Motivated by increasingly being used magnetohydrodynamic micropumps for pumping biological and chemical specimens, this study presents a simplified magnetohydrodynamic flow model based upon steady-state, incompressible and fully developed laminar flow theory in rectangular channel to offer the characteristics of magnetohydrodynamic pumps for prediction of pumping performance in magnetohydrodynamic flow. The non-linear governing equations of motion and energy including viscous and Joule dissipation are solved numerically for velocity and temperature distributions. To aim this goal a finite difference approximation based code is developed and utilized.In addition, the effects of magnetic flux density, applied electric current and channel size on flow velocity field as well as thermal behavior are investigated in various working medium with different physical properties. The entropy generation rate is discussed also. The simulation results are in good agreement with experimental data from literature.