Analytical and numerical study of MHD natural convection in a horizontal shallow cavity with heat generation

A study is presented of two-dimensional MHD natural convection flow in an internally heated horizontal shallow cavity in the presence of an external uniform vertical magnetic field. The main feature of the present flow is a symmetric double-cell Hadley circulation with the fluid ascending in the center of the cavity and descending near the vertical cold walls. All walls are electrically insulated, with the horizontal being adiabatic and the vertical isothermal. The method of the matched asymptotic expansions is used to obtain solutions of the flow and heat transfer problem. This analysis which is valid for large cavity aspect ratios and for any magnetic field strength is particularly helpful for the inexpensive determination of the flow and heat transfer characteristics. In addition, numerical simulations are performed for a range of Hartmann, Prandtl and Rayleigh numbers in order to verify the accuracy and validity of the analytical results, to calculate the constants arising by the analytical approach and to obtain details of the flow in the vicinity of the vertical side walls. The comparison of the analytical and numerical results is very good indicating the correctness of the present analysis and its applicability.