The general equations of magnetohydrodynamic convection in a liquid are expressed in non-dimensional forms, in terms of modified Hartmann and Grashof numbers. They are applied to boundary layer flow up a hot vertical plate, in the presence of a uniform horizontal magnetic field normal to the plate. The case when magnetic drag dominates viscous and inertial forces is primarily considered. Similarity solutions and solutions based on a Pohlhausen-like type of approximation are derived and are compared.