Optimization of fluid flow and internal geometric structure of volumes cooled by forced convection in an array of parallel tubes

This paper reports the optimization of a heat sink composed of parallel tubes in a solid matrix of fixed dimensions for the following cases: (i) fixed pressure drop; (ii) fixed pumping power and (iii) fixed heat transfer rate density. The method of the intersection of asymptotes is employed using the dimensionless thermal length (x∗) as primary optimization variable, and approximate theoretical expressions for predicting the optimum ratio of diameter to tube length (D/L) are presented for each case. When the system is optimized with fixed heat transfer density it is found that the optimum values of both x∗ and D/L are very close to those that correspond to the joint minimization of pressure drop and pumping power. These results are validated and complemented by means of numerical simulations.