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The mathematical modeling and numerical solutions of a biomagnetic fluid flow problem is presented. The flow takes place in a channel between two parallel plates and is under the influence of two different externally applied magnetic fields. The steady, two-dimensional flow is viscous and laminar, where the biomagnetic fluid is incompressible and is assumed to be electrically conducting. The plates of the channel are kept at different constant temperature. The flow enters the channel with parabolic and linear profiles for the velocity and temperature, respectively. No-slip boundary conditions for the velocity are imposed on the plates. All the unknowns satisfy homogeneous normal derivative conditions at the exit. The mathematical modeling of the problem results in a coupled nonlinear system of partial differential equations and is given in stream function-vorticity-temperature form. The equations are solved using two powerful numerical tools, the finite element method (FEM) and the dual reciprocity boundary element method (DRBEM) for several values of characteristic flow parameters such as Reynolds number and magnetic numbers. Treatment of nonlinear terms as inhomogeneity enables the use of only the fundamental solution of the Laplace equation in DRBEM. The discretization of only the boundary of the region is the main advantage of DRBEM giving small algebraic systems to be solved at a small expense. Finite element method on the other hand, is capable of giving more accurate results by discretizing the region affected by the magnetic field very finely which results in large sized algebraic systems requiring high computational cost. The results indicate that the flow is appreciably affected with the presence of a uniform magnetic field.