Constructal heat transfer rate maximization for cylindrical pin-fin heat sinks

Constructal optimization of the whole cylindrical pin-fin heat sinks (PFHS) is performed by the finite volume method (FVM). Maximum dimensionless heat transfer rate (MDHTR) is taken as the objective for fixed total heat sink volume and fin-material volume, and pressure drop is used to evaluate the hydraulic performance of the system. Variation of the dimensionless heat transfer rate (DHTR) and its corresponding pressure drop along the diameter of cylindrical pin-fin is studied, and the influences of the volume fraction and fluid velocity on the results are analyzed, and the flow field and temperature distribution of PFHS are shown. The results show that there exists an optimal diameter which corresponds to an optimal number of pin fins makes the DHTR maximized when the shape of PFHS is fixed, the MDHTR and its corresponding pressure drop and optimal constructs are different for different volume fraction; there exists an optimal aspect ratio of the PFHS which makes the MDHTR maximization. The sensitivity of heat transfer performance to the fin-material fraction is higher than hydraulic performance does, but with respect to the fluid velocity and the aspect ratio of PFHS, the sensitivity of hydraulic performance is higher. The results of this paper can provide theoretical support for the optimization design of cylindrical PFHS.