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Research Papers: Forced Convection

Convective Heat Transfer in a High Aspect Ratio Minichannel Heated on One Side

[+] Author and Article Information
Eric C. Forrest

Primary Standards Laboratory,
Sandia National Laboratories,
Albuquerque, NM 87185
e-mail: ecforre@sandia.gov

Lin-Wen Hu

Mem. ASME
Nuclear Reactor Laboratory,
Massachusetts Institute of Technology,
Cambridge, MA 02139
e-mail: lwhu@mit.edu

Jacopo Buongiorno

Mem. ASME
Department of Nuclear Science and Engineering,
Massachusetts Institute of Technology,
Cambridge, MA 02139
e-mail: jacopo@mit.edu

Thomas J. McKrell

Department of Nuclear Science and Engineering,
Massachusetts Institute of Technology,
Cambridge, MA 02139
e-mail: tmckrell@mit.edu

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received October 20, 2014; final manuscript received September 16, 2015; published online October 21, 2015. Assoc. Editor: Ali Khounsary.The United States Government retains, and by accepting the article for publication, the publisher acknowledges that the United States Government retains, a non-exclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for United States government purposes.

J. Heat Transfer 138(2), 021704 (Oct 21, 2015) (10 pages) Paper No: HT-14-1694; doi: 10.1115/1.4031646 History: Received October 20, 2014; Revised September 16, 2015

Experimental results are presented for single-phase heat transfer in a narrow rectangular minichannel heated on one side. The aspect ratio and gap thickness of the test channel were 29:1 and 1.96 mm, respectively. Friction pressure drop and Nusselt numbers are reported for the transition and fully turbulent flow regimes, with Prandtl numbers ranging from 2.2 to 5.4. Turbulent friction pressure drop for the high aspect ratio channel is well-correlated by the Blasius solution when a modified Reynolds number, based upon a laminar equivalent diameter, is utilized. The critical Reynolds number for the channel falls between 3500 and 4000, with Nusselt numbers in the transition regime being reasonably predicted by Gnielinski's correlation. The dependence of the heat transfer coefficient on the Prandtl number is larger than that predicted by circular tube correlations, and is likely a result of the asymmetric heating. The problem of asymmetric heating condition is approached theoretically using a boundary layer analysis with a two-region wall layer model, similar to that originally proposed by Prandtl. The analysis clarifies the influence of asymmetric heating on the Nusselt number and correctly predicts the experimentally observed trend with Prandtl number. A semi-analytic correlation is derived from the analysis that accounts for the effect of aspect ratio and asymmetric heating, and is shown to predict the experimental results of this study with a mean absolute error (MAE) of less than 5% for 4000 < Re < 70,000.

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References

Figures

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Fig. 1

Schematic of rectangular channel geometry, showing typical secondary flow profile. The dotted line represents an isovelocity line of the primary flow profile (flowing into the page). The arrows represent secondary flows, with the flow direction perpendicular to the primary flow. Adapted from Ref. [3].

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Fig. 2

Schematic of the thermal-hydraulic test facility

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Fig. 3

The narrow rectangular coolant channel test section. The channel is heated on one side, with a polysulfone viewing window on the front face. Thermocouple locations are indicated by X's in the CAD model on the right.

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Fig. 4

Experimental friction factor as a function of Reynolds number. The corresponding predictions for laminar flow (analytic result) and turbulent flow (Blasius equation), calculated using Re*, are plotted for comparison. Error bars represent total uncertainty at the 95% confidence level.

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Fig. 5

Local fully developed Nusselt number results in the high aspect ratio, narrow rectangular channel heated on one side for Re < 10,000. Error bars represent measurement uncertainty at the 95% confidence level.

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Fig. 6

Fully developed, average channel Nusselt numbers for Pr = 5.4 in a high aspect ratio, narrow rectangular channel heated on one side. Error bars represent total uncertainty at the 95% confidence level.

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Fig. 7

Fully developed, average channel Nusselt numbers for Pr = 2.2. Error bars represent total uncertainty at the 95% confidence level.

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Fig. 8

Expected effect of one-sided versus two-sided heating for parallel plates. Expressed as the ratio of the Nusselt numbers for one-sided heating (Nu1) and two-sided heating (Nu2). Adapted from the tabular results of Ref. [26].

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Fig. 9

Surface fitted to experimental data, represented by Nu = 0.0242Re0.775Pr0.548. The corresponding data range is 10,000 ≤ Re ≤ 35,000 and 2.2 ≤ Pr ≤ 5.4. The associated coefficient of determination is R2 = 0.9997.

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Fig. 10

Summary of experimental data for Re > 10,000 normalized by Pr0.4. The newly derived semi-analytical solution is plotted along with the McAdams correlation for the highest and lowest Prandtl numbers explored in this study.

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