The Effect of Slip-Velocity and Temperature –Jump on the Hydrodynamic and Thermal Behaviors of MHD Forced Convection Flows in Horizontal Microchannels
Abstract:
The effect of velocity slip and temperature jump on the hydrodynamic and thermal behaviors of MHD flows in the case of forced convection have been studied. Four mathematical models that represent those cases have been developed; those are forced convection over flat plate, and forced convection between two parallel flat 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. The case of the forced convection between two parallel flat plates has been solved also analytically using MATLAB 7 software. 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). It was noticed that when Kn=0 ,the reduction of the velocity for the same value of magnetic influence number (N=1) is about 10% while for Kn=0.1 the reduction is about 15% in the case of forced flow between two flat plates which shows that Kn and the magnetic influence number are both affecting the flow velocity at the center by decreasing its value. 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.