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Research Papers: Radiative Heat Transfer

Predicting the Effective Emissivity of an Array of Aligned Carbon Fibers Using the Reverse Monte Carlo Ray-Tracing Method

[+] Author and Article Information
Briana N. Tomboulian

Mem. ASME
Flatirons Research and Development,
University of Massachusetts, Amherst
160 Governors Drive,
Amherst, MA 01003
e-mail: flatironsrnd@gmail.com

Robert W. Hyers

Mem. ASME
Engineering Laboratory,
Mechanical and Industrial Engineering,
University of Massachusetts,
160 Governors Drive,
Amherst, MA 01003
e-mail: hyers@umass.edu

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received March 21, 2016; final manuscript received July 21, 2016; published online August 30, 2016. Assoc. Editor: Zhuomin Zhang.

J. Heat Transfer 139(1), 012701 (Aug 30, 2016) (7 pages) Paper No: HT-16-1146; doi: 10.1115/1.4034310 History: Received March 21, 2016; Revised July 21, 2016

This study investigates the bulk radiative properties of absorbing and scattering fibers. This type of problem can be applied to a group of geometrically similar applications including thermal radiators, insulation, and tube-and-shell heat exchangers. The specific application studied here is an ordered array of carbon fibers acting as a radiating fin for a space-based heat rejection system. High total emissivity is beneficial for this application, so this study focuses on how geometric factors affect the effective emissivity of an array of fibers. Photon scattering among fibers in an array can result in an effective emissivity greater than the emissivity of the fiber surfaces themselves.

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Figures

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Fig. 4

Five single-photon ray paths in a simulation with a fiber volume fraction of 0.127

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Fig. 3

Discrete probability distribution for θ2 (Eq. (6)), created using a sample size of 100,000 rays

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Fig. 2

Angles of radiative emission from a boundary element in three dimensions (left) and two dimensions (right)

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Fig. 1

Model domain for a four-fiber thick array

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Fig. 5

Configuration of two infinitely long cylinders with uniform radii, used for the view factor validation

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Fig. 6

Percent error between analytical and MCRT view factor versus number of trials (rays)

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Fig. 7

Fraction of total incident energy absorbed, reflected, and transmitted versus fiber volume fraction for an array thickness of 0.5 mm, 50,000 multiphoton rays, and a fiber emissivity of 0.8. The dotted line shows the surface emissivity of the individual fibers.

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Fig. 8

Surface plots of transmittance (left) and effective emissivity (right) versus fiber volume fraction and the number of fiber rows for simulations with fiber emissivity of 0.8

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Fig. 9

Fiber volume fraction versus total fraction of absorbed, reflected, or transmitted energy for a 0.5 mm thick fiber array, fiber emissivity of 0.8, and collimated incident rays. The vertical dotted line shows the maximum effective emissivity of this array.

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Fig. 10

Effective emissivity versus fiber volume fraction for fiber surface emissivities of 0.6, 0.7, 0.8, and 0.9 for a 0.5 mm thick array and 50,000 multiphoton rays per simulation. Each dotted line shows the fiber surface emissivity that corresponds with the effective emissivity curve directly above it at high volume fractions.

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Fig. 11

Maximum fiber array effective emissivity versus the surface emissivity of the individual fibers for an array thickness of 0.5 mm. The dotted line represents the case where the maximum effective emissivity and surface emissivity of the individual fibers are equal to show that the actual maximum effective emissivity is greater than the fiber surface emissivity by about half of the difference between the surface emissivity and one.

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Fig. 12

Reflectivity versus fiber volume fraction for fiber surface emissivities of 0.6, 0.7, 0.8, and 0.9. Each dotted line shows the fiber surface reflectivity that corresponds with the effective reflectivity curve directly below it at high volume fractions.

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Fig. 13

Transmittance versus fiber volume fraction curves for fiber surface emissivities of 0.6, 0.7, 0.8, and 0.9. The transmittance versus volume fraction is nearly identical for all fiber emissivities because the overall transmittance is much more sensitive to the fiber volume fraction than the surface emissivity of the individual fibers in this range of emissivities.

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Fig. 14

Percent of incident energy absorbed versus depth into the fiber array for a range of fiber volume fractions (array thickness = 0.5 mm, fiber emissivity = 0.8, 100,000 rays). The discrete steps indicate interactions with the individual fibers.

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