Scrutiny of mixed convection flow of a nanofluid in a vertical channel

The laminar fully developed nanofluid flow and heat transfer in a vertical channel are investigated. By means of a new set of similarity variables, the governing equations are reduced to a set of three coupled equations with an unknown constant, which are solved along with the corresponding boundary conditions and the mass flux conservation relation by the homotopy perturbation method (HPM). We have tried to show reliability and performance of the present method compared with the numerical method (Runge–Kutta fourth-rate) to solve this problem. The effects of the Grashof number (Gr), Prandtl number (Pr) and Reynolds number (Re) on the nanofluid flows are then investigated successively. The effects of the Brownian motion parameter (Nb), the thermophoresis parameter (Nt), and the Lewis number (Le) on the temperature and nanoparticle concentration distributions are discussed. The current analysis shows that the nanoparticles can improve the heat transfer characteristics significantly for this flow problem.