Numerical study of an elliptical fin inserted in a square cavity with the upper sliding surface submitted to mixed convection

This paper aims to evaluate the heat transfer in a square cavity with an elliptical fin located in different positions on the cavity bottom and with different aspect ratios. The optimal geometry was analised using the Constructal Design principle. A two-dimensional, laminar, steady state and incompressible flow was considered. The thermophysics properties were defined for Pr = 0.71 and they are considered constant, except for the specific mass that was determined by the Boussinesq approximation. A Rayleigh number (RaH) of 104 was adopted to define the natural convection, while a Reynolds number (ReH) of 102 was adopted to define the forced convection. The fin position and its dimensions were varied, keeping the ratio of the fin area to cavity area constant (ϕ = 0.05). The optimal geometry that maximizes the heat transfer rate was obtained through the Constructal Law. A mesh was created to solve the problem and it was adequately refined to ensure the accuracy of the results. The governing equations of the problem were solved numerically using the software ANSYS/Fluent®. This study shows that the position of the fin which maximizes the average Nusselt number in these conditions is at the point X1 ≈ 0.3 of the lower surface. For the aspect ratio (r) of the fin, it was observed that the minimization of the average Nusselt number occurs for r between 15 and 25. Considering all studied geometries, the optimized one can reach a performance around 50% superior if compared with the worst one, proving the importance of geometric evaluation in this kind of engineering problem, as well as the effectiveness of the Constructal approach. Keywords: Heat transfer, Constructal Law, Nusselt number, elliptical fin, mixed convection