The numerical study examines the development of steady state free convection in an open-ended vertical microchannel, heated by symmetric and asymmetric wall temperatures, and with a constant transverse magnetic field. The first order model accounts for slip velocity and temperature jumps at the channel walls. The SIMPLE-C co-located body fitted algorithm is used. For convection terms, QUICK scheme and for diffusion terms, central difference are used. The interplay among Hartmann number, Knudsen number, Grashof number, and heat flux ratio is investigated graphically to understand their influence on velocity and temperature profiles, Nusselt number, and mass flow rate. The results of this research show that, for all Grashof numbers and heat flux ratios, the mass flow rate decreases as the velocity does with an elevated Hartmann number. The Hartmann number determines the rate of temperature increase along the channel walls and through the channel’s cross section. In higher Knudsen numbers, these effects are more pronounced. In larger Grashof numbers, the impact of magnetic forces on velocity and temperature profiles wanes for all heat flux ratios, resulting in minor Nusselt number changes with growing Hartmann numbers. At lower Grashof numbers, a higher Hartmann number causes a rise in average wall temperature which decreases the Nusselt number. The mass flow rate and average Nusselt number become greater as heat flux ratio increases. For all considered Hartmann numbers, their behavior shows a near-linear trend with heat flux ratio.
