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Research Papers: Bio-Heat and Mass Transfer

Quantitative Assessment of the Overall Heat Transfer Coefficient U

[+] Author and Article Information
Eph Sparrow

e-mail: esparrow@umn.edu

John Gorman

Department of Mechanical Engineering,
University of Minnesota,
Minneapolis, MN 55455

John Abraham

School of Engineering,
University of St. Thomas,
St. Paul, MN 55105

1Corresponding author.

Manuscript received October 1, 2012; final manuscript received January 18, 2013; published online May 16, 2013. Assoc. Editor: Leslie Phinney.

J. Heat Transfer 135(6), 061102 (May 16, 2013) (7 pages) Paper No: HT-12-1534; doi: 10.1115/1.4023566 History: Received October 01, 2012; Revised January 18, 2013

This investigation was performed in order to quantify the validity of the assumed constancy of the overall heat transfer coefficient U in heat exchanger design. The prototypical two-fluid heat exchanger, the double-pipe configuration, was selected for study. Heat transfer rates based on the U = constant model were compared with those from highly accurate numerical simulations for 60 different operating conditions. These conditions included: (a) parallel and counter flow, (b) turbulent flow in both the pipe and the annulus, (c) turbulent flow in the pipe and laminar flow in the annulus and the vice versa situation, (d) laminar flow in both the pipe and the annulus, and (e) different heat exchanger lengths. For increased generality, these categories were further broken down into matched and unmatched Reynolds numbers in the individual flow passages. The numerical simulations eschewed the unrealistic uniform-inlet-velocity-profile model by focusing on pressure-driven flows. The largest errors attributable to the U = constant model were encountered for laminar flow in both the pipe and the annulus and for laminar flow in one of these passages and turbulent flow in the other passage. This finding is relevant to microchannel flows and other low-speed flow scenarios. Errors as large as 50% occurred. The least impacted were cases in which the flow is turbulent in both the pipe and the annulus. The general level of the errors due to the U = constant model were on the order of 10% and less for those cases. This outcome is of great practical importance because heat-exchanger flows are more commonly turbulent than laminar. Another significant outcome of this investigation is the quantification of the axial variations of the temperature and heat flux along the wall separating the pipe and annulus flows. It is noteworthy that these distributions do not fit either the uniform wall temperature or uniform heat flux models.

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References

Figures

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Fig. 1

Double-pipe heat exchanger schematic, relevant nomenclature, and coordinate system

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Fig. 2

Comparison of SST-based Nusselt number predictions with experimental data [11-14]

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Fig. 3

Assessment of the heat transfer rate QU predicted by the U = constant model for the same Reynolds numbers in the pipe and the annulus for laminar flow and L/Di = 20

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Fig. 4

Assessment of the heat transfer rate QU predicted by the U = constant model for the same Reynolds numbers in the pipe and the annulus for laminar flow and L/Di = 40

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Fig. 5

Assessment of the heat transfer rate QU predicted by the U = constant model for the same Reynolds numbers in the pipe and the annulus for turbulent flow and L/Di = 20

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Fig. 6

Pipe wall temperature and heat flux variations for equal Reynolds numbers of 2000 in the pipe and the annulus for laminar flow and L/Di = 20

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Fig. 7

Pipe wall temperature and heat flux variations for unmatched Reynolds numbers of 2000 in the pipe and 500 in the annulus for laminar flow and L/Di = 20

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Fig. 8

Pipe wall temperature and heat flux variations for unmatched Reynolds numbers of 2000 in the pipe and 60,000 in the annulus for a mixed regime case and L/Di = 20

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Fig. 9

Pipe wall temperature and heat flux variations for unmatched Reynolds numbers of 60,000 in the pipe and 2000 in the annulus for a mixed regime case and L/Di = 20

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Fig. 10

Pipe wall temperature and heat flux variations for equal Reynolds numbers of 60,000 in the pipe and the annulus for turbulent flow and L/Di = 20

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