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Coupled constitutive relations : a second law based higher order closure for hydrodynamics
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Rana, Anirudh Singh, Gupta, Vinay and Struchtrup, Henning (2018) Coupled constitutive relations : a second law based higher order closure for hydrodynamics. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 474 (2218). doi:10.1098/rspa.2018.0323 ISSN 1364-5021.
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Official URL: https://doi.org/10.1098/rspa.2018.0323
Abstract
In the classical framework, the Navier-Stokes-Fourier equations are obtained through the linear uncoupled thermodynamic force-flux relations which guarantee the non-negativity of the entropy production. However, the conventional thermodynamic description is only valid when the Knudsen number is sufficiently small. Here, it is shown that the range of validity of the Navier-Stokes-Fourier equations can be extended by incorporating the nonlinear coupling among the thermodynamic forces and fluxes. The resulting system of conservation laws closed with the coupled constitutive relations is able to describe many interesting rarefaction effects, such as Knudsen paradox, transpiration flows, thermal stress, heat flux without temperature gradients, etc., which can not be predicted by the classical Navier--Stokes--Fourier equations. For this system of equations, a set of phenomenological boundary conditions, which respect the second law of thermodynamics, is also derived. Some of the benchmark problems in fluid mechanics are studied to show the applicability of the derived equations and boundary conditions.
Item Type: | Journal Article | ||||||||||||
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Subjects: | Q Science > QC Physics | ||||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||
Library of Congress Subject Headings (LCSH): | Hydrodynamics, Navier-Stokes equations, Free molecular flow | ||||||||||||
Journal or Publication Title: | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences | ||||||||||||
Publisher: | The Royal Society Publishing | ||||||||||||
ISSN: | 1364-5021 | ||||||||||||
Official Date: | 1 October 2018 | ||||||||||||
Dates: |
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Volume: | 474 | ||||||||||||
Number: | 2218 | ||||||||||||
DOI: | 10.1098/rspa.2018.0323 | ||||||||||||
Status: | Peer Reviewed | ||||||||||||
Publication Status: | Published | ||||||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||||||
Date of first compliant deposit: | 24 September 2018 | ||||||||||||
Date of first compliant Open Access: | 24 September 2018 | ||||||||||||
RIOXX Funder/Project Grant: |
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