caa a22 4500 606188428 CHVBK 20210128100845.0 cr unu---uuuuu 210128e20151101xx s 000 0 eng 10.1007/s10891-015-1344-x doi (NATIONALLICENCE)springer-10.1007/s10891-015-1344-x Dmitrenko A.V. National Research Nuclear University (MIFI), 31 Kashirskoe Highway, 115409, Moscow, Russia aut Analytical Estimation of Velocity and Temperature Fields in a Circular Pipe on the Basis of Stochastic Equations and Equivalence of Measures [Elektronische Daten] [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. Springer Science+Business Media New York, 2015 equivalence of measures nationallicence stochastic equations nationallicence turbulence nationallicence Journal of Engineering Physics and Thermophysics Springer US; http://www.springer-ny.com 88/6(2015-11-01), 1569-1576 1062-0125 88:6<1569 2015 88 10891 https://doi.org/10.1007/s10891-015-1344-x text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10891-015-1344-x text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Dmitrenko A.V. National Research Nuclear University (MIFI), 31 Kashirskoe Highway, 115409, Moscow, Russia aut NATIONALLICENCE 773 0- Journal of Engineering Physics and Thermophysics Springer US; http://www.springer-ny.com 88/6(2015-11-01), 1569-1576 1062-0125 88:6<1569 2015 88 10891