EFFECTS OF COMPRESSIBILITY AND RAREFACTION ON GASEOUS FLOWS IN MICROCHANNELS

Abstract

A two-dimensional flow and heat transfer model is used to study gas compressibility and rarefaction in microchannels assuming a slip flow regime. The compressible forms of momentum and energy equations are solved with slip velocity and temperature jump boundary conditions in a parallel plate channel for both uniform wall temperature and uniform wall heat flux boundary conditions. The numerical methodology is based on the control volume finite difference scheme. To verify the model, the mass flow rate was compared with the experimental results of helium through a microchannel. Also, the normalized friction coefficient was compared with the experiments for nitrogen and helium flow in a microchannel. Finally, the axial pressure distribution was compared with the experimental results for nitrogen flow in a microchannel. The computations were performed for a wide range of kn_in, Re, dimensionless distance from the entrance, and for the wall parameters q∗ and T∗, to study the effects of rarefaction and compressibility. It was found that Nusselt number and friction coefficient were substantially reduced for slip flows compared with the continuum flows. The velocity and temperature distributions were flattened compared with continuum flows, and the axial variation of pressure became nonlinear. It was shown that the effect of compressibility was important for higher Re and that the effect of rarefaction was significant for lower Re.

Notes

Address correspondence to Dr. Mohammad Faghri, Mechanical Engineering and Applied Mechanics, University of Rhode Island, Wales Hall, Kingston, RI 02881–0805, USA. E-mail: [email protected]