Nanofluid flow and heat transfer in a cavity with variable magnetic field

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Abstract

Fe3O4–water nanofluid flow in a cavity with constant heat flux is investigated using a control volume based finite element method (CVFEM). Effects of Rayleigh and Hartmann numbers and volume fraction of Fe3O4 (nano-magnetite, an iron oxide) on flow and heat transfer characteristics are analyzed. Results indicate that the temperature gradient is an increasing function of the buoyancy force and the volume fraction of Fe3O4, but it is a decreasing function of the Lorentz force. Also, the rate of heat transfer is augmented with an increase in the Lorentz force. However, the opposite is true on the rate of heat transfer with the buoyancy force. Furthermore, the core vortex moves downward with an increase in the Lorentz force. It is expected that the results presented here will not only provide useful information for cooling of electronic components but also complement the existing literature.

Introduction

Magneto-hydrodynamic free convection has various applications such as cooling of electronic components, combustion modeling, fire engineering etc. In recent years, nanotechnology offered an innovative passive method for heat transfer improvement. Alsabery et al. [1] studied the nanofluid conjugate free convection with sinusoidal temperature variation. Pal et al. [2] examined the Soret impact on nanofluid thermal radiation in the presence of a magnetic field. They showed that the shear stress reduces with an increase in the Soret number. Brownian motion effects on the velocity field have been reported by Abdel-wahed et al. [3]. Peristaltic magnetic nanofluid flow in a duct was presented by Akbar et al. [4]. The effect of atherosclerosis on hemodynamics of stenosis has been analyzed by Nadeem and Ijaz [5]. They showed that the velocity gradient on the wall of stenosed arteries decreases with the augmentation of the Strommers number. Ahmad and Mustafa [6] investigated the rotating nanofluid flow induced by an exponentially stretching sheet. Their results revealed that the temperature gradient is a decreasing function of the angular velocity. Hayat et al. [7] presented the influence of radiation on mass transfer of a nanofluid. They showed that the temperature gradient decreases with an increase in the thermal radiation. Bhatti and Rashidi [8] presented the impact of thermo-diffusion on Williamson nanofluid flow over a sheet. Effect of magnetic nanofluid on film condensation was studied by Heysiattalab et al. [9]. They concluded that the Nusselt number increases with a reduction in the size of the nanoparticles.

Selimefendigil and Öztop [10] examined conjugate convection in a cavity with nanofluids. They showed that the temperature gradient increases with an increase in the Grashof number. Garoosi et al. [11] used the Buongiorno model for nanofluid free convection in a heat exchanger. Magnetic and Radiation source terms were considered by Sheikholeslami et al. [12] in final formulae. They reported that Lorentz forces can reduce the temperature gradient. Sheremet and Pop [13] presented the Buongiorno model for nanofluid convection in an enclosure with moving wall. The effect of non-uniform Lorentz force on nanofluid flow has been studied by Sheikholeslami Kandelousi [14]. Lorentz forces impact on flow in an enclosure with oscillating wall was investigated by Selimefendigil and Öztop [15]. They concluded that maximum performance occurs at tilted angle of 90°. Noreen et al. [16] presented nanofluid motion in a curved channel. They showed that the curvature can enhance the longitudinal velocity. Sheikholeslami and Chamkha [17] studied flow and heat transfer of a ferro-nanofluid. Sheikholeslami et al. [18] examined the influence of a magnetic field on forced convection. Farooq et al. [19] investigated two layer nanofluid flow and mass transfer. They illustrated the dissipation effects on the nanofluid motion. In recent decade, several researchers examined nanofluid heat transfer in existence of magnetic field [20], [21], [22], [23], [24], [25], [26], [27], [28], [29].

In this paper, the impacts of variable magnetic field on the hydrothermal nanofluid flow in a cavity heated from below are examined. The control volume based finite element method (CVFEM) is chosen to simulate the pertinent results. Effects of the Hartmann number, the volume fraction of Fe3O4 and the Rayleigh number on hydrothermal characteristics are analyzed. It is expected that the results presented here will not only provide useful information for cooling of electronic components but also complement the existing literature.

Section snippets

Flow geometry and boundary conditions

The geometry for our numerical model is a two-dimensional square cavity with length of side walls equal to L, which represents the characteristic length for the problem (see Fig. 1(a)). The heat source is centrally located on the bottom surface with length L/3. The cooling is achieved by the two vertical walls. The heat source has constant heat flux q″ while the cooling walls have a constant temperature Tc; all the other surfaces are adiabatic. A magnetic source is considered by placing a

Formulation of the problem

Let us consider a steady incompressible two-dimensional laminar flow. The magnetic Reynolds number is assumed to be small, compared to the applied magnetic field so that the induced magnetic field can be neglected. Using the Boussinesq approximation, the governing equations of fluid flow and heat transfer for a nanofluid can be written as vy+ux=0,ρnf(vuy+uux)=Px+μnf(2ux2+2uy2)σnfBy2u+σnfBxByv,ρnf(vvy+uvx)=Py+ρnfβnfg(TTc)+μnf(2vx2+2vy2)+σnfBxByuσnfBx2v,(ρCp)nf(vTy+u

Mesh independency and validation

In order to have a mesh independency output, several grid patterns are examined (see Table 2 for details) and a grid size of 61 × 61 should be considered to reach grid independence outputs. Table 3 illustrates that our results are in very good agreement with those of Rudraiah [32] for free convection flow. In Fig. 3, the accuracy of current results with those of Sharif and Mohammad [33], Khanafer et al. [34], and Calcagni et al. [35] for nanofluid flow with constant heat flux have been compared (

Results and discussion

Effects of a variable magnetic field on Fe3O4–water nanofluid flow in a cavity are presented. The cavity is heated by a uniform heat flux. Different values for volume fraction of Fe3O4 = 0 and 0.04), Hartmann number (Ha = 0 to 10) and Rayleigh number (Ra = 103, 104 and 105) are considered. Also, Ec and Pr are equal to 10−5 and 6.8, respectively.

Influences of Rayleigh and Hartmann numbers on streamlines and isotherms are depicted in Fig. 5 when ϕ = 0.04. According to this figure, the mode of heat

Conclusions

Influence of external magnetic source on Fe3O4–water nanofluid flow and heat transfer in a cavity is investigated. The cavity is heated by a constant flux heating element. Cooling of electronic components can be mentioned as application of this geometry. CVFEM is used to simulate the results. Temperature and velocity contours are presented for different values of the volume fraction of Fe3O4, the Hartmann number, and the Rayleigh number. Results indicate an increase in the thermal boundary

Acknowledgments

The authors thank the reviewers for constructive and helpful comments that led to definite improvement in the paper. Also, the authors thank Professor Michael Taylor for his constructive comments which led to definite improvement in the readability of the paper.

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