Journal of Engineering Physics and Thermophysics

, Volume 88, Issue 6, pp 1569–1576 | Cite as

Analytical Estimation of Velocity and Temperature Fields in a Circular Pipe on the Basis of Stochastic Equations and Equivalence of Measures

  • A.V. Dmitrenko

A stream of nonisothermal Newtonian liquid in a circular smooth pipe is considered on the basis of systems of stochastic equations and of the physical law of equivalence of measures between laminar and turbulent motions. Analytical expressions were previously obtained for isothermal flows for the first and second critical Reynolds numbers, critical point, indices of velocity profiles, second-order correlation moments, correlation functions, and spectral functions depending on the parameters of initial turbulence. Analytical expressions, obtained with the use of the earlier derived formulas for the critical Reynolds numbers and the critical points, are presented for the indices of velocity and temperature profiles as functions of the initial turbulence parameters as well as of the Eckert and Prandtl numbers.


equivalence of measures stochastic equations turbulence 


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© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.National Research Nuclear University (MIFI)MoscowRussia
  2. 2.Moscow State University of Railways (MIIT)MoscowRussia

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