Coupled constitutive relations: A second law based higher-order closure for hydrodynamics

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dc.contributor.authorRana, Anirudh Singh
dc.contributor.authorGupta, Vinay Kumar
dc.contributor.authorStruchtrup, Henning
dc.date.accessioned2018-10-18T13:49:53Z
dc.date.available2018-10-18T13:49:53Z
dc.date.copyright2018en_US
dc.date.issued2018
dc.description.abstractIn 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 descrip- tion 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 cannot 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.en_US
dc.description.reviewstatusRevieweden_US
dc.description.scholarlevelFacultyen_US
dc.description.sponsorshipThis work has been financially supported in the UK by EPSRC grant no. EP/N016602/1. A.S.R. gratefully acknowledges the funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska Curie grant agreement no. 713548. V.K.G. gratefully acknowledges the financial support through the Commonwealth Rutherford Fellowship. H.S. gratefully acknowledges support through an NSERC Discovery grant.en_US
dc.identifier.citationProc. R. Soc. A 474: 20180323en_US
dc.identifier.urihttp://dx.doi.org/10.1098/rspa.2018.0323
dc.identifier.urihttp://dx.doi.org/10.6084/m9. figshare.c.4258202.
dc.identifier.urihttp://hdl.handle.net/1828/10170
dc.language.isoenen_US
dc.publisherThe Royal Society Publishingen_US
dc.subjectcoupled constitutive relationsen_US
dc.subjectNavier–Stokes–Fourier equationsen_US
dc.subjectsecondlaw consistent boundary conditionsen_US
dc.subjectrarefaction effectsen_US
dc.titleCoupled constitutive relations: A second law based higher-order closure for hydrodynamicsen_US
dc.typeArticleen_US

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