The Effect of Slip-Velocity and Temperature –Jump on the Hydrodynamic and Thermal Behaviors of MHD Free Convection Flows in Vertical Microchannels
Abstract:
The effect of velocity slip and temperature jump on the hydrodynamic and thermal behaviors of MHD flows in the case of free convection have been studied. Four mathematical models that represent those cases have been developed; those are free convection over vertical flat plate, and free convection between two parallel vertical plates. The continuum model of fluid has been used with Knudsen (Kn) number regime 0.001 <Kn<0.1, with the Maxwell slip velocity being applied along with the Smoluchowski temperature jump boundary on the solid-fluid surface interface. Software COMSOL multi physics was used to solve those four models numerically. It was found that the applied transverse magnetic produces Lorentz force that acts as an external body force tends to retard the flow velocity; this retardation was found to be directly proportional with both the magnetic field number (N) and the Knudsen Number (Kn). Also it was found that the increase in the magnetic field applied and the increase of Kn number both will decrease the skin friction factor, decrease the Nusselt number, and decrease the thickness of the velocity boundary layer. The findings of this work were in agreement with the theory and with other related works in that the mutual interaction between the applied transverse magnetic field and the conducting fluid will produce a retarding external body force called Lorentz force acts on the opposite direction of the flow and tends to decrease the flow velocity in the case of two parallel plates and decreases the thickness of the velocity boundary layer in the case of a single plate, also the applied magnetic field will raise the fluid temperature. As a result both the friction coefficient factor and Nusselt number will be decreased by the increase of both Kn number and the magnetic influence number N.