The unsteady and laminar biomagnetic fluid flow of a viscous, incompressible, Newtonian and electrically conducting fluid is numerically investigated. Specifically, the two-dimensional flow driven in an infinite channel containing multiple stenosis and subject to a spatially varying external magnetic field is considered. The numerical method is based on the use of finite element method (FEM) in spatial discretization and unconditionally stable backward finite difference scheme for the time integration, for solving coupled nonlinear differential equations in terms of stream function, vorticity and temperature. Due to nonlinearity, an iterative process is employed between the equations. The study focuses on the alteration of the flow and its temperature behaviors due to the irregular constrictions along the channel. Also, the effects of the external magnetic field, its location and its intensity on the biomagnetic fluid flow are analyzed. The numerical results are presented in terms of streamlines, equivorticity and temperature contours for several values of magnetic field intensity in irregularly and multiply stenosed channels. It is shown that the lengths of the vortices appeared due to the stenosis and magnetic source, increase with an increase in the intensity of the magnetic field and the severity of the constriction. (c) 2014 Elsevier Ltd. All rights reserved.