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# Chebyshev Collocation Spectral Method for Three-Dimensional Transient Coupled Radiative–Conductive Heat Transfer

[+] Author and Article Information
Ya-Song Sun, Jing Ma

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

Ben-Wen Li1

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

1

Corrersponding author.

J. Heat Transfer 134(9), 092701 (Jul 02, 2012) (8 pages) doi:10.1115/1.4006596 History: Received August 05, 2011; Revised February 02, 2012; Published July 02, 2012; Online July 02, 2012

## Abstract

A Chebyshev collocation spectral method (CSM) is presented to solve transient coupled radiative and conductive heat transfer in three-dimensional absorbing, emitting, and scattering medium in Cartesian coordinates. The walls of the enclosures are considered to be opaque, diffuse, and gray and have specified temperature boundary conditions. The CSM is adopted to solve both the radiative transfer equation (RTE) and energy conservation equation in spatial domain, and the discrete ordinates method (DOM) is used for angular discretization of RTE. The exponential convergence characteristic of the CSM for transient coupled radiative and conductive heat transfer is studied. The results using the CSM show very satisfactory calculations comparing with available results in the literature. Based on this method, the effects of various parameters, such as the scattering albedo, the conduction–radiation parameter, the wall emissivity, and the optical thickness, are analyzed.

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## Figures

Figure 7

For ω=0, ɛ=1, and Ncr=0.01, dimensionless temperature on the centerline (x*=0.5,y*, z*=0.5) with different t*. (a) τL=0.1 and (b) τL=5.0

Figure 6

For τL=1.0, Ncr=0.01, and ω=0, dimensionless temperature on the centerline (x*=0.5, y*, z*=0.5) with different t*. (a) ɛS=0.1 and (b) ɛS=0.5

Figure 5

For τL=1.0, ɛ=1, and ω=0, dimensionless temperature on the centerline (x*=0.5, y*, z*=0.5) with different t*. (a) Ncr=0.1 and (b) Ncr=1.0

Figure 4

For τL=1.0, ɛ=1, and Ncr=0.01, dimensionless temperature on the centerline (x*=0.5,y*, z*=0.5) with different t*. (a) ω=0.5 and (b) ω=0.9

Figure 3

For different dimensionless time t*, isotherms at the center plane (x*=0.5, y*, z*) for the case of τL=1.0, ω=0, ɛ=1, and Ncr=0.01. (a) t*=0.005; (b) t*=0.015; (c) t*=0.050; and (d) t*=SS

Figure 2

The exponential convergence rate of CSM for the transient coupled radiation–conduction heat transfer according to the total number of spatial nodes

Figure 1

Physical model and notations

## Errata

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