Analysis of mixed convection flow of a nanofluid in a vertical channel with the Buongiorno mathematical model

The laminar, fully developed mixed convection flow between two paralleled vertical flat plates filled by a nanofluid is 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. The exact solutions are obtained by means of the homotopy analysis method for both the buoyancy-assisted and the buoyancy-opposing cases and their accuracies are checked in detail. The effects of the Grashof number Gr and the Prandtl number Pr on the nanofluid flows are then investigated successively. We further consider the effects of the buoyancy ratio Nr, the Brownian motion parameter Nb, the thermophoresis parameter Nt on the pressure parameter σ and the Nusselt number Nu. It is found that the heat transfer characteristic can be improved significantly as the proper nanofluids are applied.