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Research Papers: Fundamental Issues and Canonical Flows

# Numerical Simulation and Modeling of Laminar Developing Flow in Channels and Tubes With Slip

[+] Author and Article Information
Y. S. Muzychka

Professor
Faculty of Engineering and Applied Science,
Memorial University of Newfoundland, St. John's,
e-mail: y.s.muzychka@mun.ca

R. Enright

Thermal Management Research Group,
Efficient Energy Transfer (ηET) Department,
Bell Labs Ireland,
Alcatel-Lucent Ireland Ltd.,
e-mail: ryan.enright@alcatel-lucent.com

Contributed by the Fluids Engineering Division of ASME for publication in the Journal of Fluids Engineering. Manuscript received November 19, 2012; final manuscript received May 14, 2013; published online August 6, 2013. Assoc. Editor: Prof. Ali Beskok.

J. Fluids Eng 135(10), 101204 (Aug 06, 2013) (8 pages) Paper No: FE-12-1584; doi: 10.1115/1.4024808 History: Received November 19, 2012; Revised May 14, 2013

## Abstract

Analytical solutions for slip flows in the hydrodynamic entrance region of tubes and channels are examined. These solutions employ a linearized axial momentum equation using Targ's method. The momentum equation is subjected to a first order Navier slip boundary condition. The accuracy of these solutions is examined using computational fluid dynamics (CFD) simulations. CFD simulations utilized the full Navier–Stokes equations, so that the implications of the approximate linearized axial momentum equation could be fully assessed. Results are presented in terms of the dimensionless mean wall shear stress, $τ⋆$, as a function of local dimensionless axial coordinate, ξ, and relative slip parameter, β. These solutions can be applied to either rarefied gas flows when compressibility effects are small or apparent liquid slip over hydrophobic and superhydrophobic surfaces. It has been found that, under slip conditions, the minimum Reynolds number should be $ReDh>100$ in order for the approximate linearized solution to remain valid.

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## Figures

Fig. 1

(a) Simple channel and (b) tube configurations

Fig. 2

Theoretical results for Φ for different channel shapes, after Duan and Yovanovich [10] for fully developed flows with slip

Fig. 3

Theoretical results for Φ for the channel (dashed) and tube (line) for β = 0.02, 0.1, 0.2 for developing slip flows

Fig. 4

Numerical results for Φ for (a) the channel and (b) the tube. The simple asymptotic values are shown as solid symbols in each plot. The solid line represents the theoretical linearized solutions for each duct shape (Eqs. (19) and (26)).

Fig. 5

Model predictions for τ⋆ for (a) the channel and (b) the tube for β = 0.02, 0.1, and 0.2. The short duct asymptotic limit is shown as the dashed line, exact solution as points, and the model Eq. (40) as the solid line.

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