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RESEARCH PAPERS: Forced Convection

Laminar Flow and Heat Transfer in the Entrance Region of Trapezoidal Channels With Constant Wall Temperature

[+] Author and Article Information
Metin Renksizbulut1

Mechanical Engineering Department, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1metin@uwaterloo.ca

Hamid Niazmand

Mechanical Engineering Department, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

1

Corresponding author.

J. Heat Transfer 128(1), 63-74 (Jul 14, 2005) (12 pages) doi:10.1115/1.2130405 History: Received February 22, 2005; Revised July 14, 2005

Simultaneously developing three-dimensional laminar flow and heat transfer in the entrance region of trapezoidal channels have been investigated using numerical methods in the Reynolds number range from 10 to 1000. The principal and secondary velocity fields, the temperature field, and all associated heat and momentum exchange parameters have been examined. The present results for the fully developed flow region of the channels compare well with the available literature. In the entrance region, it is observed that the axial velocity profiles develop overshoots near the walls and particularly at the channel corners. It is shown that boundary-layer type of approximations, which lead to Reynolds-number-independent Poiseuille and Nusselt numbers, can be used for Reynolds numbers over 50 and after a few hydraulic diameters from the channel inlet. It is also shown that hydrodynamic entrance lengths calculated with methods based on fully developed flow data are grossly in error. New correlations are proposed for the entrance length, and for the friction and heat transfer coefficients.

Copyright © 2006 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Flow geometry and the coordinate system

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Figure 2

Grid distribution in the xy plane

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Figure 3

Axial grid resolution

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Figure 4

Centerline velocity and pressure drop in pipe flow

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Figure 5

Axial pressure distribution in a square duct

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Figure 6

Velocity vectors and pressure contours in the xy plane at three axial locations: (a) z+=5.21×10−5, (b) z+=6.83×10−4, and (c) z+=1.50×10−3

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Figure 7

Axial velocity profiles along the y=0 plane

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Figure 8

Three-dimensional velocity profiles at four axial locations: (a) z+=4.39×10−4, (b) z+=2.18×10−3, (c) z+=8.91×10−3, and (d) z+=5.26×10−1

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Figure 9

Velocity contours for a square channel at two axial locations: (a) entrance region z+=2.52×10−3 and (b) fully developed region z+=6.07×10−1

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Figure 10

Variation of apparent friction factor along the axial direction for different aspect ratios

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Figure 11

Variation of hydraulic diameter (arbitrary units) with channel aspect ratio and side angle

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Figure 12

Variation of apparent friction factor in the flow direction for different side angles

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Figure 13

Variations of the momentum flux and kinetic energy correction factors along the axial flow direction for different side angles

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Figure 14

Variations of the momentum flux and kinetic energy correction factors along the axial flow direction for different aspect ratios

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Figure 15

Three-dimensional temperature profiles at four axial locations: (a) z+=4.39×10−4, (b) z+=2.18×10−3, (c) z+=8.91×10−3, and (d) z+=5.26×10−1

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Figure 16

Variation of Nusselt number in the main flow direction for different side angles and three aspect ratios: (a) α=0.5, (b) α=1, and (c) α=2

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Figure 17

Isotherms for various aspect ratios at axial location z+=1×10−2 for flow at Re=100 and ϕ=45deg: (a) α=0.5, (b) α=1, and (c) α=2

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Figure 18

Axial variation of the apparent friction factor with Reynolds number

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Figure 19

Axial variation of Nusselt number with Reynolds number

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Figure 20

Comparison of available data to the proposed friction coefficient correlation

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Figure 21

Comparison of available data to the proposed heat transfer coefficient correlation

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Figure 22

Comparison of the numerical data to the proposed entrance length correlation

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