Research Papers: Bio-Heat and Mass Transfer

Measuring Transport Coefficients in Heterogeneous and Hierarchical Heat Transfer Devices

[+] Author and Article Information
David Geb

e-mail: dvdgb15@ucla.edu

Ivan Catton

Morrin-Gier-Martinelli Heat Transfer Memorial Laboratory,
School of Engineering and Applied Science,
Department of Mechanical and Aerospace Engineering,
University of California, Los Angeles,
48-121 Engineering IV,
420 Westwood Plaza,
Los Angeles, CA 90095-1597

Reference cited in Fig. 6 are [43].

1Corresponding author.

Manuscript received August 21, 2012; final manuscript received January 14, 2013; published online May 16, 2013. Assoc. Editor: Leslie Phinney.

J. Heat Transfer 135(6), 061101 (May 16, 2013) (9 pages) Paper No: HT-12-1447; doi: 10.1115/1.4023547 History: Received August 21, 2012; Revised January 14, 2013

Experimental determination of transport coefficients, in particular internal heat transfer coefficients, in heterogeneous and hierarchical heat transfer devices such as compact heat exchangers and high surface density heat sinks has posed a persistent challenge for designers. This study presents a unique treatment of the experimental determination of such design data. A new combined experimental and computational method for determining the internal heat transfer coefficient within a heterogeneous and hierarchical heat transfer medium is explored and results are obtained for the case of cross flow of air over staggered cylinders to provide validation of the method. Along with appropriate pressure drop measurements, these measurements allow for thermal-fluid modeling of a heat exchanger by closing the volume averaging theory (VAT)-based equations governing transport phenomena in porous media, which have been rigorously derived from the lower-scale Navier–Stokes and thermal energy equations. To experimentally obtain the internal heat transfer coefficient the solid phase is subjected to a step change in heat generation rate via induction heating, while the fluid flows through under steady flow conditions. The transient fluid phase temperature response is measured. The heat transfer coefficient is then determined by comparing the results of a numerical simulation based on the VAT model with the experimental results. The friction factor is determined through pressure drop measurements, as is usually done. With the lower-scale heat transfer coefficient and friction factor measured, the VAT-based equations governing the transport phenomena in the heat transfer device are closed and readily solved. Several configurations of staggered cylinders in cross flow were selected for this study. Results for the heat transfer coefficient and friction factor are compared to widely accepted correlations and agreement is observed, lending validation to this experimental method and analysis procedure. It is expected that a more convenient and accurate tool for experimental closure of the VAT-based equations modeling transport in heterogeneous and hierarchical media, which comes down to measuring the transport coefficients, will allow for easier modeling and subsequent optimization of high performance compact heat exchangers and heat sinks for which design data does not already exist.

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Fig. 1

Conceptual illustration of the application of VAT with closure relationships to (a) a pin fin heat sink and (b) a tube bank heat exchanger

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Fig. 2

Experimental diagram

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Fig. 3

Test section diagram

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Fig. 4

Schematic of automated iteration procedure. Each simulation corresponds to a different heat transfer coefficient value.

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Fig. 5

Heat exchanger core pressure drop. Adapted from Kays and London [39].

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Fig. 6

The minimum intertube space in a staggered tube bank may occur in the transverse plane, i.e., A1, or in the diagonal plane, i.e., A2. Adapted from Ref. [43].

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Fig. 7

Nusselt number data plotted against Reynolds number

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Fig. 8

Experimental heat transfer results obtained in the present study compared to the correlation given by Zukauskas and Ulinskas [37]

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Fig. 9

Experimental flow friction results obtained in the present study compared to the correlation given by Zukauskas and Ulinskas [38]



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