In continuum mechanics, a branch of mathematics, the Burnett equations is a set of higher-order continuum equations for non-equilibrium flows and the transition regimes where the Navier–Stokes equations do not perform well.[1][2][3]
They were derived by the English mathematician D. Burnett.[4]
Series expansion
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Extensions
editThe Onsager-Burnett Equations, commonly referred to as OBurnett, which form a superset of the Navier-Stokes equations and are second-order accurate for Knudsen number.[5]
Eq. (1)
Eq. (2) [6]
Derivation
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Starting with the Boltzmann equation
See also
editReferences
edit- ^ https://chempedia.info/page/181144203140177134020048169072027076118072084254/
- ^ https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/abs/burnett-equations-in-cylindrical-coordinates-and-their-solution-for-flow-in-a-microtube/F89FC9C029F70CC2669E61C6E5DB0A6B
- ^ https://link.springer.com/chapter/10.1007/978-3-030-10662-1_5
- ^ Burnett, D. (1936). "The Distribution of Molecular Velocities and the Mean Motion in a Non-Uniform Gas". Proceedings of the London Mathematical Society, Volume S2-40, Issue 1, 1936, Pages 382–435. s2-40 (1): 382–435. doi:10.1112/plms/s2-40.1.382.
- ^ Jadhav, Ravi Sudam; Agrawal, Amit (December 23, 2021). "Shock Structures Using the OBurnett Equations in Combination with the Holian Conjecture". Fluids. 6 (12): 427. Bibcode:2021Fluid...6..427J. doi:10.3390/fluids6120427.
- ^ Agarwal, Ramesh K.; Yun, Keon-Young; Balakrishnan, Ramesh (October 1, 2001). "Beyond Navier–Stokes: Burnett equations for flows in the continuum–transition regime". Physics of Fluids. 13 (10): 3061–3085. Bibcode:2001PhFl...13.3061A. doi:10.1063/1.1397256 – via aip.scitation.org (Atypon).
Further reading
edit- García-Colín, L.S.; Velasco, R.M.; Uribe, F.J. (August 2008). "Beyond the Navier–Stokes equations: Burnett hydrodynamics". Physics Reports. 465 (4): 149–189. Bibcode:2008PhR...465..149G. doi:10.1016/j.physrep.2008.04.010.
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