DORODNITZYN'S SHEAR STRESS
REYNOLDS' LIMIT FORMULA

Abstract

A previous analysis by the author (published previously in this Journal) showed that a limit formula could be deduced from Dorodnitzyn's compressible boundary layer model by the application of Bayada and Chambat's diffeomorphism. This article is the second part of the same research. Now, a limit formula in terms of the shear stress is deduced from Dorodnitzyn's shear stress model.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 35
Issue: 4
Year: 2022

DOI: 10.12732/ijam.v35i4.1

Download Section



Download the full text of article from here.

You will need Adobe Acrobat reader. For more information and free download of the reader, please follow this link.

References

  1. [1] M.K. Kerimov, On the centenary of the birth of academician Anatolii Alekseevich Dorodnicyn, Comput. Math. and Math. Phys., 50 (2010), 1969- 1974; DOI: 10.1134/S0965542510120018.
  2. [2] G. Bayada and M. Chambat, The transition between the Stokes equations and the Reynolds equation: A mathematical proof, Appl. Math. Optim., 14, No 1 (1986), 73-93; DOI: 10.1007/BF01442229.
  3. [3] V.G. Maz’ya and S.V. Poborchi, Differentiable Functions on Bad Domains, World Scientific (1998); DOI: 10.1142/3197.
  4. [4] V.G. Maz’ya, Sobolev Spaces, Springer, Berlin-Heidelberg (2013); DOI: 10.1007/978-3-642-15564-2.
  5. [5] J. Nečas, Les Méthodes directes en théorie des équations elliptiques, Masson et Cie (1967).
  6. [6] H. Blasius, The boundary layers in fFluids with little friction, NACA-TM- 1256, 56, No 1 (1950).
  7. [7] A.A. Dorodnitzyn, Laminar boundary layer in compressible fluid, Comptes Rendus l’Académie des Sciences de l’URSS, 34, No 8 (1942), 213-219.
  8. [8] D. Bolton, The computation of equivalent potential temperature, Monthly Weather Review, 108, No 7 (1980), 1046-1053.
  9. [9] K. Saha, The Earth’s Atmosphere, Springer, Berlin-Heidelberg (2008); DOI: 10.1007/978-3-540-78427-2.
  10. [10] O.G. Tietjens, Fundamentals of Hydro- and Aerodynamics, Dover Publications Inc., New York (1934).
  11. [11] A.J. Smits and J.-P. Dussauge, Turbulent Shear Layers in Supersonic Flow. Springer-Verlag, New York (2006).
  12. [12] C.V. Valencia-Negrete, C. Gay-Garcı́a, A.A. Carsteanu, Reynolds’ limit formula for Dorodnitzyn’s atmospheric boundary layer in convective conditions, Int. J. Appl. Math., 31, No 4 (2018), 673-695; DOI: 10.12732/ijam.v31i4.12.
  13. [13] L. Chupin and R. Sart, Compressible flows: New existence results and justification of the Reynolds asymptotic in thin films, Asymptotic Analysis 76, No 3-4 (2012), 193-231; DOI: 10.3233/ASY-2011-1070.
  14. [14] L. Crocco, Transmission of heat from a flat plate to a fluid flowing at high velocity, NACA-TM-690 (1932).
  15. [15] R.G. Bartle, The Elements of Integration and Lebesgue Measure, John Wiley & Sons, Inc. (1966); DOI: 10.1002/9781118164471.
  16. [16] L.C. Evans, A survey of entropy methods for partial differential equations, Bull. Amer. Math. Soc., 41 (2004), 409-438; DOI: 10.1090/S0273-0979-04- 01032-8.
  17. [17] V.A. Zorich, Mathematical Analysis I, Springer, Berlin-Heidelberg (2009); DOI: 10.1007/978-3-662-48792-1.
  18. [18] N.F. Krasnov, Aerodynamics 2: Methods Of Aerodynamic Calculations, MIR, USSR (1985).
  19. [19] A. Bressan, Lecture Notes on Functional Analysis: With Applications to Linear Partial Differential Equations, American Mathematical Soc. (2013).