Effects of moving lid direction on MHD mixed convection in a linearly heated cavity Khaled Al-Salem a , Hakan F. Öztop b,a , Ioan Pop c,⇑ , Yasin Varol b a Department of Mechanical Engineering, King Saud University, College of Engineering, Riyadh, Saudi Arabia b Department of Mechanical Engineering, Technology Faculty, Fırat University, Elazig, Turkey c Faculty of Mathematics, University of Cluj, 3400 Cluj-Napoca, CP 253, Romania article info Article history: Received 10 April 2011 Received in revised form 27 August 2011 Accepted 4 September 2011 Available online 7 November 2011 Keywords: Mixed convection Lid-driven Enclosure Magnetic field Numerical solution abstract Effects of moving lid-direction on MHD mixed convection in a cavity with the bottom wall being linearly heated are analyzed using a numerical technique. Vertical walls of the enclosure are adiabatic and the sliding wall at the top has constant temperature. The lid moves in the negative and positive x-direction. Finite volume method has been used to solve the governing equations. Results are presented for different values of Hartmann number (0 6 Ha 6 30), Reynolds number (100 6 Re 6 1000) and Grashof number (10 4 6 Gr 6 10 6 ). It is found that direction of lid is more effective on heat transfer and fluid flow in the case of mixed convection than it is the case in forced convection. Heat transfer is also decreased with increasing of magnetic field for all studied parameters. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction Mixed convection heat transfer and fluid flow in cavities with moving lid are important subjects of investigation due to their ef- fect on many engineering applications and nature phenomena, such as lakes and large reservoirs, solar collectors, crystal growth, food processing and float glass production [1–3]. Heat transfer in low speed lid-driven cavity flow is treated mostly as mixed convec- tion. The flow driven by the movement of one or two of the walls is creating a forced convection conditions while temperature differ- ence across the cavity causes a buoyancy driven, secondary flow. Thus, complicated patterns of heat and mass transfer occur inside the cavity. In the open literature, lid-driven cavity flow under linearly varying temperature boundary condition is investigated without the effect of magnetic field. For example, Aydin [4] studied the aid- ing and constricting mechanisms to mixed convection in a shear and buoyancy driven cavity flows. He showed the forced, mixed and natural convection regimes for different Richardson numbers. In another study of Aydin and Yang [5], mixed convection in double sided square cavity with partial heating is investigated. Oztop and Dag ˘tekin [6] studied the opposite moving side walls cavity flow using SIMPLEM algorithm. They observed different regimes at dif- ferent value of Richardson number. Iwatsu et al. [7] studied mixed convection heat transfer in a lid-driven cavity flow with a stable vertical temperature gradient. They showed conventional lid-dri- ven cavity flow patterns for a non-stratified fluid for small values of the Richardson number. Oztop et al. [8] inserted a circular body inside the lid-driven cavity to control heat and fluid flow. Both thermally stable and unstable lid-driven flows in cavities are inves- tigated by Torrance et al. [9] for constant values of Reynolds num- ber. The Richardson number, which represents the ratio of buoyancy to shear forces, is a controlling parameter for heat and fluid flow. Few investigators have studied the lid driven cavity flow with varying temperature boundary conditions. For example, Basak et al. [10] investigated mixed convection flows in a lid-driven square cavity filled with porous medium using penalty finite ele- ment method. In their study, the bottom wall of the cavity is uni- formly heated and temperature of one side wall varies linearly. It is found that average Nusselt numbers for bottom, left and right walls are almost invariant with Grashof number at Pr ¼ 0:7 for all values of Darcy number on linearly heated side walls or cooled right wall. Oztop and Varol [11] analyzed the combined convection in an inclined cavity under sinusoidally varying temperature boundary condition. The inclination angle can be a control param- eter for both heat transfer and fluid flow inside the cavity. In an- other study by Basak et al. [12], different type of linear boundary condition was applied for the same problem. The influence of a magnetic field is of great importance in many industrial applications such as crystal growth, metal casting and li- quid metal cooling blankets for fusion reactors. It is effective for both natural and mixed convection. Chamkha [1] studied the prob- lem of unsteady, laminar, mixed convection flow in a square cavity 0017-9310/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijheatmasstransfer.2011.09.062 ⇑ Corresponding author. E-mail addresses: hfoztop1@gmail.com (H.F. Öztop), popm.ioan@yahoo.co.uk (I. Pop). International Journal of Heat and Mass Transfer 55 (2012) 1103–1112 Contents lists available at SciVerse ScienceDirect International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt