Slip Flow Models for Gas Flows in Rectangular, Trapezoidal, and Hexagonal Microchannels

A compact slip flow model is proposed for isothermal, incompressible gas flows in long microchannels of rectangular (square), trapezoidal (triangular), and double-trapezoidal (rhombic) cross sections in the slip flow regime. The model is based on superposition of the dimensionless mean continuum velocity and the dimensionless average slip velocity. The characteristic length used in the Poiseuille and Knudsen numbers is the hydraulic diameter. A novel slip flow parameter is introduced to account for the relationship between the average slip velocity and the average wall shear stress. The novel slip flow parameter lies in the range 0.5-0.6 for equilateral triangular microducts to very narrow rectangular microchannels when the characteristic length is the hydraulic diameter. The agreement between the proposed compact slip flow model and extensive numerical data is within 1% for a wide range of microchannel shapes and aspect ratios.