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A perturbation-based solution of Burnett equations for gaseous flow in a long microchannel

Published online by Cambridge University Press:  16 April 2018

Aishwarya Rath ,
Narendra Singh  and
Amit Agrawal Open the ORCID record for Amit Agrawal [Opens in a new window]
Aishwarya Rath
Affiliation:
Department of Mechanical Engineering, Indian Institute of Technology Bombay, Mumbai, 400076, India
Narendra Singh
Affiliation:
Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN 55455, USA
Amit Agrawal*
Affiliation:
Department of Mechanical Engineering, Indian Institute of Technology Bombay, Mumbai, 400076, India
*
†Email address for correspondence: [email protected]
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Abstract

In this paper, an analytical investigation of two-dimensional conventional Burnett equations has been undertaken for gaseous flow through a long microchannel. The analytical solution is obtained by using perturbation analysis around the classical Navier–Stokes solution with appropriate boundary conditions. The perturbation expansion is employed with the smallness parameter $\unicode[STIX]{x1D716}$, taken as the ratio of height to length of the microchannel. The solution for pressure is obtained by solving the cross-stream momentum equation while the velocity distribution is obtained from the streamwise momentum equation. The resulting ordinary differential equations in pressure and velocity are third-order and second-order, respectively. The required boundary conditions for pressure are obtained from direct simulation Monte Carlo (DSMC) data. The obtained analytical solution matches the available DSMC solution well. This is perhaps the first analytical solution of the Burnett equations using the perturbation approach.

JFM classification

Micro-/Nano-fluid dynamics: Micro-/Nano-fluid dynamics Micro-/Nano-fluid dynamics: Non-continuum effects Rarefied Gas Flow: Rarefied Gas Flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 844 , 10 June 2018 , pp. 1038 - 1051
Copyright
© 2018 Cambridge University Press 

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