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Research Papers: Radiative Heat Transfer

Collocation Spectral Method for the Transient Conduction–Radiation Heat Transfer With Variable Thermal Conductivity in Two-Dimensional Rectangular Enclosure

[+] Author and Article Information
Guo-Jun Li

School of Materials and Metallurgy,
Northeastern University,
Shenyang 110819, China

Jian Ma

Key Laboratory of National Education Ministry
for Electromagnetic Processing of Materials,
Northeastern University,
Shenyang 110819, China

Ben-Wen Li

Institute of Thermal Engineering,
School of Energy and Power Engineering,
Dalian University of Technology,
Dalian 116024, China
e-mail: heatli@hotmail.com;
heatli@dlut.edu.cn

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received April 27, 2014; final manuscript received November 19, 2014; published online December 17, 2014. Assoc. Editor: Zhuomin Zhang.

J. Heat Transfer 137(3), 032701 (Mar 01, 2015) (11 pages) Paper No: HT-14-1247; doi: 10.1115/1.4029237 History: Received April 27, 2014; Revised November 19, 2014; Online December 17, 2014

The collocation spectral method (CSM) is further developed to solve the transient conduction–radiation heat transfer in a two-dimensional (2D) rectangular enclosure with variable thermal conductivity. The energy equation and the radiative transfer equation (RTE) are all discretized by Chebyshev–Gauss–Lobatto collocation points in space after the discrete ordinates method (DOM) discretization of RTE in angular domain. The treatment of variable thermal conductivity is executed using the array multiplication. The present method can deal with different boundary conditions with high accuracy, the Dirichlet one and mixed one, for example. Based on our new method, the effects of several parameters on heat transfer processes are analyzed.

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Figures

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Fig. 1

Physical model with coordinates

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Fig. 6

Isotherms for different conduction–radiation parameter for (a) Ncr = 0.01, (b) Ncr = 0.1, and (c) Ncr = 1.0, when γ = 1.0, τ = 1.0, ω = 0, and ɛ = 1.0

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Fig. 7

Distributions of dimensionless temperature along (a) Y = 0.5 and (b) X = 0.5 for different conduction–radiation parameter, when γ = 1.0, τ = 1.0, ω = 0, and ɛ = 1.0

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Fig. 8

Dimensionless heat flux on the hot wall for different conduction radiation parameter for (a) conduction heat flux, (b) radiation heat flux, and (c) total heat flux

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Fig. 5

Dimensionless heat flux on the hot wall for different variable thermal conductivity parameter for (a) conduction heat flux, (b) radiation heat flux, and (c) total heat flux

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Fig. 4

Distributions of dimensionless temperature along (a) Y = 0.5 and (b) X = 0.5 for different variable thermal conductivity parameter, when Ncr = 0.1, τ = 1.0, ɛ = 1.0, and ω = 0

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Fig. 3

Isotherms for different variable thermal conductivity parameter for (a) γ = -1.0, (b) γ = 0, and (c) γ = 1.0, when Ncr = 0.1, τ = 1.0, ɛ = 1.0, and ω = 0

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Fig. 2

Comparisons of temperature distribution along the center line (Y = 0.5) between present and Ref. [19] for (a) γ = 1.0 and (b) γ = -1.0

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Fig. 9

Isotherms for different variable thermal conductivity parameter for (a) γ = -1.0, (b) γ = 0, and (c) γ = 1.0 under mixed boundary conduction, when Ncr = 0.1, τ = 1.0, ω = 0, and ɛ = 1.0

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Fig. 10

Distributions of dimensionless temperature along (a) Y = 0.5 and (b) X = 0.5 for different variable thermal conductivity parameter under mixed boundary conduction, when Ncr = 0.1, τ = 1.0, ω = 0, and ɛ = 1.0

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Fig. 11

Dimensionless heat flux on the hot wall for different variable thermal conductivity parameter for (a) conduction heat flux and (b) radiation heat flux under mixed boundary conduction

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