RESEARCH PAPERS: Radiative Heat Transfer

Radiative Characteristic of Spherical Cavities With Specular Reflectivity Component

[+] Author and Article Information
F. Kowsary

Mechanical Engineering Department, Faculty of Engineering, University of Tehran, Tehran, Iranfkowsary@chamran.ut.ac.ir

J. R. Mahan

Mechanical Engineering Department, Georgia Tech Lorraine, Technopôle Metz 2000, 2-3, rue Marconi, 57070 Metz, Francemahan@georgiatech-metz.fr

J. Heat Transfer 128(3), 261-268 (Jul 28, 2005) (8 pages) doi:10.1115/1.2151196 History: Received March 23, 2005; Revised July 28, 2005

An exact analytical method is presented for determination of emissive as well as absorptive performance of spherical cavities having diffuse-specular reflective walls. The method presented utilizes a novel coordinate transformation technique, which provides convenient means for setting up the governing radiant exchange integral equations. These equations are then solved by the usual iterative method devized for the Fredholm integral equation of the second kind. The suggested coordinate transformation is also utilized for determination of directional absorptivity of a fully specular spherical cavity when collimated radiation enters through its mouth from a specified direction. Results show that for a spherical cavity the dependence of the apparent emissivity on the degree of specularity is high when the emissivity of the cavity wall is low, but this dependence decreases as the emissivity of the cavity wall increases. Also there are situations, unlike cases of cylindrical and conical cavities, for which the purely diffuse spherical cavity is a more efficient emitter than the purely specular cavity having an identical geometry and wall emissivity. Moreover, it is shown that the apparent directional absorptivity of specular spherical cavities having small openings becomes highly fluctuating as the direction of the incident radiation changes

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

Geometry for a specular spherical cavity

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Figure 2

Great circle for rays traveling between two arbitrary points by specular reflections

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Figure 3

Four possible specular routes for a ray leaving S1 to reach S2

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Figure 4

Defining a new (source-oriented) coordinate system that is suitable for analysis of radiant exchange by specular reflections

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Figure 5

A great circle that has intersected the opening

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Figure 6

(a) A collimated beam of flux q0 entering a spherical cavity at angle γ; and (b) the same cavity as in (a) rotated through angle γ about the z-axis

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Figure 7

Parallel rays entering a great circle (i.e., a spherical sector)

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Figure 8

Apparent emissivity of spherical cavities for various geometrical and surface conditions

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Figure 9

(a) Directional apparent absorptivity of spherical cavities, opening angle=15deg; (b) opening angle=45deg; (c) opening angle=90deg; and (d) opening angle=150deg



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