A mathematical model is presented to study the role of an applied magnetic field on heat transfer during melting of a semi-infinite slab swept by a laminar flow of an electrically conducting liquid. The integral forms of the governing equations were solved by taking into account the sensitivity of the velocity profile to the magnetic field. Numerical results were obtained for a specified set of characteristic dimensionless numbers, i.e. Reynolds number, Prandtl number, Stefan numbers and magnetic parameter and their influence on heat transfer and melt generation is reported.