Slip flow and heat transfer in rectangular and circular microchannels using hybrid FE/FV method

Abstract

SUMMARYRarefied gas flows typically encountered in MEMS systems are numerically investigated in this study. Fluid flow and heat transfer in rectangular and circular microchannels within the slip flow regime are studied in detail by our recently developed implicit, incompressible, hybrid (finite element/finite volume) flow solver. The hybrid flow solver methodology is based on the pressure correction or projection method, which involves a fractional step approach to obtain an intermediate velocity field by solving the original momentum equations with the matrix‐free, implicit, cell‐centered finite volume method. The Poisson equation resulting from the fractional step approach is then solved by node based Galerkin finite element method for an auxiliary variable, which is closely related to pressure and is used to update the velocity field and pressure field. The hybrid flow solver has been extended for applications in MEMS by incorporating first order slip flow boundary conditions. Extended inlet boundary conditions are used for rectangular microchannels, whereas classical inlet boundary conditions are used for circular microchannels to emphasize on the entrance region singularity. In this study, rarefaction effects characterized by Knudsen number (Kn) in the range of 0 ⩽ Kn ⩽ 0.1 are numerically investigated for rectangular and circular microchannels with constant wall temperature. Extensive validations of our hybrid code are performed with available analytical solutions and experimental data for fully developed velocity profiles, friction factors, and Nusselt numbers. The influence of rarefaction on rectangular microchannels with aspect ratios between 0 and 1 is thoroughly investigated. Friction coefficients are found to be decreasing with increasing Knudsen number for both rectangular and circular microchannels. The reduction in the friction coefficients is more pronounced for rectangular microchannels with smaller aspect ratios. Effects of rarefaction and gas‐wall surface interaction parameter on heat transfer are analyzed for rectangular and circular microchannels. For most engineering applications, heat transfer is decreased with rarefaction. However, for fluids with very large Prandtl numbers, velocity slip dominates the temperature jump resulting in an increase in heat transfer with rarefaction. Depending on the gas‐wall surface interaction properties, extreme reductions in the Nusselt number can occur. Present results confirm the existence of a transition point below and above wherein heat transfer enhancement and reduction can occur. Copyright © 2011 John Wiley & Sons, Ltd.