Effects of velocity slip and temperature jump on the heat transfer and entropy generation in micro porous channels under magnetic field

Abstract

A thermodynamic analysis was performed for thick walled microchannels using the velocity slip and temperature jump at the interface of the solid–fluid phases. The slip velocity and temperature jump effects were assumed to be equal for both the upper and lower walls. A Darcy–Brinkman model was used in the application of the momentum equation in the porous section of the channel and the effects of the magnetic field were considered. The thermal boundary conditions for two separate cases were proposed; case one assumed a constant high temperature for the lower wall and a constant low temperature for the upper wall, and case two which assumed constant heat flux boundary conditions for the lower wall and convective heat transfer for the upper wall. Constant, but different, internal heat generations were incorporated into the energy equations for all three parts of the system, and a combined analytical–numerical solution procedure was then applied. A comprehensive investigation of the effects of the slip velocity and temperature jump on the velocity field, temperature distribution, Nusselt number, and local entropy generation rate was performed. The results indicate that a variation on the magnetic field may change the fluid velocity at the solid–fluid interface. Interestingly, it was shown that by using a specific value for the temperature jump coefficient and variations in the thickness of the upper and/or lower wall thickness, it may be possible to achieve the maximum Nusselt number. However, depending on the value of the temperature jump, the Nusselt number may continuously increase or decrease, depending on the wall thickness.