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Research Papers: Porous Media

Internal Heat Transfer Coefficient Determination in a Packed Bed From the Transient Response Due to Solid Phase Induction Heating

[+] Author and Article Information
David Geb1

Morrin-Gier-Martinelli Heat Transfer Memorial Laboratory, Department of Mechanical and Aerospace Engineering, School of Engineering and Applied Science,  University of California, Los Angeles, 48-121 Engineering IV, 420 Westwood Plaza, Los Angeles, CA 90095-1597dvdgb15@ucla.edu

Feng Zhou, Ivan Catton

Morrin-Gier-Martinelli Heat Transfer Memorial Laboratory, Department of Mechanical and Aerospace Engineering, School of Engineering and Applied Science,  University of California, Los Angeles, 48-121 Engineering IV, 420 Westwood Plaza, Los Angeles, CA 90095-1597dvdgb15@ucla.edu

1

Corresponding author.

J. Heat Transfer 134(4), 042604 (Feb 15, 2012) (10 pages) doi:10.1115/1.4005098 History: Received December 10, 2010; Revised September 04, 2011; Published February 15, 2012; Online February 15, 2012

Nonintrusive measurements of the internal heat transfer coefficient in the core of a randomly packed bed of uniform spherical particles are made. Under steady, fully-developed flow the spherical particles are subjected to a step-change in volumetric heat generation rate via induction heating. The fluid temperature response is measured. The internal heat transfer coefficient is determined by comparing the results of a numerical simulation based on volume averaging theory (VAT) with the experimental results. The only information needed is the basic material and geometric properties, the flow rate, and the fluid temperature response data. The computational procedure alleviates the need for solid and fluid phase temperature measurements within the porous medium. The internal heat transfer coefficient is determined in the core of a packed bed, and expressed in terms of the Nusselt number, over a Reynolds number range of 20 to 500. The Nusselt number and Reynolds number are based on the VAT scale hydraulic diameter, dh=4ɛ/S. The results compare favorably to those of other researchers and are seen to be independent of particle diameter. The success of this method, in determining the internal heat transfer coefficient in the core of a randomly packed bed of uniform spheres, suggests that it can be used to determine the internal heat transfer coefficient in other porous media.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 3

Near-wall porosity and preferential flow (velocity is scaled with centerline velocity) in a randomly packed bed of uniform spheres (spheres were not heated), Test Section 1, Re = 305. Porosity distribution taken from the formula given in Eq. 2, where ɛC  = 0.39, and ɛmin  = 0.23.

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Figure 4

Modeling the near-wall bypass or channeling effect

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Figure 5

Measured ratio of core superficial velocity U to upstream superficial velocity U' for the three test sections over the flow rate ranges in each. Umin' and Umax', respectively correspond to the minimum and maximum flow rates achieved in the experiment for each of the three test sections.

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Figure 6

Simulated dimensionless transient fluid temperature response profile

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Figure 7

Experimental dimensionless transient fluid temperature response profile

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Figure 8

Iteration sequence

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Figure 1

Experimental configuration schematic

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Figure 2

Test section diagram, not shown to scale. Item # 8 in Fig. 1.

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Figure 9

Variation of δsim versus t̂ with effective thermal conductivity (W m− 1 K− 1 ). Nusselt number is unity, Re = 300.

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Figure 10

Variation of δsim Versus t̂ with Nusselt number. keff  = 20Wm−1 K−1 , Re = 300

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Figure 11

Experimental heat transfer coefficient data

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Figure 12

Experimental data for Test Sections 1,2, and 3. Correlations are from Kays and London [2], Whitaker [29], and Nie [12].

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Figure 13

Internal effective heat transfer coefficient in porous media, reduced based on VAT scale transformations, from experiments by 1, Kar and Dybbs [30] for laminar regime; 2, Rajkumar [31]; 3, Achenbach [21]; 4, Younis and Viskanta [11]; 5, Galitseysky and Moshaev [32]; 6, Kokorev [33]; 7, Gortyshov [34]; 8, Kays and London [2]; 9, Heat Exchangers Design Handbook [35]; 10, Nie [12]; 11, Whitaker [29]; 12, Eq. 38. Adapted from Travkin and Catton [26].

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