Magnetohydrodynamic unsteady natural convection slip flow in a vertical parallel plate microchannel heated with constant heat flux

This research presents a numerical study over the unsteady natural convection of an electrically conducting fluid in an open-ended vertical parallel plate microchannel under uniform and asymmetric heat flux subjected to a uniform lateral magnetic field. Slip velocity, as well as temperature jump at channel walls, are modeled using a first-order model. The effects of Knudsen number)<i>Kn</i>(, heat flux ratio)rq(, Grashof number)<i>Gr</i>(, and Hartmann number)M(on mass flow rate, the maximum temperature of the wall, and average Nusselt (<i>Nu</i>) as a function of time are discussed. In this research, the flow in the limit of 0≥ M ≥ 2; 0≥<i>Kn</i> ≥ 0.1; 0.1≥ rq ≥ 1, and 0.0001≥ L ≥ 0.01 were simulated numerically. Furthermore, and study is conducted on steady-state velocity and temperature profiles. The research showed that increasing the <i>Ha</i> value, causes a reduction in the mass flow and an increase in the maximum temperature of the wall with respect to time. As M increases, the average Nusselt number as a function of time diminishes. Also, these variables present at least one overshoot or undershoot in time. The overshoot and undershoot decrease with increasing <i>Ha</i>. It is also revealed that the magnetic force effect decreases the fluid flow and thermal behavior with an increase in <i>Kn</i>. In addition, in higher <i>Gr</i>, magnetic force influence on profiles of velocity and temperature decreases for all rq and <i>Kn</i> values. Moreover, the magnetic field has no significant effect on the time at which steady state condition is attained for all rq and <i>Gr</i> number values.