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Research Papers: Forced Convection

Determination of Heat Transfer in Ducts With Axial Conduction by Variational Calculus

[+] Author and Article Information
A. Haji-Sheikh

Department of Mechanical and Aerospace Engineering, University of Texas at Arlington, Arlington, TX 76019-0023

J. Heat Transfer 131(9), 091702 (Jun 26, 2009) (11 pages) doi:10.1115/1.3122776 History: Received October 29, 2008; Revised December 23, 2008; Published June 26, 2009

This study uses a methodology based on the calculus of variation to determine the heat transfer in passages with two-dimensional velocity fields such as rectangular channels and in the presence of axial conduction. The mathematical procedure is presented and the subsequent numerical computations provide the Nusselt number values. To verify the accuracy of this numerical procedure, the Nusselt number values are acquired for parallel-plate channels and circular pipes and compared with similar data from the Graetz-type exact analyses. Then, rectangular passages are selected to show the capability and a square duct is used to study the domain of accuracy for this procedure. The results for small Peclet numbers lead to a simple correlation for determination of the bulk temperature and they compare well with those obtained from an asymptotic solution.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic of a duct with temperature change at x̂=0

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Figure 2

A comparison of the WRM solutions with the Graetz-type solutions for parallel-plate and circular ducts

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Figure 3

Computed values of h0a/k in parallel-plate ducts as a function of x̂/a by WRM for different Pe numbers

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Figure 4

Computed values of h0ro/k in circular ducts as a function of x̂/rο by WRM for different Pe numbers

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Figure 5

Asymptotic behavior of the Nusselt number h0a/k as a function of x̂/a and its comparison to slug flow over an infinite flat plate

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Figure 6

Computed values of the bulk temperature θb in square ducts as a function of x̂/a by WRM for different Pe numbers: (a) when x<0 and (b) when x>0

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Figure 7

Computed values of h0a/k in rectangular ducts as a function of x̂/a by WRM for different Pe numbers: (a) when x<0 and (b) when x>0

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Figure 8

Nusselt number NuD for a square duct as a function of axial coordinate (x̂/a)/Pe for different Pe numbers

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