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Research Papers: Radiative Heat Transfer

Spectral Collocation Method for Transient Combined Radiation and Conduction in an Anisotropic Scattering Slab With Graded Index

[+] Author and Article Information
Ya-Song Sun

Key Laboratory of National Education Ministry for Electromagnetic Processing of Materials, Northeastern University, P.O. Box 314, Shenyang 110004, China

Ben-Wen Li1

Key Laboratory of National Education Ministry for Electromagnetic Processing of Materials, Northeastern University, P.O. Box 314, Shenyang 110004, Chinaheatli@hotmail.com, heatli@epm.neu.edu.cn

1

Corresponding author.

J. Heat Transfer 132(5), 052701 (Mar 08, 2010) (9 pages) doi:10.1115/1.4000444 History: Received January 18, 2009; Revised July 23, 2009; Published March 08, 2010; Online March 08, 2010

The spectral collocation method for transient combined radiation and conduction heat transfer in a planar participating medium with spatially variable refractive index is introduced and formulated. The angular dependence of the problem is discretized by discrete ordinates method and the space dependence is expressed by Chebyshev polynomial and discretized by spectral collocation method. Due to the exponential convergence of spectral methods, very high accuracy can be obtained even using a small resolution for present problem. Numerical results in one-dimensional planar slab by Chebyshev collocation spectral-discrete ordinates method (SP-DOM) are compared with those available data in references. Effects of various parameters such as the variable thermal conductivity, the scattering albedo, the emissivity of boundary, the conduction-radiation parameter, the optical thickness, and the graded index are studied for absorbing, emitting, and anisotropic scattering medium. The SP-DOM has been found to successfully and efficiently deal with transient combined radiation and conduction heat transfer problem in graded index medium.

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Figures

Grahic Jump Location
Figure 1

Physical geometry of slab

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Figure 2

Comparisons of dimensionless temperature profiles of SP-DOM with those of CRT-PSA for the cases of n(x)=1.2+0.6(x/L) and n(x)=1.8−0.6(x/L)

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Figure 3

Effect of variable thermal conductivity on dimensionless temperature profile in linear refractive index medium: (a) a=−2.0, (b) a=0.0, and (c) a=2.0

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Figure 4

Effect of scattering albedo on dimensionless temperature profile in graded index medium: (a) ω=0.1, (b) ω=0.5, and (c) ω=0.9

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Figure 5

Effect of emissivity of boundary on dimensionless temperature profile in graded index medium: (a) εW=1.0, εE=0.1; (b) εW=0.1, εE=0.1; and (c) εW=0.1, εE=1.0

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Figure 6

Effect of conduction-radiation parameter on dimensionless temperature profile in graded index medium: (a) Ncr=0.02, (b) Ncr=0.1, and (c) Ncr=0.5

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Figure 7

Effect of optical thickness on dimensionless temperature profile in graded index medium: (a) τL=0.2, (b) τL=1.0, and (c) τL=5.0

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Figure 8

Effect of graded index on dimensionless temperature profile: (a) n(x)=1.2+0.6 sin(πx/L), (b) n(x)=1.5, and (c) n(x)=1.8−0.6 sin(πx/L)

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