Maxwell's original slip boundary condition is widely misapplied in current rarefied gas flow calculations (e.g. in hypersonics, microfluidics). If its commonly-accepted form is applied in simulations of gas flows over curved or moving surfaces, crucial physics can be lost. We give examples of such cases. We also propose a new higher-order boundary condition which is based on Maxwell's original equation and the constitutive relations derived by Burnett. Unlike other higher-order models this is generally applicable to three-dimensional moving surfaces. It is shown that these 'MaxwellBurnett' boundary conditions give much closer agreement with experimental data for Poiseuille flow than existing higher-order models and can also predict Sone's thermal-stress slip flow -a phenomenon which cannot be captured by conventional slip boundary conditions.

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This version is available at https://strathprints.strath.ac.uk/5019/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the Strathprints administrator: strathprints@strath.ac.ukThe Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output. The Knudsen layer is an important rarefaction phenomenon in gas flows in and around microdevices. Its accurate and efficient modeling is of critical importance in the design of such systems and in predicting their performance. In this paper we investigate the potential that higher-order continuum equations may have to model the Knudsen layer, and compare their predictions to high-accuracy DSMC ͑direct simulation Monte Carlo͒ data, as well as a standard result from kinetic theory. We find that, for a benchmark case, the most common higher-order continuum equation sets ͑Grad's 13 moment, Burnett, and super-Burnett equations͒ cannot capture the Knudsen layer. Variants of these equation families have, however, been proposed and some of them can qualitatively describe the Knudsen layer structure. To make quantitative comparisons, we obtain additional boundary conditions ͑needed for unique solutions to the higher-order equations͒ from kinetic theory. However, we find the quantitative agreement with kinetic theory and DSMC data is only slight.