Analysis of the slip flow in the hydrodynamic entrance region of a 2D microchannel

Abstract

Two-dimensional developing flow in the entrance of a microchannel has been studied numer-ically. Due to its nature, a microchannel can be used in tight space applications and the length of channel can get very small values. Furthermore, if the hydrodynamic development length of flow in microchannel has comparably the same value with the channel length, the channel entrance parameters play critical role on the flow performance of a microscale channel. Lattice Boltzmann Method (LBM) was considered for studying and simulating the developing slip flows through a rectangular microchannel. A unique computational code for this study was developed by using LBM. The slip velocity boundary condition along with Knudsen number values in the slip flow regime was used for this model. The bounce-back boundary condition was considered at the top and bottom walls of the microchannel. The effects of the Reyn-olds numbers (1-100) and Knudsen numbers (0.001, 0.01, 0.1) on the hydrodynamic entrance length has been examined. The numerical results have been compared with the previous stud-ies in the literature and the similarities have been found satisfactory. The entrance length is found to be increasing with the increase of Reynolds and Knudsen numbers. A correlation for hydrodynamic development length as a function of Knudsen and Reynolds numbers was obtained by using the data extracted from LBM simulations performed in this study.