Determination of the geometric dimensions of diamond-shaped heat sinks using numerical optimization methods

In this study, the optimum geometric dimensions and operating conditions of pin-fin heat sinks (PFHS) and diamond-shaped pin-fin heat sinks (DS-PFHS) are numerically investigated within the framework of multi-objective optimization problems aiming to minimize the base plate temperature and the mass. Accordingly, two separate optimization studies are conducted: the first focuses on determining the optimum configurations of PFHS designs, while the second addresses those of DS-PFHS designs. For both designs, a constraint is imposed such that the maximum base plate temperature (T_base) remains below 70 °C. The optimization variables D, H_fin, V_g, N_L, N_T are commonly defined for both PFHS and DS-PFHS models, whereas an additional optimization variable (a_r) representing the diamond geometry is included for the DS-PFHS models. The optimization problems are solved using a Multi-Objective Genetic Algorithm (MOGA), and three-dimensional parametric models are analyzed using the finite volume method. The results indicate that when lower base plate temperatures are targeted, DS-PFHS designs achieve lower mass values compared to PFHS designs. In this context, while the PFHS ID 20 design attains a base plate temperature of 53.16 °C with a mass of 0.146 kg, the DS-PFHS ID 47 design provides a similar base plate temperature (54.41 °C) with approximately 9.6% lower mass (0.132 kg). These findings demonstrate that the diamond-shaped pin-fin geometry enables lighter and more efficient heat sink designs.