Effect of an external magnetic field is numerically investigated on heat transfer of a horizontal constant laminar pipe flow of a paramagnetic fluid. A single current-carrying coil is presumed for the magnet and the pipe is heated at a constant heat flux. It is found that the effect on the heat and fluid flow strongly depends on the coil location, resulting in local heat transfer enhancement/suppression. Only when the coil is placed at threshold of the heating zone, the enhancement is achieved. This is due to the magnetothermal force which attracts cold fluid toward the coil, and the force induces boundary layer thinning behind the coil. In the case, the heat transfer enhancement at the threshold remains approximately 10% at Reynolds number of 10 in no-gravitational field, although the enhancement decreases with the increase of the Reynolds number under constant magnetic induction. Computations in the presence of the gravity reveals that the magnetothermal force becomes effective especially at upper region. It is found that the effectiveness is in a same order as cases without gravity in slow flow field. The contribution of the magnetic field merges to the no-gravity case in higher flow field. (C) 2015 Elsevier Ltd. All rights reserved.