Multi-objective optimization of porous fins in closed cavity with heat source of sinusoidal periodic temperature boundary condition

This paper investigates the effect of porous fin parameters on natural convection heat transfer performance in a closed cavity under sinusoidal periodic temperature boundary conditions. The study examines the impact of periodic boundary parameter variation on the Nusselt number, which represents the ratio of convective heat transfer to conduction heat transfer close to the wall region. The study results indicate that the average Nu number on the heat source surface fluctuates with different sinusoidal patterns, and the top surface of the heat source has a greater impact on convective heat transfer in the cavity. The analysis of the response surface method reveals that the interaction between the fin height S_a and the fin length L_a has the most significant influence on the average Nu of the heat source surface. The optimal combination of fin parameters coming from the response surface method is: S_a (0.35 ≤ S_a ≤ 0.65), L_a (0.06 ≤ L_a ≤ 0.3), ΔS_ab (0.05 ≤ ΔS_ab ≤ 0.25), A(0.5 ≤ A ≤ 1), B (0.004 ≤ B ≤ 0.016), θ (30° ≤ θ ≤ 150°). Under the combination of these parameters, the time-average Nu number on surface of heat source reaches the maximum value 11.63, which is 13.00% higher than that without fins. The convective heat transfer intensity in the cavity increases with the increasing dimensionless amplitude a. In addition, the time-averaged Nu number on the surface of the heat source has a negative correlation with the dimensionless period τ_p.