Magnetohydrodynamic (MHD) is a new and important branch of fluid dynamics. It focuses on fluid flow and magnetic field interaction. Any movement of an electrically conducting fluid in the presence of a magnetic field leads to induce a body force to the fluid flow. This force can change hydrodynamic and thermal behaviors of the flow. In this study, natural, mixed and forced convection of a laminar flow in microchannels under the effect of a uniform transverse magnetic field are investigated numerically. In the case of natural convection, steady and unsteady behaviors are studied. It is revealed that magnetic force decreases mass flow rate. It increases temperature along the channel walls and causes to an increase in cross section one. Nusselt number also decreases with magnetic field. Mass flow rate and maximum wall temperature as a function of time detect at least one overshoot. The overshoot decreases with an increase in magnetic field strength. Moreover, it is observed that the time at which steady state condition is attained has insignificant change with magnetic force. Mixed convection in a vertical microchannel is investigated. In this case, increasing magnetic force, leads to a decrease in maximum velocity value and causes to an increase in velocity gradient near the channel walls. Temperature increases slightly with Lorentz force and hence, Nusselt number increase. In higher considered Knudsen number, magnetic force effect on the fluid flow and thermal characteristic increases. In addition, with an increase in buoyancy force, magnetic field influence decreases. Forced convection in a horizontal channel under the effect of magnetic field also is studied. This field leads to a decrease in the maximum velocity value and hence causes to a significant increase in velocity gradient close the channel walls. This effect causes to a significant increase in friction factor coefficient. Nusselt number increase slightly with an increase in magnetic force. In addition, increasing magnetic force leads to increase on the fully developed temperature, but, it has insignificant effect on the channel entrance region. It is very interested to note that in all cases of natural, mixed and forced convection, magnetic force influence on the fluid flow behavior is almost more significant with respect to thermal one. Keywords: MHD, Slip flow, Transient, Microchannels, Unsteady, Natural convection, Mixed convection, Forced convection