In the present work, steady state, laminar, hydrodynamically and thermally developing flow in a trapezoidal microchannel heat sink (MCHS) is investigated. Navier-Stokes equations are solved using finite volume method. A new correlation for the dispersion model is suggested to explain the heat transfer enhancement of nanofluids. Two kinds of nanofluids, Al2O3-water and CuO-water were considered and the results were validated using open literature data. It is shown that the proposed correlation gives the best result among other models. Furthermore, the effects of nanoparticle size and volume fraction on heat transfer are evaluated. The results show that the average Nusselt number increases rapidly with decrease of diameter of nanoparticles, but increasing nanoparticle size more than 60 nm does not affect heat transfer considerably. Moreover, when the Reynolds number is low, adding more nanoparticles increases heat transfer slightly, so using nanofluid in applications where the Reynolds number is not commonly high (e.g. in microchannel fluid flow) sounds ineffective. (C) 2016 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder Technology Japan. All rights reserved.