This paper is devoted to an analytical analysis of fully-developed laminar wall driven channel flow of nanofluids. Initially, the pure fluid flow and thermal layer are resolved. Buongiorno model is later adopted to capture the Brownian motion and thermophoresis influences by the presence of nanofluids. The prime emphasize is to fulfil the zero net particle flux at the walls of the channel which is not true in the general case. By describing a well-posed asymmetric problem, dissimilar to the symmetric cousins of the problem already available in the literature, the distributions of temperature field and nanoparticles volume fraction across the channel are analytically determined via a small perturbation approximation. Such a configuration may be relevant to the design of nuclear reactors. Results clearly explain the combined effects of thermophoresis and Brownian on the physical motion. Particularly, it is shown why the Nusselt number of high practical concern should be enhanced under the influence of this combined phenomena leading to cooling of the system. (C) 2018 Elsevier Ltd. All rights reserved.