The present work applies Constructal Design to study numerically a fin-cavity system under mixed convection flow. The system is composed of a heat triangular fin inserted in a squared cavity. The flow is driven by the superior wall (lid) displacement. The main purpose is to study the effect of the fin geometry and area ratio (φ) over the dimensionless convective heat transfer coefficient (Nusselt number). The effect of Rayleigh (RaH) and Reynolds (ReH) numbers over the thermal performance and optimal geometries is also evaluated. For all cases the Prandtl number is constant (Pr = 0.71). The conservation equations of mass, momentum and energy are solved numerically with a code based in the Finite Volume Method (FVM). Results showed that the thermal performance increased with the increase of Reynolds and Rayleigh numbers and with the decrease of fin area ratio (φ). Otimal geometries for the triangular fin are compared to optimal rectangular fins, for RaH = 105 results showed a better performance (up to 8%) of the triangular fin for low Reynolds numbers (ReH < 200), while rectangular fins performed better than triangular ones for the highest magnitudes of ReH numbers. In general, results showed that different conditions change the optimal shape of a flow system, always evolving to architectures that facilitate the access to the flows that flow through it.
This article investigates numerically, using the Constructal Design method, a system that combines a square cavity with upper sliding wall and a triangular fin subjected to the mixed convection effect. The objectives are to evaluate the influence of the fin aspect ratio (H1/L1) on the average Nusselt number on the fin surface and to analyze the effect of the fraction of the area of the triangular fin relative to the square cavity (φ). The proposed problem is assumed two-dimensional, laminar, incompressible and steady flows. For the buoyancy forces it is considered the Boussinesq approximation. In order to generalize the results, the problem is solved in dimensionless form. The fluid flowing through the cavity presents the thermophysical properties defined by the Prandtl number (Pr = 0.71). The buoyancy force in the flow is defined by the Rayleigh number (RaH = 104), while the flow regime is governed by the Reynolds number (ReH = 102). The optimum fin geometry that maximizes the heat transfer between the finned cavity and the surrounding fluid is obtained through the Constructal Design method. The numerical solution of the conservation equations of mass, momentum and energy is calculated with the finite volume method, using the commercial fluid dynamics software FLUENT®. The geometry and mesh computational domain were developed in GAMBIT® package. As results, it was found that the optimal configurations of H1/L1 presented a gain in the thermal performance of up to 15% in relation to the other geometries. In addition, the heat transfer has great dependence on the variation of the fraction of area (φ).
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