Proposal of a critical test of the Navier-Stokes-Fourier paradigm for compressible fluid continua
A critical, albeit simple experimental and/or molecular-dynamic (MD) simulation test is proposed whose outcome would, in principle, establish the viability of the Navier-Stokes-Fourier (NSF) equations for compressible fluid continua. The latter equation set, despite its longevity as constituting the...
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| Format: | Article |
| Language: | en_US |
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American Physical Society
2013
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| Online Access: | http://hdl.handle.net/1721.1/78288 |
| _version_ | 1811082243696754688 |
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| author | Brenner, Howard |
| author2 | Massachusetts Institute of Technology. Department of Chemical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Chemical Engineering Brenner, Howard |
| author_sort | Brenner, Howard |
| collection | MIT |
| description | A critical, albeit simple experimental and/or molecular-dynamic (MD) simulation test is proposed whose outcome would, in principle, establish the viability of the Navier-Stokes-Fourier (NSF) equations for compressible fluid continua. The latter equation set, despite its longevity as constituting the fundamental paradigm of continuum fluid mechanics, has recently been criticized on the basis of its failure to properly incorporate volume transport phenomena—as embodied in the proposed bivelocity paradigm [ H. Brenner Int. J. Eng. Sci. 54 67 (2012)]—into its formulation. Were the experimental or simulation results found to accord, even only qualitatively, with bivelocity predictions, the temperature distribution in a gas-filled, thermodynamically and mechanically isolated circular cylinder undergoing steady rigid-body rotation in an inertial reference frame would not be uniform; rather, the temperature would be higher at the cylinder wall than along the axis of rotation. This radial temperature nonuniformity contrasts with the uniformity of the temperature predicted by the NSF paradigm for these same circumstances. Easily attainable rates of rotation in centrifuges and readily available tools for measuring the expected temperature differences render experimental execution of the proposed scheme straightforward in principle. As such, measurement—via experiment or MD simulation—of, say, the temperature difference ΔT between the gas at the wall and along the axis of rotation would provide quantitative tests of both the NSF and bivelocity hydrodynamic models, whose respective solutions for the stated set of circumstances are derived in this paper. Independently of the correctness of the bivelocity model, any temperature difference observed during the proposed experiment or simulation, irrespective of magnitude, would preclude the possibility of the NSF paradigm being correct for fluid continua, except for incompressible flows. |
| first_indexed | 2024-09-23T12:00:00Z |
| format | Article |
| id | mit-1721.1/78288 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T12:00:00Z |
| publishDate | 2013 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/782882022-09-27T23:21:30Z Proposal of a critical test of the Navier-Stokes-Fourier paradigm for compressible fluid continua Brenner, Howard Massachusetts Institute of Technology. Department of Chemical Engineering Brenner, Howard A critical, albeit simple experimental and/or molecular-dynamic (MD) simulation test is proposed whose outcome would, in principle, establish the viability of the Navier-Stokes-Fourier (NSF) equations for compressible fluid continua. The latter equation set, despite its longevity as constituting the fundamental paradigm of continuum fluid mechanics, has recently been criticized on the basis of its failure to properly incorporate volume transport phenomena—as embodied in the proposed bivelocity paradigm [ H. Brenner Int. J. Eng. Sci. 54 67 (2012)]—into its formulation. Were the experimental or simulation results found to accord, even only qualitatively, with bivelocity predictions, the temperature distribution in a gas-filled, thermodynamically and mechanically isolated circular cylinder undergoing steady rigid-body rotation in an inertial reference frame would not be uniform; rather, the temperature would be higher at the cylinder wall than along the axis of rotation. This radial temperature nonuniformity contrasts with the uniformity of the temperature predicted by the NSF paradigm for these same circumstances. Easily attainable rates of rotation in centrifuges and readily available tools for measuring the expected temperature differences render experimental execution of the proposed scheme straightforward in principle. As such, measurement—via experiment or MD simulation—of, say, the temperature difference ΔT between the gas at the wall and along the axis of rotation would provide quantitative tests of both the NSF and bivelocity hydrodynamic models, whose respective solutions for the stated set of circumstances are derived in this paper. Independently of the correctness of the bivelocity model, any temperature difference observed during the proposed experiment or simulation, irrespective of magnitude, would preclude the possibility of the NSF paradigm being correct for fluid continua, except for incompressible flows. 2013-04-04T17:22:00Z 2013-04-04T17:22:00Z 2013-01 2012-07 Article http://purl.org/eprint/type/JournalArticle 1539-3755 1550-2376 http://hdl.handle.net/1721.1/78288 Brenner, Howard. “Proposal of a Critical Test of the Navier-Stokes-Fourier Paradigm for Compressible Fluid Continua.” Physical Review E 87.1 (2013): [11 pages]. CrossRef. Web. ©2013 American Physical Society. en_US http://dx.doi.org/10.1103/PhysRevE.87.013014 Physical Review E Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Physical Society APS |
| spellingShingle | Brenner, Howard Proposal of a critical test of the Navier-Stokes-Fourier paradigm for compressible fluid continua |
| title | Proposal of a critical test of the Navier-Stokes-Fourier paradigm for compressible fluid continua |
| title_full | Proposal of a critical test of the Navier-Stokes-Fourier paradigm for compressible fluid continua |
| title_fullStr | Proposal of a critical test of the Navier-Stokes-Fourier paradigm for compressible fluid continua |
| title_full_unstemmed | Proposal of a critical test of the Navier-Stokes-Fourier paradigm for compressible fluid continua |
| title_short | Proposal of a critical test of the Navier-Stokes-Fourier paradigm for compressible fluid continua |
| title_sort | proposal of a critical test of the navier stokes fourier paradigm for compressible fluid continua |
| url | http://hdl.handle.net/1721.1/78288 |
| work_keys_str_mv | AT brennerhoward proposalofacriticaltestofthenavierstokesfourierparadigmforcompressiblefluidcontinua |