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Method of Differential Equations

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Mechanics of Flow Similarities
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Abstract

First we state that the governing equations, which describe general three dimensional flow fields, can be found in more or less all fluiddynamic textbooks. Some of them give the complete mathematical derivations of the equations both in integral and differential form, [1–6].

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Notes

  1. 1.

    We have made use of the assumption, that the bulk viscosity can be neglected compared to the dynamic viscosity, [1], which is the same conclusion as to say, that Stokes relation is valid \(2\mu +3\lambda = 0\) with \(\lambda \) being the second viscosity component, [6].

  2. 2.

    The density \(\rho \) is a constant and also the kinematic viscosity \(\nu \), which does not depend on the temperature T.

References

  1. Hirschel, E.H.: Basics of Aerothermodynamics, 2nd edn. Springer, Berlin (2015)

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  2. Hirschel, E.H., Weiland, C.: Selected Aerothermodynamic Design Problems of Hypersonic Flight Vehicles. Springer, Berlin (2009) (Progress in Astronautics and Aeronautics, vol. 229, AIAA, Reston, Va.)

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  3. Becker, E.: Gasdynamik. Teubner Verlag, Stuttgart (1966)

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  4. Zierep, J.: Theoretische Gasdynamik. G. Braun Verlag, Karlsruhe (1972)

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  5. Bird, R.B., Stuart, W.E., Lightfoot, E.N.: Transport Phenomena, 2nd edn. Wiley, New York (2002)

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  6. Hirsch, C.: Numerical Computation of Internal and External Flows, vol. I. Wiley, New York, Reprint (1997)

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  7. Krause, E.: Strömungslehre, Gasdynamik und aerodynamisches Laboratorium. Teubner Verlag, Stuttgart (2003)

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Correspondence to Claus Weiland .

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Weiland, C. (2020). Method of Differential Equations. In: Mechanics of Flow Similarities. Springer, Cham. https://doi.org/10.1007/978-3-030-42930-0_4

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  • DOI: https://doi.org/10.1007/978-3-030-42930-0_4

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