Friction and Heat Transfer in Liquid and Gas Flows in Micro- and Nanochannels

Abstract

Abstract Models and corresponding correlations are proposed for Poiseuille flow in long micro- and nanochannels of circular and noncircular cross sections. The Poiseuille number is based on the Fanning friction factor, and the characteristic lengths are the conventional hydraulic diameter and the square root of the flow area. The accurate correlations are applicable for regular polygonal and trapezoidal microducts, elliptical, rectangular, and circular annular microchannels. Models and correlations are developed for Poiseuille flow in isosceles trapezoidal and hexagonal microchannels which are KOH-etched in silicon substrates. The equivalent circular annular model is proposed for Poiseuille flows in doubly connected microchannels such as circular microchannels with polygonal cores and polygonal microchannels with circular cores. A comprehensive model and correlation are advanced for Poiseuille flow in arbitrary (scalene) microducts. Models and correlations are proposed for convective heat transfer for Poiseuille flow in circular and noncircular microchannels with isoflux and isothermal walls. A compact model is given for the slip flow regime for circular and noncircular microducts and microchannels, which is based on slip flow parameters and the continuum Poiseuille number. All numerical results for regular polygonal and trapezoidal microducts and elliptical, rectangular, circular annular, and trapezoidal microchannels are in very good agreement with the slip flow model which is extended into the transition regime down to the Knudsen minimum. Rarefied gas flows in elliptical and rectangular microchannels in the slip flow and transition regimes are found to be similar for identical aspect ratios.