The effect of a strong magnetic field on the temperature and velocity fields of laminar flow was examined. The magnetizing force and gravity term were included in the momentum conservation equation. Biot-Savart's law was applied to obtain the distribution of magnetic field. Three-dimensional computations were performed for straight pipe and pipe with elbow. The single circular magnetic coil was oriented perpendicularly to the flow axis and divided the straight pipe in two equal parts, while in the case of pipe with elbow was just at the beginning of elbow. The wall of the first straight part was adiabatic while the second was isothermal. Half of the elbow was heated, while the reamining part was adiabatic. Various boundary conditions were applied to estimate their influence on the velocity and temperature distributions. Low entrance velocity, high wall temperature and strong magnetic field led to deceleration of the flow in the central area, acceleration near the wall and formation of recirculation zone in between for the straight pipe. Flow structure and temperature field in the pipe with elbow were significantly modified by the magnetic force. Increasing entrance velocity reduced influence of magnetic field, therefore the flow was less modified. High temperature and magnetic induction resulted in significant changes of the velocity profile. The analysis was conducted with an application of software with special user-defined function. The magnetic field had an influence on the forced convection but its scale depended on the fluid and flow properties, boundary conditions and magnetic field induction.