Abstract

In this study effect of magnetic field dependent (MFD) viscosity on free convection heat transfer of nanofluid in an enclosure is investigated. The bottom wall has constant flux heating element. Single phase nanofluid model is utilized considering Brownian motion. Control Volume based Finite Element Method is applied to simulate this problem. The effects of viscosity parameter, Hartmann number and Rayleigh number on hydrothermal behavior have been examined. Results show that Nusselt number is an increasing function of Rayleigh number and volume fraction of nanoparticle while it is a decreasing function of viscosity parameter and Hartmann number. Also it can be found that reduction of Nusselt number due to MFD viscosity effect are more sensible for high Rayleigh number and low Hartmann number.

Introduction

Magnetohydrodynamic has attracted noteworthy attention due to its numerous applications in petroleum industries and agricultural Journal of Molecular Liquids 218 (2016) 393–۳۹۹ ⁎ Corresponding author. E-mail addresses: m_sh_3750@yahoo.com, m.sheikholeslami@stu.nit.ac.ir (M. Sheikholeslami). http://dx.doi.org/10.1016/j.molliq.2016.02.093 0167-7322/© ۲۰۱۶ Elsevier B.V. All rights reserved. Contents lists available at ScienceDirect Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq engineering. Sheikholeslami et al. [1] used two phase model for simulation of magnetic nanofluid forced convective heat transfer in the presence of variable magnetic field. Rudraiah et al. [2] investigated numerically magnetic field effect on natural convection in a rectangular enclosure. They found that the magnetic field reduces the rate of heat transfer. Hayat et al. [3] investigated the magnetohydrodynamic twodimensional flow with heat and mass transfer over a stretching sheet in the presence of Joule heating and thermophoresis. Force convective heat transfer of magnetic nanofluid in a lid driven semi annulus enclosure has been investigated by Sheikholeslami et al. [4]. Their results showed that Nusselt number has a direct relationship with Reynolds number, nanoparticle volume fraction while it has reverse relationship with Hartmann number. Ferrofluid heat transfer treatment in the presence of variable magnetic field has been studied by Sheikholeslami and Rashidi [5]. They found that Nusselt number increases by considering magnetic field dependent viscosity. Nanjundappa et al. [6] studied the effect of magnetic field dependent (MFD) viscosity on the onset of ferro convection in a ferrofluid saturated horizontal porous layer. Sheikholeslami et al. [7] investigated the effect of variable magnetic field on force convection heat transfer. Their results indicated that the effects of Kelvin forces are more pronounced for high Reynolds number. Thermal radiation effects on MHD forced convection flow adjacent to a non-isothermal wedge were investigated by Chamkha et al. [8]. They showed that local Nusselt number was predicted to decrease as the thermal radiation parameter increased