Article
Version 2
Preserved in Portico This version is not peer-reviewed
Exact Similarity Solutions of Unsteady Laminar Boundary Layer Flows
Version 1
: Received: 28 September 2023 / Approved: 29 September 2023 / Online: 30 September 2023 (09:49:14 CEST)
Version 2 : Received: 30 October 2023 / Approved: 31 October 2023 / Online: 1 November 2023 (06:12:57 CET)
Version 2 : Received: 30 October 2023 / Approved: 31 October 2023 / Online: 1 November 2023 (06:12:57 CET)
How to cite: Sun, B. Exact Similarity Solutions of Unsteady Laminar Boundary Layer Flows. Preprints 2023, 2023092117. https://doi.org/10.20944/preprints202309.2117.v2 Sun, B. Exact Similarity Solutions of Unsteady Laminar Boundary Layer Flows. Preprints 2023, 2023092117. https://doi.org/10.20944/preprints202309.2117.v2
Abstract
The studies of laminar unsteady boundary layer flows is crucial for understanding laminar-turbulence transition and origins of turbulence. However, the task of finding its solutions poses a significant challenge. In this paper, we propose a novel approach by introducing a similar transformation to convert the 2D unsteady laminar boundary layer equations into a single partial differential equation. By applying this transformation, we are able to obtain the "exact" similarity solutions for the 2D unsteady laminar boundary layer equations, specifically for the case of flat plate boundary flow. Notably, this is the first time that such an exact solution has been obtained. Application of this exact solution is being used to solve Stokes' first problem in 2D boundary layer. Perspectives on the transition fron Rayleigh solution to Blasius solution is provided.
Keywords
Navier-Stokes equation;2D unsteady boundary layers; similar transformation; exact solutions
Subject
Physical Sciences, Fluids and Plasmas Physics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Comments (1)
We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.
Leave a public commentSend a private comment to the author(s)
* All users must log in before leaving a comment
Commenter: Bohua Sun
Commenter's Conflict of Interests: Author