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. (C) 2011 Elsevier Ltd. All rights reserved.