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Research Papers

Effect of Velocity-Slip Boundary Conditions on Jeffery–Hamel Flow Solutions

[+] Author and Article Information
M. A. Al-Nimr

Department of Mechanical Engineering, Jordan University of Science and Technology, Irbid 22110, Jordan

Vladimir A. Hammoudeh, M. A. Hamdan

Department of Mechanical Engineering, University of Jordan, Amman 11942, Jordan

J. Appl. Mech 77(4), 041010 (Apr 12, 2010) (8 pages) doi:10.1115/1.4000918 History: Received June 26, 2009; Revised November 18, 2009; Published April 12, 2010; Online April 12, 2010

In the present work, the Jeffery–Hamel flow problem has been studied using both first- and second-order velocity-slip models, and then compared with the no-slip model. The objectives are to observe the behavior of the flow predicted by the two slip models and to establish criteria for using the two velocity-slip models. The study concentrates on examining the effect of the change in the Knudsen number (Kn) on the velocity profiles, magnitude of slip at the wall, and skin friction coefficient. Assuming that a difference between the two slip models of the order of 10% or less justifies the use of the simple first-order model, the transitional Kn numbers have been found. These Kn numbers depend on the flow direction, being either inflow or outflow. Also, there are three distinct regions that specify where to use each of the no-slip, first-order, and second-order slip models. Further, the reversal of the flow has been investigated as a function of the Kn number and for different Reα, where Re is Reynolds number and α is the wall angle. Using the second-order slip models, it is found that as the Kn number increases, reversal occurs at Reα smaller than the 10.31 value at which flow reversal happens in the no-slip model, and increasing the Kn number leads to a reduction in the skin friction coefficient in all cases except when reversal occurs.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 8

Normalized difference between the first- and second-order model predicted velocity slips at the wall

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Figure 9

Friction coefficient Cf comparison at α=−0.1 and different Re: (a) for Re=10, (b) for Re=50, and (c) for Re=100

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Figure 10

Friction coefficient Cf comparison at α=+0.1 and different Re: (a) for Re=10, (b) for Re=50, and (c) for Re=100

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Figure 11

Second order model predicted velocity slip at the wall for different Kn numbers as a function of Re⋅α

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Figure 12

Second order model predicted velocity slip at the wall for different Re⋅α as a function of the Kn number

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Figure 1

Schematic diagram of the problem (12)

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Figure 2

Velocity profiles for the Jeffery–Hamel flow at Re⪢α with no-slip boundary conditions (12)

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Figure 3

Velocity profiles for the Jeffery–Hamel flow at Re⪢α with first-order velocity-slip boundary condition at Kn=0.02

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Figure 4

Comparison of the velocity profiles for the Jeffery–Hamel flow at Re⋅α=−10 using the three models: no-slip, first-order, and second-order velocity-slip boundary conditions

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Figure 5

Comparison of the velocity profiles for the Jeffery–Hamel flow at Re⋅α=0 using the three models: no-slip, first-order, and second-order velocity-slip boundary conditions

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Figure 6

Comparison of the velocity profiles for the Jeffery–Hamel flow at Re⋅α=+10 using the three models: no-slip, first-order, and second-order velocity-slip boundary conditions

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Figure 7

First- and second-order model predicted slip velocities at the wall

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