Abstract—This paper is concerned with the effect of Hartmann number on the free convective flow in a square cavity with different positions of heated square block. The two-dimensional Physical and mathematical model have been developed, and mathematical model includes the system of governing mass, momentum and energy equations are solved by the finite element method. The calculations have been computed for Prandtl number Pr = 0.71, the Rayleigh number Ra = 1000 and the different values of Hartmann number. The results are illustrated with the streamlines, isotherms, velocity and temperature fields as well as local Nusselt number. Keywords—Finite element method, free convection, Hartmann number, square cavity. I. INTRODUCTION REE convection is one of the most important phenomena in thermal system; this is due to its wide applications in nature and engineering such as oceanic currents, sea-wind, fluid flows around shrouded heat dissipation fins, free air cooling without the aid of fans, electronics cooling, heat exchangers and so on. MHD natural convection flow and heat transfer in a laterally heated partitioned enclosure is investigated by Kahveci and Oztuna [1]. Taghikhani and Chavoshi [2] investigated two dimensional magneto-hydrodynamics (MHD) free convection with internal heating in a square cavity and observed the effect of the magnetic field which is to reduce the convective heat transfer inside the cavity. Parvin and Nasrin [3] analyzed the flow and heat transfer characteristics for MHD free convection in an enclosure with a heated obstacle and found that, buoyancy-induced vortex in the streamlines increase as well as the thermal layer near the heated surface becomes thick with increasing Rayleigh number. Ganzarolli and Milanez [4] numerically investigated natural convection in rectangular enclosure heated from below and symmetrically cooled from the sides. Sathiyamoorty et al. [5] studied the steady natural convection flow in a square cavity with linearly heated side walls. Nawaf [6] investigated the natural convection in a square porous cavity with an oscillating wall temperature. The results are presented to demonstrate the Abdul Halim Bhuiyan is with the Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka-1000, Bangladesh (phone: +8801740574576; e-mail: ahalim@math.buet.ac.bd). M. A. Alim and Md. Nasir Uddin are with the Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka-1000, Bangladesh (e-mail: maalim@math.buet.ac.bd mnasiruddin07@gmail.com). temporal variation of the streamlines, the isotherms and the Nusselt number. The peak value of the average Nusselt number is observed to occur at the resonance nondimensional frequency of 450 in the range considered (1–2000) for Rayleigh number 10 3 . Hakan et al. [7] analyzed the laminar MHD mixed convection flow in a top sided lid- driven cavity heated by corner heater and considered the temperature of the lid is lower than that of heater. Also Hakan et al. [8] studied the effects of volumetric heat sources on Natural convection in wavy-walled enclosures are studied numerically. Bakhshan and Ashoori [9] investigated the analysis of a fluid behavior in a rectangular enclosure under the effect of magnetic field. They observed that Nusselt number rises with increasing Grashof and Prandtl numbers and decreasing Hartmann and orientation of magnetic field. Therefore, in the light of above literatures, the aim of the present work is to investigate the effects of Hartmann number on free convective flow in a square cavity with different positions of heated square block. II. MODEL AND MATHEMATICAL FORMULATION Fig. 1 shows a schematic diagram and the coordinates of a two-dimensional square cavity, where the bottom wall is maintained at a uniform temperature T h and the top wall may be maintained cooled whereas side walls are kept insulated. Fig. 1 The flow configuration and coordinate system A heated square block is considered in a square cavity with different positions and Fig. 1 treats as left bottom Abdul Halim Bhuiyan, M. A. Alim, Md. Nasir Uddin Effect of Hartmann Number on Free Convective Flow in a Square Cavity with Different Positions of Heated Square Block F L T c T h g x y B 0 World Academy of Science, Engineering and Technology International Journal of Physical and Mathematical Sciences Vol:8, No:2, 2014 385 International Scholarly and Scientific Research & Innovation 8(2) 2014 scholar.waset.org/1307-6892/9997701 International Science Index, Physical and Mathematical Sciences Vol:8, No:2, 2014 waset.org/Publication/9997701