Mixed convection in a square cavity of sinusoidal boundary temperatures at the sidewalls in the presence of magnetic field is investigated numerically. The horizontal walls of the cavity are adiabatic. The governing equations are solved by finite-volume method. The results are obtained for various combinations of amplitude ratio, phase deviation, Richardson number, and Hartmann number. The heat transfer rate increases with the phase deviation up to phi = pi/2 and then it decreases for further increase in the phase deviation. The heat transfer rate increases on increasing the amplitude ratio. The flow behavior and heat transfer rate inside the cavity are strongly affected by the presence of the magnetic field. (C) 2010 Elsevier Ltd. All rights reserved.