This article describes the design of an optimal rectangular microchannel made of a high thermal conductive graphite (HTCG). For simulating the proposed microchannel heat sink, the total resistance model and the entropy generation minimization criterion were used. For solving the optimization problem, the unifi ed particle swarm optimization algorithm (UPSO), was used. Results showed a marked effect of using this high thermal conductor when compared to traditional materials, such as aluminum, and while using air and ammonia gas as the working fl uids. It is also reported the relative effect of the constriction, convective and fl uid thermal resistances on the overall equivalent thermal resistance. As a demonstrative example when changing the nature of the coolant, a titanium dioxide nanofl uid was selected. It was found that the Nusselt number is perceptibly lower, when the coolant is a nanofl uid and the material for the making of the microchannel is an HTCG.