining 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. Galerkin weighted residual method of finite element analysis is implemented to discretise the governing equations. The analysis has been carried out for the cavity Aspect ratio (Ar = 1, 2, 3), the three positions of heating source: left position (Lp), middle position (Mp), right position (Rp) and the three positions of cooling source: top cold (Tc), middle cold (Mc), and bottom cold (Bc) with various heater length and fixed Darcy number (Da), Porosity (ε), Prandtl number (Pr) for two values of Grashof number (Gr = 10⁵, 10⁶) with respect to time (τ). Results are presented in terms of isotherms, streamlines, average Nusselt number along the partially active thermal wall for different combinations of the governing parameters. The results indicate that both the flow and the thermal fields strongly depend on the above-mentioned 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 also shown in tabular form.

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