In the present paper, the fluid flow and heat transfer of a nanofluid are numerically investigated. More specifically, reference is made to a nanofluid, described by means of Buongiorno’s model, subjected to Couette flow. The considered domain consists of a channel that displays a cavity shortly after the inlet section. The transport model for the nanofluid, that is the mass conservation, momentum, and nanoparticles equation, is written in a dimensionless form and solved by employing the software package Comsol Multiphysics. Many ideas emerged from this work: the visualization of the velocity stream function, the dimensionless temperature, and nanoparticle concentration fields are provided, as a function of the governing parameters: Reynolds, Peclet, Lewis, Brownian diffusivity number, and thermophoretic diffusivity number. Concerning the nanofluid typical effects, the thermophoretic diffusion seems to affect the solution much more than the Brownian diffusion. The Nusselt number on the upper wall is calculated as well, and the results show that it proves to be, in most of the considered cases, an increasing function of the Reynolds number. Moreover, concerning the Nusselt number, the Brownian diffusion effects are shown to be negligible.

This paper investigated numerically a natural convection in a porous cavity saturated by nanofluide. The left and right wall of the cavity are maintained at the hot-cold temperature respectively, the other walls are adiabatic. The two-phase Buongiorno model has been adopted to take account Brownian and thermophoretic diffusion in order to demonstrate the spatial distribution of the local nanoparticles concentration. After following the temporal evolution of the different structures (0<τ<5), Numerical simulations are performed to explore the effect of density buoyancy (104<Ra<106), the permeability of the homogeneous porous medium (10-5<Da<10-2), on the hydrodynamic, thermal and mass behavior. An original motivation was also introduced in our work to examine the effect of linearly variable permeability along the opposite direction of the cavity by varying the initial Darcy number from (10-5<Da<10-2) and fixing the final Darcy number Daf =10-5. The dimensionless partial differential equations are solved using the finite element method. The effects of the governing parameters on heat transfer are analyzed. Results indicate that the stationary regime is formed after the unsteady regime at dimensionless time τ = 0.3. The movement of nanofluide is strongly influenced by thermal buoyancy forces and depends on the Darcy number, heat transfer is accentuated for the homogenous medium compared to this one with variable permeability. It is found that the convective flow in a homogeneous porous medium is considerably affected by the variation of permeability and consequently the heat transfer is reduced.

In this paper, a numerical study of forced convection on a backward facing step containing a single-finned fixed cylinder has been performed, using a ferrofluid and external magnetic field with different inclinations. The partial differential equations, which determine the conservation equations for mass, momentum and energy, were solved using the finite element scheme based on Galerkin’s method. The analysis of heat transfer characteristics by forced convection was made by taking different values of the Reynolds number (Re between 10 and 100), Hartmann number (Ha between 0 and 100), nanoparticles concentration ( φ between 0 and 0.1) and magnetic field inclination ( γ between 0° and 90°); also, several fin positions α [0°–180°] were taken in the counter clockwise direction by a step of 5. After analysing the results, we concluded that Hartmann number, nanoparticles concentration, Reynolds number and magnetic field angles have an influence on the heat transfer rate. However, the fin position on the cylinder has a big impact on the Nusselt number and therefore on heat transfer quality. The best position of the fin is at ( α = 150°), which gives the best Nusselt number and therefore the best heat transfer, but the fin position at ( α = 0°) remains an unfavourable case that gives the lowest Nusselt values.