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Analytical Approach of Unsteady Boundary-Layer Flows Over a Semi-Infinite Plate for All Strouhal Numbers

[+] Author and Article Information
Mohamed Bachiri

Thermodynamics and Energetical Systems Laboratory, Faculty of Physics, USTHB, BP 32 El Alia, 16111 Bab Ezzouar-Algiers, Algeriamabach73@yahoo.fr

Ahcene Bouabdallah

Thermodynamics and Energetical Systems Laboratory, Faculty of Physics, USTHB, BP 32 El Alia, 16111 Bab Ezzouar-Algiers, Algeria

J. Appl. Mech 78(2), 024501 (Nov 08, 2010) (5 pages) doi:10.1115/1.4002571 History: Received October 02, 2009; Revised August 23, 2010; Posted September 16, 2010; Published November 08, 2010; Online November 08, 2010

In this paper, the unsteady boundary-layer flow over a semi-infinite flat plate is solved by means of an analytic approach. Via an ad hoc technique based on the boundary-layer flow evolution, an analytic expression of the velocity profile is proposed. The proposed formula verifies well the results given by Rayleigh, Blasius, and Williams–Rhyne for all time, thus for all Strouhal number values, which is the characteristic of the studied problem. As the main results, the local skin friction depending on a Strouhal number is given in an aim to show an explanation on the flow evolutions from the initial solution to the steady solution in the whole spatial region. This approach permits us to take many applications in engineering technology when the analytic expressions of the velocity, temperature, and matter are looked for.

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Figures

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Figure 1

Strouhal number: characterization of the unsteady boundary-layer flow over a plate

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Figure 2

Comparison of the skin friction with the results of Williams–Rhyne

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Figure 3

The variation of F″(0,ξ) for 0≤ξ≤1

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Figure 4

Dimensionless velocity profile F′(η,St) for different Strouhal number values

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Figure 5

The variation of F″(0,St) for all Strouhal number

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Figure 6

Skin friction variations for all Strouhal number values

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