The two-dimensional unsteady, laminar flow of a viscous, Newtonian, incompressible and electrically conducting biofluid in a channel with a stenosis, under the influence of a spatially varying magnetic field, is considered. The mathematical modeling of the problem results in a coupled nonlinear system of equations and is given in stream function-vorticity-temperature formulation for the numerical treatment. These equations together with their appropriate boundary conditions are solved iteratively using the finite element method for the spatial discretization, and an unconditionally stable backward difference scheme is employed for the time integration. The numerical results obtained are illustrated using streamlines, vorticity and temperature contours. The behavior of the biofluid along the thin channel is investigated for a symmetric stenosis of degrees 40% and 60%, with a magnetic source placed below the lower plate. The results indicate that the flow is appreciably affected by the presence of stenosis and the magnetic source in terms of vortices. The lengths of the vortices and the temperature increase with increase in the intensity of the magnetic field and the degree of the constriction. (C) 2013 Elsevier B.V. All rights reserved.