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Technical Briefs

Analytical Solution for Newtonian Laminar Flow Through the Concave and Convex Ducts

[+] Author and Article Information
M. Firouzi

Computational Fluid Dynamics Research Laboratory, School of Chemical Engineering, Iran University of Science and Technology, Narmak, Tehran 16846, Iran

S. H. Hashemabadi

Computational Fluid Dynamics Research Laboratory, School of Chemical Engineering, Iran University of Science and Technology, Narmak, Tehran 16846, Iranhashemabadi@iust.ac.ir

J. Fluids Eng 131(9), 094501 (Aug 14, 2009) (6 pages) doi:10.1115/1.3184026 History: Received May 20, 2008; Revised June 21, 2009; Published August 14, 2009

In this paper, the motion equation for steady state, laminar, fully developed flow of Newtonian fluid through the concave and convex ducts has been solved both numerically and analytically. These cross sections can be formed due to the sedimentation of heavy components such as sand, wax, debris, and corrosion products in pipe flows. The influence of duct cross section on dimensionless velocity profile, dimensionless pressure drop, and friction factor has been reported. Finally based on the analytical solutions three new correlations have been proposed for the product of Reynolds number and Fanning friction factor (CfRe) for these geometries.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic descriptions of (a) flow passage cross section and (b) bipolar coordinate

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Figure 2

Some examples of the clogged pipe: (a) mud sediment in pipes, (b) clogged pipe with grease, (c) fouling in heat exchangers, and (d) deposit of the sludge pipe (2)

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Figure 3

Comparison of numerical and analytical dimensionless velocity profiles for the case of the semicircle cross section (φ1=π/2 and φ2=π) at ξ=0 (along the meridian)

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Figure 4

Comparison of numerical and analytical solutions for the dimensionless velocity profile at φ=2π/3 with cross section specification: φ1=π/3 and φ2=π

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Figure 5

Comparison of numerical and analytical solutions for various duct cross sections due to different bottom wall shapes: φ1=π/3 and ξ=0

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Figure 6

Velocity variation with ξ for different upper wall shapes, φ2=2π/3

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Figure 7

Variation in the dimensionless pressure drop with aspect ratio (h/D) for various duct cross sections (different φ1 and φ2)

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Figure 8

Comparison of analytical solution and correlation results for Cf Re

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