Force convective heat transfer of alumina/water nanofluid inside a cooled parallel-plate channel in the creeping flow regime and the presence of heat generation is investigated theoretically. A modified two-component four-equation non-homogeneous equilibrium model is employed for the alumina/water nanofluid that fully accounts for the effects of nanoparticles volume fraction distribution. To impose the temperature gradients across the channel, the upper wall is subjected to a prescribed wall heat flux while the bottom wall is kept adiabatic. Moreover, due to the nanoparticle migration in the fluid, the no-slip condition of the fluid-solid interface at the walls is abandoned in favor of a slip condition that appropriately represents the non-equilibrium region near the interface. The results indicated that nanoparticles move from the adiabatic wall (nanoparticles depletion) toward the cold wall (nanoparticles accumulation) and construct a non-uniform nanoparticle distribution. Moreover, the anomalous heat transfer rate occurs when the Brownian motion takes control of the nanoparticle migration (smaller nanoparticles). (C) 2014 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder Technology Japan. All rights reserved.