Nanoparticle migration and natural convection heat transfer of Cu-water nanofluid inside a porous undulant-wall enclosure using LTNE and two-phase model

Using Buongiomo's model, the natural convection of Cu-water nanofluid flowing within a wavy wall porous enclosure at the presence of a cylindrical heater was numerically investigated. The problem is considered such that there is no local thermal equilibrium between two phases of porous media. The effects of Rayleigh number (10(3) <= Ra <= 10(6)), the Lewis number (1 <= 5 Le <= 50), Brownian motion parameter (0.1 <= Nb <= 0.5), the thermophoresis parameter (0.1 <= Nt <= 0.5), the buoyancy ratio (0.1 <= Nr <= 0.5), the Darcy number (10(-5) <= Da <= 10(-1)), porosity (0.1 <= epsilon <= 0.9), the ratio of the thermal conductivity of the nanofluid to the solid phase (0.1 <= gamma(s) <= 10), coefficient of heat transfer at the interface (1 <= Nh(s) <= 1000) on hydrodynamic and thermal parameter have been studied. Streamlines, distribution of temperature and concentration of nanoparticles are presented and discussed. Increasing in the Rayleigh, the Darcy, the Lewis numbers, the thermal conductivity ratio and the Brownian parameter of the nanoparticle motions homogenizes the nanofluid. Meanwhile, the homogeneity is reduced as thermophoresis is increased. The results show that the thermal equilibrium model for porous media is applicable for the cases with large heat transfer coefficient at the interface between the solid matrix and the nanofluid. Moreover, the average Nusselt number of both porous phases' increases with the Brownian parameter, while the Nusselt number is reduced as the thermophoresis is increased. (C) 2018 Elsevier B.V. All rights reserved.