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.

The purpose of research presented in this paper is to study the thermal and hydrodynamic effect of the non-isothermal laminar flow of a Al2O3-water nanofluid having shear thinning behavior in a mechanically stirred tank using the finite element method. Numerical simulation has been performed for a non-stationary two-dimensional flow controlled by certain influencing parameters such as the Reynolds number (1 ≤ Re ≤ 200), the behavior index (0.6 ≤ n ≤ 1) and the volume fraction of the alumina nanoparticles (0 ≤ φ ≤ 0.1). The simulation results obtained show that the addition of the Al2O3 nanoparticles in the base fluid leads to a significant enhancement in the heat transfer in the stirred tank compared to the base fluid. On the other hand, we note a slight decrease in the heat transfer with the decrease in the behavior index. It has also been noted, that the agitation power increases relatively with the volume fraction of the Alumina nanoparticles.

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.

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In this paper, a numerical investigation using the finite element method on the cooling capacity of an electronic heat sink has been presented. This heat sink is intended for cooling applications of micro-computer CPUs. It deals with a parallelepipedal block with rectangular fins, filled with a nanofluid and crossed by four cylindrical pipes in which a cooling gas flows and dissipates the heat generated by the processor. Indeed, the cooling occurs by three transfers: the first one evacuates the heat from the processor towards the gas, the second one transfers this heat towards the nanofluid and the last one is cooled from the ambient air by means of the fins laterally arranged on the block. From this work, it has been planned to contribute to the study of the behavior of a nanofluid in the heat sink in the presence of a uniform magnetic field in order to enhance the operating and cooling performances. The effects of some control parameters have been highlighted on the hydrodynamic, thermal, and mass behavior of the nanofluid, namely: the Rayleigh number (103 ≤ Ra ≤ 105), the Hartmann number (0 ≤ Ha ≤ 100), the angle of inclination of the magnetic field (0 ≤ γ ≤ 90°) and the nanoparticles diameter (1 nm ≤ dp ≤ 10 nm). On the other hand, a new fin design has been proposed in this study allowing the enhancement of the heat exchange rate with ambient medium. The studied phenomenon is governed by the equations of the two-phase nanofluid model proposed by Buongiorno and which describe the following balances: mass, momentum, energy and nanoparticles. The system of partial differential equations with initial-boundary conditions has been solved by the finite element method. After performing a mesh independence check and validating with previous papers, the results of the investigation were presented. They showed that the application of a magnetic field significantly reduces the rate of heat exchange. However, increasing the angle of inclination of this field promotes convective heat transfer. Moreover, the use of zigzag fins improves the cooling rate by about 4% for amplitude of 0.05 compared to the standard configuration.