IE Lobanov*

Federal State Budgetary Educational Institution of Higher Education "Moscow Aviation Institute (National Research University)", Moscow, Russia

*Corresponding Author: IE Lobanov, Federal State Budgetary Educational Institution of Higher Education "Moscow Aviation Institute (National Research University)", Moscow, Russia.

Received: January 05, 2022; Published: January 19, 2022

Abstract

In this scientific article, approximate solutions were implemented for theoretical profiles for dimensionless velocities in the thickness of boundary layers for turbulent flows in boundary layers, which are based on the exact analytical solutions of differential equations for tangential stresses in turbulent boundary layers obtained earlier by the author of the article, which in turn are special cases of Abelian ordinary differential equations of the second order of the second kind using Lambert special function that have no solutions in quadrature’s.

Keywords: Theoretical; Modeling; Mathematical; Approximate; Velocity; Method of Sequential Approximation; Coordinate; Dimensionless; Profile; Heat Transfer; Turbulent; Flow; Boundary Layer; Abelian Differential Equation; Second Order; Second Kind; Lambert Function

References

1. Kutateladze SS. “Fundamentals of the theory of heat transfer”. Atomizdat (1979):
2. Isachenko VP., et al. “Heat transfer”. Energiya (1975):
3. “Theory of heat and mass transfer”. Edited by A.I.Leontiev. Publishing House of Bauman Moscow State Technical University (1997): 688.
4. Lobanov IE. “Solving the problem of the theoretical profile of dimensionless velocity in the thickness of the boundary layer with turbulent flow in the boundary layer based on the solution of the Abel differential equation of the second kind using the Lambert function”. Bulletin of Scientific and Technical Development: Online Magazine 11.135 (2018): 29-38.
5. Lobanov IE. “Theoretical determination of the profile of a dimensionless longitudinal velocity in a turbulent boundary layer based on the solution of an ordinary differential Abel equation of the second kind using a special Lambert function”. Innovative Approaches in Industries and Spheres 4.3 (2019).
6. Lyakhov VK and Migalin KV. “Effect of thermal or diffusion roughness”. Saratov: Saratov University Press (1990):
7. Bateman G and Erdei A. “Higher transcendental functions: Bessel functions, parabolic cylinder functions, orthogonal polynomials”. Nauka (1966):
8. Dubinov AE., et al. “Lambert's W-function and its application in mathematical problems of physics”. Sarov: FSUE "RFNC-VNIIEF" (2006):
9. Kamke E. “Handbook of ordinary differential equations”. Nauka (1965):

Citation

Citation: IE Lobanov. “Approximate Analytical Solution of the Problem of the Theoretical Profile of Dimensionless Velocity in the Thickness of the Boundary Layer with Turbulent Flow in the Boundary Layer Based on the Solution of the Abel Differential Equation of the Second Kind by the Method of Successive Approximations with Additional Assumptions". Acta Scientific Computer Sciences 4.2 (2022): 51-55.

Copyright

Copyright: © 2022 IE Lobanov. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.