RESEARCH PAPERS: Radiative Heat Transfer

Modification of Planck Blackbody Emissive Power and Intensity in Particulate Media Due to Multiple and Dependent Scattering

[+] Author and Article Information
Ravi Prasher1

Ch5-157,  Intel Corporation, 5000 W. Chandler Blvd., Chandler, Arizona 85226ravi.s.prasher@intel.com


Adjunct Professor, Department of Mechanical and Aerospace Engineering, Arizona State University

J. Heat Transfer 127(8), 903-910 (Mar 01, 2005) (8 pages) doi:10.1115/1.1928912 History: Received July 06, 2004; Revised March 01, 2005

The dispersion relation for an electromagnetic wave is obtained in particulate media using effective field approximation (EFA) and quasi-crystalline approximation (QCA). Due to multiple and dependent scattering the density of states, phase velocity and group velocity of photons are modified. Modification of these parameters modifies the Planck blackbody equilibrium radiation intensity and emissive power. Results show that EFA can accurately capture the dependence of density of states, phase velocity, and the group velocity on volume fraction of scatterers whereas QCA can capture the dependence of effective attenuation as well as density of states, phase velocity, and the group velocity. Comparisons of the temperature, heat flux, and effective attenuation are made between EFA, QCA, and work done by C. L. Tien and co-workers. Results show that heat flux and temperature predictions made by models in the literature for multiple and dependent scattering are not correct as these models do not take the modification of the equilibrium intensity into account. Finally we introduce a new model called dependent effective field approximation (DEFA) which accurately captures the effect of volume fraction on the equilibrium intensity and effective attenuation.

Copyright © 2005 by American Society of Mechanical Engineers
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Figure 1

Ratio of the imaginary and the real part of the effective wave vector in the particulate media

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Figure 8

Percent error in heat flux if the wall emissivity is not modified due to change in the effective refractive index of the medium for DEFA

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Figure 9

(a) Ratio of dimensionless temperature w.r.t. independent scattering for τL=1. (b) Ratio of dimensionless temperature w.r.t. independent scattering for τL=100.

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Figure 2

Comparison of the dimensionless effective attenuation

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Figure 3

Comparison of the dimensionless effective attenuation obtained from Tien’s approach and QCA

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Figure 4

Comparison between the square of effective refractive index obtained from QCA and EFA

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Figure 5

Effect of multiple scattering on the effective emissivity

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Figure 6

(a) Comparison between the heat flux prediction from different models for τL=0. (b) Comparison between the heat flux prediction from different models for τL=10.

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Figure 7

Difference between the heat flux predictions of DEFA and QCA




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