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Burnett Equations: Derivation and Analysis

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Microscale Flow and Heat Transfer

Part of the book series: Mechanical Engineering Series ((MES))

Abstract

The Burnett equations is a superset of the Navier–Stokes equations, and one of the most important higher-order continuum transport equations. The derivation and nature of the equation in both Cartesian and cylindrical coordinates is presented in this chapter. The equations involve large number of terms, which makes them quite formidable to solve, both analytically and numerically. Nonetheless there has been some recent success in obtaining analytical solution of the Burnett equations, as discussed here. An order of magnitude analysis of the various terms reveals that the Burnett-order terms in the equations are of order Knudsen number square. A stability analysis of the equations for one-dimensional wave reveals the unstable nature of the equations.

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Notes

  1. 1.

    Pressure tensor, P ij and stress tensor, τ ij as defined in Chap. 2 have opposite sign, i.e. P ij = −τ ij.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Technology, Bombay, Mumbai, Maharashtra, India

    Amit Agrawal, Hari Mohan Kushwaha & Ravi Sudam Jadhav

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  1. Amit Agrawal
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  2. Hari Mohan Kushwaha
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  3. Ravi Sudam Jadhav
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Agrawal, A., Kushwaha, H.M., Jadhav, R.S. (2020). Burnett Equations: Derivation and Analysis. In: Microscale Flow and Heat Transfer. Mechanical Engineering Series. Springer, Cham. https://doi.org/10.1007/978-3-030-10662-1_5

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  • DOI: https://doi.org/10.1007/978-3-030-10662-1_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-10661-4

  • Online ISBN: 978-3-030-10662-1

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