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)Kn(, heat flux ratio)rq(, Grashof number)Gr(, and Hartmann number)M(on mass flow rate, the maximum temperature of the wall, and average Nusselt (Nu) as a function of time are discussed. In this research, the flow in the limit of 0≥ M ≥ 2; 0≥Kn ≥ 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 Ha 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 Ha. It is also revealed that the magnetic force effect decreases the fluid flow and thermal behavior with an increase in Kn. In addition, in higher Gr, magnetic force influence on profiles of velocity and temperature decreases for all rq and Kn values. Moreover, the magnetic field has no significant effect on the time at which steady state condition is attained for all rq and Gr number values.