of Heat and(015)1 Contents lists available at ScenceDirect International Journal of Heat and Mass Transfer ELSEVIER journal homepage:www.elsevier.com/locate/ijhmt Numerical simulation of thermomagnetic convection of air in a porous square enclosure under a magnetic quadrupole field using LTNE models Changwei Jiang,Er Shi,Zhangmao Hu,Xianfeng Zhu,Nan Xie ARTICLE INFO ABSTRACT convection of air in a tw 23m March 2015 in this paper. ddle pla of decrease at first and then i 2015 Elsevier Ltd.All rights reserved. 1.Introduction etic field the heattransfer and uid fow has There are electro ic packaging purific al gro porousmedium using the homotopy analysis method. sfe dary con ditions have an important influence on the ngth and field have a strons porous square cavities.Chankim et al.analyzed theoretically porous medium4.Sathiyam 5analWzedtheconveCtw gnetic field.Magnetohydr in E-ma 7oo2aS2aa2&Numerical simulation of thermomagnetic convection of air in a porous square enclosure under a magnetic quadrupole field using LTNE models Changwei Jiang ⇑ , Er Shi, Zhangmao Hu, Xianfeng Zhu, Nan Xie School of Energy and Power Engineering, Changsha University of Science and Technology, Changsha 410114, China Key Laboratory of Efficient and Clean Energy Utilization, College of Hunan Province, Changsha 410114, China article info Article history: Received 21 August 2014 Received in revised form 3 March 2015 Accepted 23 July 2015 Available online 6 August 2015 Keywords: Thermomagnetic convection Numerical simulation Porous media Magnetic quadrupole field Magnetic force abstract In this paper, thermomagnetic convection of air in a two-dimensional porous square enclosure under a magnetic quadrupole field has been numerically investigated. The scalar magnetic potential method is used to calculate the magnetic field. A generalized model, which includes a Brinkman term, a Forcheimmer term and a nonlinear convective term, is used to solve the momentum equations and the energy for fluid and solid are solved with the local thermal non-equilibrium (LTNE) models. The results are presented in the form of streamlines and isotherms and local and average Nusselt numbers. Numerical results are obtained for a range of the magnetic force parameter from 0 to 100, the Darcy num￾ber from 105 to 101 and dimensionless solid-to-fluid heat transfer coefficient from 1 to 1000. The results show that the magnetic force number, Darcy number, Rayleigh number and dimensionless solid-to-fluid heat transfer coefficient have significant effect on the flow field and heat transfer in a por￾ous square enclosure. The flow characteristics presents two cellular structures with horizontal symmetry about the middle plane of the enclosure and the Nusselt numbers are increased as the magnetic force number increases under the non-gravitational condition. The average Nusselt number respects the trend of decrease at first and then increases when the magnetic force number increases under gravitational condition. The non-equilibrium effect on fluid phase temperature and solid phase temperature gradually reduces with the increase of value of H. 2015 Elsevier Ltd. All rights reserved. 1. Introduction Natural convection heat transfer in porous enclosure is widely used in many industrial applications such as cooling of electronic devices, solar collectors, heat exchangers and so on. There are many open literature related to natural convection in porous enclosures [1–3]. Ellahi et al. [4,5] have analyzed the influence of variable viscosity and viscous dissipation on the non-Newtonian flow in porous medium using the homotopy analysis method. Numerical investigation of natural convection within porous square enclosures for various thermal boundary conditions has been done by Ramakrishna et al. [6]. It is found that thermal boundary conditions have an important influence on the flow and heat transfer characteristics during natural convection within porous square cavities. Chankim et al. [7] analyzed theoretically the onset of convection motion in an initially quiescent, horizontal isotropic porous layer. Magnetic field effect on the heat transfer and fluid flow has received much attention in recent years due to its importance in electronic packaging, purification of molten metals, crystal growth in liquids and many others [8–11]. Saleh et al. [12] analyzed the effect of a magnetic field on steady convection in a trapezoidal enclosure filled with a fluid-saturated porous medium by the finite difference method. Grosan et al. [13] examined the effects of a magnetic field and internal heat generation on natural convection heat transfer in an inclined square enclosure filled with a fluid-saturated porous medium. It was shown that both the strength and inclination angle of the magnetic field have a strong influence on convection modes. Nield studied MHD convection in porous medium [14]. Sathiyamoorthy [15] analyzed the convective heat transfer in a square cavity filled with porous medium under a magnetic field. Magnetohydrodynamic natural convection in a rectangular cavity under a uniform magnetic field at different angles with respect to horizontal plane has been investigated by Yu et al. [16]. They concluded that the heat transfer is not only determined by the strength of the magnetic field, but also http://dx.doi.org/10.1016/j.ijheatmasstransfer.2015.07.103 0017-9310/ 2015 Elsevier Ltd. All rights reserved. ⇑ Corresponding author at: School of Energy and Power Engineering, Changsha University of Science and Technology, Changsha 410114, China. Tel./fax: +86 731 85258409. E-mail address: cw_jiang@163.com (C. Jiang). International Journal of Heat and Mass Transfer 91 (2015) 98–109 Contents lists available at ScienceDirect International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt