Thermal Optimization of an Array of Needle-Shaped using Constructal Theory

In the present paper, the constructal theory is employed to determine the optimal configuration of three rows of needle-shaped fins. The heat transfer across the fins is due to laminar forced convection. Second order upwind scheme is used for discretization of the diffusion terms of governing equations. The pressure–velocity coupling is performed using the SIMPLE algorithm. The heat transfer is optimized subject to constant fin volume. The effect of Reynolds number and thermal conductivity on the optimal configuration is investigated. The results obtained from the present simulations are in good agreement with the numerical results. The results show that pin–fins flow structure leads to the best performance when the pin–fin diameters and heights are non-uniform. At Re = 100 and 200, the optimal value of 𝐻3/𝐻1is 1.3. It is revealed that at Re = 50, the optimal value for 𝐷3/𝐷1 is approximately 1.1. The results demonstrate that heat transfer rate is an increasing function of the Reynolds number.