Laminar flow in trapezoidal grooves at finite Bond numbers with shear stress at the liquid-vapor interface by the method of fundamental solutions

  • Hubert Jopek Poznań University of Technology
  • Jan A. Kołodziej Poznań University of Technology
  • Tomasz Stręk Poznań University of Technology

Abstract

The problem of determination of Poiseuille number for a steady gravitational flow of liquid in an inclined open trapezoidal groove is addressed. The solution comprises of two parts. First, for a given groove's dimension, liquid-solid contact angle, and the Bond number, the shape of the free surface is determined starting from the Young- Laplace equation. The shooting method is used for solution of a two-point boundary value problem. Then, having determined the shape of the free surface and slope the groove, the fully developed laminar flow is determined. The boundary value problem is solved using the method of fundamental solutions. Given the distribution of liquid velocity, the Poiseuille number, as a function of the other parameters of the model is analysed.

Keywords

flow in trapezoidal groove, liquid-vapor interface, method of fundamental solutions, Bond number, Mathematica,

References

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[2] G. Fairweather, A. Karageorghis. The method of fundamental solutions for elliptic boundary value problems. Advances in Computational Mathematics , 9: 69- 95, 1998.
[3] D. Khrustalev , A. Faghri . Coupled liquid and vapor flow in miniature passages with micro grooves. ASME J. Heat Transfer, 121: 729- 733.
[4] J.A. Kołodziej, G. Musielak, M. Kaczmarek, T. Stręk. Determination of free surface and gravitational flow of liquid in triangular groove. Computational Mechanics , 24: 110- 117, 1999.
[5] L. Lin, A. Faghri. Steady-state performance of a rotating miniature heat pipe. AIAA .J. Thermophys. Heat Transfer, 11: 513- 518, 1997.
Published
Nov 17, 2022
How to Cite
JOPEK, Hubert; KOŁODZIEJ, Jan A.; STRĘK, Tomasz. Laminar flow in trapezoidal grooves at finite Bond numbers with shear stress at the liquid-vapor interface by the method of fundamental solutions. Computer Assisted Methods in Engineering and Science, [S.l.], v. 13, n. 3, p. 395-405, nov. 2022. ISSN 2956-5839. Available at: <https://cames.ippt.pan.pl/index.php/cames/article/view/941>. Date accessed: 07 oct. 2024.
Section
Articles

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