Avaliação geométrica de três aletas inseridas em uma cavidade aplicando design construtal e o método superfície de resposta

Abstract

Lid-driven cavities are often used as a simplified case to study and understand various complex engineering problems, such as heat exchangers and heat sinks, in order to identify which geometry offers the best performance. In this context, the present work conducted a numerical study and geometric evaluation of a mixed convection flow with heat transfer. The objective was to assess the effects of the geometry of three fins inserted inside a lid-driven cavity subjected to mixed convection on the heat transfer between the fins and the fluid, indicating the configurations with the best performance under different conditions through the application of the Constructal Design method. The study involved the investigation of the following stages: (i) evaluating the effect of the aspect ratios of each of the three fins on the heat transfer rate; (ii) evaluating the effect of the fin area fractions (ϕ1, ϕ2, and ϕ3), keeping the left fin area fraction (ϕ1) and the ratio H1/L1 fixed, associated with a search space screening; (iii) evaluating the effect of different total area fractions (ϕT = 0.05, 0.1, and 0.2) for different fin area ratios for Ri = 0.1 and 1, using the Response Surface Methodology (RSM) combined with Design of Experiments; (iv) comparing the system performance for different Richardson numbers. When associated with a search space screening, the results indicated that the best performance was achieved when fin 3 (ϕ3) has the largest area and the highest H3/L3 ratio, suggesting that the dominance of fin 3 enhances thermal exchange, particularly for higher H3/L3 ratios, while the predominance of fin 2 is observed for lower H3/L3 ratios. The best geometry found was H1/L1 = 0.1, H2/L2 = 0.5, and H3/L3 = 19, resulting in the highest heat transfer rate for the configuration ϕ1 = 0.05, ϕ2 = 0.04, ϕ3 = 0.01. The evaluation of Constructal Design combined with RSM allowed for the determination of the geometry that achieves the best thermal performance by varying the fraction of the area occupied by the fins. The results showed that the largest total area fraction provides the most favorable performance, attributed to the increase in the heat exchange area provided by the fins. The best thermal performance for Ri = 0.1 was 32% higher compared to the best performance for Ri = 1. It was observed that the use of Constructal Design associated with RSM required fewer simulations compared to a search space sweep for similar aspect ratios (Hn/Ln).