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Highlights • The Buongiorno’s nanofluid model is introduced for cavity nanofluid flow. • The buoyancy term is given more concisely. • Non-uniform heating types of practical importance overlooked in literature are presented. • A novel wavelet-homotopy technique is proposed. • Physical mechanisms on cavity flows with various types of heated and lid-driven walls are conducted. Abstract The laminar mixed convection flow in an inclined lid-driven cavity filled with a nanofluid is investigated in the presence of internal heat generation. The two sidewalls of the enclosure are sinusoidally heated while the top and bottom walls are insulted. The Buongiorno’s model that incorporates the effects of Brownian motion and thermophoresis is applied to describe the nanofluid behaviours. Parametrical studies are given on the regimes of the complex flow, temperature and concentration fields. The developed equations are nondimensionalized and then solved numerically by the newly developed wavelet-homotopy technique. Comparisons with previously studies in literature are presented and found to be in excellent agreement. The results of this work indicate that the Grashof number, the slipping parameters, the nanoparticles related parameters, the inclination, the boundary coefficients including amplitude ratios of temperature and concentration, as well as the phase deviation have significant effects on characteristics of the cavity flow. [ABSTRACT FROM AUTHOR]

Abstract: 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. [Copyright &y& Elsevier]