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Article

Numerical Solution of the Newtonian Plane Couette Flow with Linear Dynamic Wall Slip

by
Muner M. Abou Hasan
1,
Ethar A. A. Ahmed
2,
Ahmed F. Ghaleb
3,
Moustafa S. Abou-Dina
3 and
Georgios C. Georgiou
4,*
1
Faculty of Mathematics and Data Sciences, Emirates Aviation University, Dubai P.O. Box 53044, United Arab Emirates
2
School of Engineering and Applied Sciences, Nile University, Giza 12588, Egypt
3
Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt
4
Department of Mathematics and Statistics, University of Cyprus, P.O. Box 20537, Nicosia 1678, Cyprus
*
Author to whom correspondence should be addressed.
Fluids 2024, 9(8), 172; https://doi.org/10.3390/fluids9080172
Submission received: 19 June 2024 / Revised: 23 July 2024 / Accepted: 25 July 2024 / Published: 27 July 2024
(This article belongs to the Topic Fluid Mechanics, 2nd Edition)
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Abstract

An efficient numerical approach based on weighted-average finite differences is used to solve the Newtonian plane Couette flow with wall slip, obeying a dynamic slip law that generalizes the Navier slip law with the inclusion of a relaxation term. Slip is exhibited only along the fixed lower plate, and the motion is triggered by the motion of the upper plate. Three different cases are considered for the motion of the moving plate, i.e., constant speed, oscillating speed, and a single-period sinusoidal speed. The velocity and the volumetric flow rate are calculated in all cases and comparisons are made with the results of other methods and available results in the literature. The numerical outcomes confirm the damping with time and the lagging effects arising from the Navier and dynamic wall slip conditions and demonstrate the hysteretic behavior of the slip velocity in following the harmonic boundary motion.
Keywords: plane Couette flow; dynamic wall slip; Navier slip; weighted-average finite differences; hysteretic behavior plane Couette flow; dynamic wall slip; Navier slip; weighted-average finite differences; hysteretic behavior

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MDPI and ACS Style

Abou Hasan, M.M.; Ahmed, E.A.A.; Ghaleb, A.F.; Abou-Dina, M.S.; Georgiou, G.C. Numerical Solution of the Newtonian Plane Couette Flow with Linear Dynamic Wall Slip. Fluids 2024, 9, 172. https://doi.org/10.3390/fluids9080172

AMA Style

Abou Hasan MM, Ahmed EAA, Ghaleb AF, Abou-Dina MS, Georgiou GC. Numerical Solution of the Newtonian Plane Couette Flow with Linear Dynamic Wall Slip. Fluids. 2024; 9(8):172. https://doi.org/10.3390/fluids9080172

Chicago/Turabian Style

Abou Hasan, Muner M., Ethar A. A. Ahmed, Ahmed F. Ghaleb, Moustafa S. Abou-Dina, and Georgios C. Georgiou. 2024. "Numerical Solution of the Newtonian Plane Couette Flow with Linear Dynamic Wall Slip" Fluids 9, no. 8: 172. https://doi.org/10.3390/fluids9080172

APA Style

Abou Hasan, M. M., Ahmed, E. A. A., Ghaleb, A. F., Abou-Dina, M. S., & Georgiou, G. C. (2024). Numerical Solution of the Newtonian Plane Couette Flow with Linear Dynamic Wall Slip. Fluids, 9(8), 172. https://doi.org/10.3390/fluids9080172

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