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Need for Looking Beyond the Navier–Stokes Equations

  • Amit Agrawal
  • Hari Mohan Kushwaha
  • Ravi Sudam Jadhav
Chapter
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Part of the Mechanical Engineering Series book series (MES)

Abstract

The need for looking beyond the Navier–Stokes equations is addressed in this chapter through specific examples where these equations fail. We also examine some extensions of the Navier–Stokes equations, which have been recently proposed in the literature. Similarly, attempts to modify the Fourier law to account for non-Fourier effects are reviewed. An example of shock wave where these alternative forms of Navier–Stokes equations have been applied is also included.

References

  1. 8.
    Akintunde A, Petculescu A (2014) Infrasonic attenuation in the upper mesosphere–lower thermosphere: a comparison between Navier–Stokes and Burnett predictions. J Acoust Soc Am 136(4):1483–1486CrossRefGoogle Scholar
  2. 16.
    Balaj M, Roohi E, Mohammadzadeh A (2017) Regulation of anti-Fourier heat transfer for non-equilibrium gas flows through micro/nanochannels. Int J Thermal Sci 118:24–39CrossRefGoogle Scholar
  3. 25.
    Brenner H (2005) Navier–Stokes revisited. Phys A Stat Mech Appl 349(1–2):60–132MathSciNetCrossRefGoogle Scholar
  4. 38.
    Date AW (2005) Introduction to computational fluid dynamics. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  5. 60.
    Gembarovič J, Majernik V (1988) Non-Fourier propagation of heat pulses in finite medium. Int J Heat Mass Transf 31(5):1073–1080CrossRefGoogle Scholar
  6. 66.
    Greenshields CJ, Reese JM (2007) The structure of shock waves as a test of Brenner’s modifications to the Navier–Stokes equations. J Fluid Mech 580:407–429MathSciNetCrossRefGoogle Scholar
  7. 99.
    Mohammadzadeh A, Rana AS, Struchtrup H (2015) Thermal stress vs. thermal transpiration: a competition in thermally driven cavity flows. Phys Fluids 27(11):112001Google Scholar
  8. 109.
    Özişik M, Vick B (1984) Propagation and reflection of thermal waves in a finite medium. Int J Heat Mass Transf 27(10):1845–1854CrossRefGoogle Scholar
  9. 112.
    Petculescu A (2016) Acoustic properties in the low and middle atmospheres of Mars and Venus. J Acoust Soc Am 140(2):1439–1446CrossRefGoogle Scholar
  10. 123.
    Sambasivam R (2012) Extended Navier–Stokes equations: derivations and applications to fluid flow problems. PhD thesis, Universität Erlangen-NürnbergGoogle Scholar
  11. 128.
    Sharma A (2016) Introduction to computational fluid dynamics: development, application and analysis. Wiley, New YorkCrossRefGoogle Scholar
  12. 133.
    Singh N, Gavasane A, Agrawal A (2014) Analytical solution of plane Couette flow in the transition regime and comparison with direct simulation Monte Carlo data. Comput Fluids 97:177–187MathSciNetCrossRefGoogle Scholar
  13. 152.
    Tzou D, Chiu K (2001) Temperature-dependent thermal lagging in ultrafast laser heating. Int J Heat Mass Transf 44(9):1725–1734CrossRefGoogle Scholar
  14. 153.
    Uribe FJ (2011) The shock wave problem revisited: the Navier–Stokes equations and Brenner’s two velocity hydrodynamics. In: Coping with complexity: model reduction and data analysis. Springer, Berlin, pp 207–229CrossRefGoogle Scholar
  15. 173.
    Yang R, Chen G, Laroche M, Taur Y (2005) Simulation of nanoscale multidimensional transient heat conduction problems using ballistic-diffusive equations and phonon Boltzmann equation. J Heat Transf 127(3):298–306CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Amit Agrawal
    • 1
  • Hari Mohan Kushwaha
    • 1
  • Ravi Sudam Jadhav
    • 1
  1. 1.Department of Mechanical EngineeringIndian Institute of Technology, BombayMumbaiIndia

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