Continuum Mechanics and Thermodynamics

, Volume 29, Issue 6, pp 1197–1205 | Cite as

Analytical determination of the heat transfer coefficient for gas, liquid and liquid metal flows in the tube based on stochastic equations and equivalence of measures for continuum

Original Article


The stochastic equations of continuum are used for determining the heat transfer coefficients. As a result, the formulas for Nusselt (Nu) number dependent on the turbulence intensity and scale instead of only on the Reynolds (Peclet) number are proposed for the classic flows of a nonisothermal fluid in a round smooth tube. It is shown that the new expressions for the classical heat transfer coefficient Nu, which depend only on the Reynolds number, should be obtained from these new general formulas if to use the well-known experimental data for the initial turbulence. It is found that the limitations of classical empirical and semiempirical formulas for heat transfer coefficients and their deviation from the experimental data depend on different parameters of initial fluctuations in the flow for different experiments in a wide range of Reynolds or Peclet numbers. Based on these new dependences, it is possible to explain that the differences between the experimental results for the fixed Reynolds or Peclet numbers are caused by the difference in values of flow fluctuations for each experiment instead of only due to the systematic error in the experiment processing. Accordingly, the obtained general dependences of Nu for a smooth round tube can serve as the basis for clarifying the experimental results and empirical formulas used for continuum flows in various power devices. Obtained results show that both for isothermal and for nonisothermal flows, the reason for the process of transition from a deterministic state into a turbulent one is determined by the physical law of equivalence of measures between them. Also the theory of stochastic equations and the law of equivalence of measures could determine mechanics which is basis in different phenomena of self-organization and chaos theory.


Stochastic equations Equivalence of measures Turbulence The heat transfer coefficient 


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This work was supported by the program of increasing the competitive ability of National Research Nuclear University MEPhI (agreement with the Ministry of Education and Science of the Russian Federation of August 27, 2013, Project No. 02.a03.21.0005).


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of Thermal PhysicsNational Research Nuclear University MEPhIMoscowRussia
  2. 2.Department of Power EngineeringMoscow State University of Railway Engineering (MIIT)MoscowRussia

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