International Journal of Fluid Mechanics Research, Vol. 41, No. 5, 2014 Numerical Investigation of Hydro-Magnetic Flow of Air in a Lid Driven Cavity for an Optimum Magnetic Situation † Amir Javad Ahrar and Mohamad Hassan Djavareshkian Ferdowsi University of Mashhad, Mashhad, Iran E-mail: am ah47@stu-mail.um.ac.ir In the present paper, Magneto Hydro Dynamics of air flow in a lid driven cavity is assessed numerically. In this process, the finite volume technique and pressure- based algorithm are used for discretisation. The main scope of this research is to find a suitable magnetic field situation to improve the heat transfer rate. Thus several cases with different Ha numbers and magnetic field angles are investigated in order to find the maximum Nusselt number for the heated wall. Generally, it is considered that with the increase of Ha, the Nu number is reduced. Here it will be shown that although this idea is valid for most cases of Ha numbers and magnetic field angles but there are a few exceptions that refute this fact. *** Introduction Generally, cavities can be classified into two major groups; namely closed and open cavities. The lid driven cavities can be considered in the closed cavities group. The lid driven cavities’ heat transfer and mass flow have been investigated widely due to their significant applications in many industries such as: solar concentrators, lakes and reservoirs, refrigeration, cooling process of electric devices and fire researches [1–5]. Also, the problems of natural convection and hydro magnetic flow have been major topics of research during the last decade. Their wide occurrence in many industrial cases like: crystal growth, oil extraction, electronic cooling and solar collectors make them undeniable [6–9]. In 1992, Braga and Viskanta [10] reported an experimental and theoretical investigation of tran- sient natural convection in a rectangular cavity. In 1995 Al-Nimr [11] obtained analytical solutions for MHD fully developed upward (heating) or downward (cooling) natural convection in open ended porous annuli. Later on in 1999, Al-Nimr and Hader [12] modified their solution for more general thermal boundary conditions. Ishikawa et al. [13] numerically investigated the natural convection with density inversion in † Received 26.10.2013 ISSN 1064-2277 c ⃝ 2014 Begell House, Inc. 460