Exact Similarity Solutions of Unsteady Laminar Boundary Layer Flows

Bohua Sun

doi:10.20944/preprints202309.2117.v2

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preprints.org > physical sciences > fluids and plasmas physics > doi: 10.20944/preprints202309.2117.v2

Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

Exact Similarity Solutions of Unsteady Laminar Boundary Layer Flows

Bohua Sun

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)

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

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MDPI and ACS Style

Sun, B. Exact Similarity Solutions of Unsteady Laminar Boundary Layer Flows. Preprints 2023, 2023092117. https://doi.org/10.20944/preprints202309.2117.v2

APA Style

Sun, B. (2023). Exact Similarity Solutions of Unsteady Laminar Boundary Layer Flows. Preprints. https://doi.org/10.20944/preprints202309.2117.v2

Chicago/Turabian Style

Sun, B. 2023 "Exact Similarity Solutions of Unsteady Laminar Boundary Layer Flows" Preprints. 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.

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Comments (1)

Comment 1

Received: 1 November 2023
Commenter: Bohua Sun
Commenter's Conflict of Interests: Author

Comment: Based on the first version of this paper, the new version is almost completely rewritten. In this version, I have provided more detailed contents and conducted in-depth research on the mechanics challenges.

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