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Technical Briefs

Development Length in Planar Channel Flows of Newtonian Fluids Under the Influence of Wall Slip

[+] Author and Article Information
L. L. Ferrás1

 Institute for Polymers and Composites/I3N, University of Minho, Campus de Azurém, 4800-058 Guimarães, Portugalluis.ferras@dep.uminho.pt

A. M. Afonso

 Departamento de Engenharia Química, Centro de Estudos de Fenómenos de Transporte, Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias s/n, 4200-465 Porto, Portugalaafonso@fe.up.pt

M. A. Alves

 Departamento de Engenharia Química, Centro de Estudos de Fenómenos de Transporte, Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias s/n, 4200-465 Porto, Portugalmmalves@fe.up.pt

J. M. Nóbrega

 Institute for Polymers and Composites/I3N, University of Minho, Campus de Azurém, 4800-058 Guimarães, Portugalmnobrega@dep.uminho.pt

F. T. Pinho

 Centro de Estudos de Fenómenos de Transporte, Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias s/n, 4200-465 Porto, Portugalfpinho@fe.up.pt

1

Corresponding author.

J. Fluids Eng 134(10), 104503 (Sep 28, 2012) (5 pages) doi:10.1115/1.4007383 History: Received May 14, 2012; Revised July 18, 2012; Published September 24, 2012; Online September 28, 2012

This technical brief presents a numerical study regarding the required development length (L=Lfd/H) to reach fully developed flow conditions at the entrance of a planar channel for Newtonian fluids under the influence of slip boundary conditions. The linear Navier slip law is used with the dimensionless slip coefficient k¯l=kl(μ/H), varying in the range 0<k¯l1. The simulations were carried out for low Reynolds number flows in the range 0<Re100, making use of a rigorous mesh refinement with an accuracy error below 1%. The development length is found to be a nonmonotonic function of the slip velocity coefficient, increasing up to k¯l0.1-0.4 (depending on Re) and decreasing for higher k¯l. We present a new nonlinear relationship between L, Re, and k¯l that can accurately predict the development length for Newtonian fluid flows with slip velocity at the wall for Re of up to 100 and k¯l up to 1.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic representation of the geometry

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Figure 2

Variation of the development length (L) with the slip coefficient (k¯l ) for three different values of Re

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Figure 3

Variation with Re of the difference in L of Eq. 5 relative to the no-slip case results of Durst [8] as a function of the slip coefficient k¯l

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Figure 4

Nonlinear functional correlations for L=f(Re,k¯l ) for channel flows

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Figure 5

Dimensionless velocity profiles along the channel for two different values of the slip coefficient (k¯l  = 0.0001 and 0.1) and Re = 10−3 at five different positions y/H. Inset: detailed view near the wall.

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Figure 6

Velocity profiles at different axial locations for k¯l = 0.0001 (low slip velocity-black), 0.1 (moderate slip velocity-blue), and 1.0 (high slip velocity-green): (a) Re = 10−3 and (b) Re = 100

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Figure 7

Variation along the channel of the dimensionless centerplane velocity as a function of the slip coefficient for Re = 10−3 . Inset: detailed view of the development length for the different slip coefficients.

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