ANALYTICAL ESTIMATION OF VELOCITY AND TEMPERATURE FIELDS IN A CIRCULAR PIPE ON THE BASIS OF STOCHASTIC EQUATIONS AND EQUIVALENCE OF MEASURES

A stream of nonisothermalNewtonian 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 fl ows for the fi rst and second critical Reynolds numbers, critical point, indices of velocity profi les, 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 profi les as functions of the initial turbulence parameters as well as of the Eckert and Prandtl numbers.
   
Author:  A.V. Dmitrenko
Keywords:  equivalence of measures, stochastic equations, turbulence
Page:  1569