An analytical examination of a couple stress fluid in respect of the applied magnetic field was carried out using an asymmetric channel with slip condition and heat transfer. The flow problem had been formulated and then simplified by employing lubrication theory. By using wave parameter MHD flow of couple stress fluid was reduced to ODEs, of the governing PDEs. The expression for the axial velocity, pressure rise, stream function and axial pressure gradient are presented graphically and the physical applications discussed. The trapping phenomena and pumping characteristic are presented for couple stress parameter; slip parameter and Hartmann number are discussed. The present analysis revealed that the velocity of the blood increased as the viscosity of blood reduced by influencing the magnetic field strength. This result was very much important at the time of strokes and heart attacks during thicker blood damage in blood vessels.