This paper is concerned with the effects of flow and migration of nanoparticles on heat transfer in a straight channel occupied with a porous medium. Investigation of forced convective heat transfer of nanofluids in a porous channel has not been considered completely in the literature and this challenge is generally considered to be an open research topic that may require more study. The fully-developed flow and steady Darcy-Brinkman equation is employed in the porous channel. The local thermal non-equilibrium model is assumed between the pure fluid, solid and the nanoparticle phases. It is assumed that the nanoparticles are distributed non- uniformly inside the channel. As a result, the volume fraction distribution equation is also coupled with governing equations. The effects of Lewis number, Schmidt number and modified diffusivity ratio (Nbt ) on the heat transfer are completely studied. The results show that the non-dimensional heat flux absorbed by fluid is decreased when the Lewis number is increased. This behaviour can also be observed in the heat flux absorbed by the particles and the solid. The effects of Scmith number, Lewis number and Nbt on the volume fraction distribution and the heat flux are also studied numerically. The results indicate that when the Schmith number is increased the particle distribution tend to the entrance distribution. The effect of Nbt on the heat flux and the volume fraction is studied and discussed as well.

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