IE Lobanov*

Doctor of Technical Sciences, Professor of the Federal State Budgetary Educational Institution of Higher Education “Technological University” Named After Twice Hero of the Soviet Union, Pilot-Cosmonaut A.A. Leonov, Russia

*Corresponding Author: IE Lobanov, Doctor of Technical Sciences, Professor of the Federal State Budgetary Educational Institution of Higher Education “Technological University” Named After Twice Hero of the Soviet Union, Pilot-Cosmonaut A.A. Leonov, Russia.

Received: July 02, 2025; Published: July 10, 2025

Abstract

In the article an exact analytical solution of the differential equation for shear stresses in a turbulent boundary layer, which is a special case of the so-called Abel differential equation of the second kind, was found, obtained using a special Lambert function, while previously it was believed that it is not solvable in quadratures. In addition, several other important solved special cases of this equation were obtained. The analytical solutions obtained in the article mainly differ from the previously available either numerical or approximate solutions of the problem. The obtained solution in dimensionless form is a theoretical profile of the dimensionless velocity along the thickness of the boundary layer in turbulent flow in the boundary layer. An approximate solution of this equation by the method of successive approximations with additional assumptions, as well as the corresponding analytical approximation dependence, were also obtained.

Keywords: Theoretical; Modeling; Mathematical; Velocity; Coordinate; Dimensionless; Profile; Heat Exchange; Turbulent; Flow; Boundary Layer; Abel Differential Equation; Of the Second Kind; Of the First Kind; Lambert Function; Approximate; Method of Successive Approximations.

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Citation

Citation: IE Lobanov. “Approximate Analytical Solution to the Problem on the Theoretical Profile of Dimensionless Velocity According to the Thickness of the Boundary Layer in Turbulent Boundary Layer Flow Based on the Solution of the Abele Second Differential Equation Genus by the Method of Successive Approximations with Additional Assumptions".Acta Scientific Computer Sciences 7.5 (2025): 18-24.

Copyright

Copyright: © 2025 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.