1 Copyright © 2012 by ASME Proceedings of the ASME 2012 10th International Conference on Nanochannels, Microchannels, and Minichannels ICNMM2012 July 8-12, 2012, Rio Grande, Puerto Rico ICNMM2012-73006 THERMAL TRANSPIRATION FLOW IN ANNULAR MICROCHANNELS Peyman Taheri Laboratory for Alternative Energy Conversion (LAEC) Mechatronic Systems Engineering School of Engineering Science Simon Fraser University Surrey, British Columbia, Canada E-mail: ptaherib@sfu.ca Majid Bahrami Associate Professor Mechatronic Systems Engineering School of Engineering Science Simon Fraser University Surrey, British Columbia, Canada E-mail: mbahrami@sfu.ca ABSTRACT Thermal transpiration flows of rarefied gases in annular channels are considered, where the driving force for the flow is a temperature gradient applied in the channel walls. The influence of gas rarefaction, aspect ratio of the annulus, and surface accommodation coefficient on mass and heat transfer in the process are investigated. For this, the linearized Navier– Stokes–Fourier (NSF) and regularized 13-moment (R13) equations are solved analytically, and a closed-form expression for Knudsen boundary layers is obtained. The results are compared to available solutions of the Boltzmann equation to highlight the advantages of the R13 over the NSF equations in describing rarefaction effects in this particular thermally- driven flow. Through comparisons with kinetic data it is shown that R13 equations are valid for moderate Knudsen numbers, i.e., Kn < 0.5, where NSF equations fail to describe the flow fields properly. NOMENCLATURE A model dependent coefficient B model dependent coefficient C integrating constant e  heat flow rate [J s -1 ] F e thermodynamic force for heat transfer [J s -1 ] F m thermodynamic force for mass transfer [kg s -1 ] I unit tensor I 0 zeroth-order modified Bessel function of the first kind e J  dimensionless thermodynamic heat fluxes m J  dimensionless thermodynamic mass fluxes K 0 zeroth-order modified Bessel function of the second kind Kn Knudsen number L channel length A macroscopic length for flow L arbitrary length m  mass flow rate [kg s -1 ] m high-order moment tensor [N m -1 s -1 ] p pressure [Pa] Pr Prandtl number q heat-flux vector R high-order moment tensor [N s -2 ] R gas constant [J kg -1 K -1 ] r radial coordinate ∆r circular gap size [m] T temperature [K] v velocity vector V slip velocity [m s -1 ] z axial coordinate [m] Greek α dimensional axial temperature gradient [J kg -1 m -1 ] δ rarefaction parameter ε ratio of inner to outer radii θ temperature in energy unit [J kg -1 ] κ thermal conductivity [kg m -1 s -1 ] λ molecular mean free path [m]