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Research Papers: Conduction

# Analysis of a Hyperbolic Heat Conduction-Radiation Problem With Temperature Dependent Thermal Conductivity

[+] Author and Article Information
Subhash C. Mishra1

Department of Mechanical Engineering, Indian Institute of Technology Guwahati, Guwahati, Assam 781039, Indiascm_iitg@yahoo.com

T. B. Pavan Kumar2

Department of Mechanical Engineering, Indian Institute of Technology Guwahati, Guwahati, Assam 781039, India

1

Corresponding author.

2

Mr. Kumar contributed to this work when he was an MTech student at IIT Guwahati from July 2006 to July 2008.

J. Heat Transfer 131(11), 111302 (Aug 19, 2009) (7 pages) doi:10.1115/1.3154621 History: Received June 12, 2008; Revised April 28, 2009; Published August 19, 2009

## Abstract

This article deals with the analysis of a hyperbolic conduction and radiation heat transfer problem in a planar participating medium. Thermal conductivity of the medium is temperature dependent. Hyperbolic conduction is due to non-Fourier effect. The boundaries of the medium can be either at prescribed temperatures and/or fluxes. With both boundaries insulated, effects of a short pulse internal heat source in the medium are also considered. The problem is analyzed using the lattice Boltzmann method. The finite volume method is employed to compute the radiative information required. Transient temperature distributions in the medium are studied for the effects of various parameters.

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## Figures

Figure 1

Validation of results for dimensionless temperature θ distribution in a pure conducting medium (ω=1.0) with three values of γ (=−0.1, 0.0, and 0.1) for (a) a temperature boundary condition problem, (b) a nonlinear boundary condition (surface radiative cooling) problem with Er=0.0, and (c) a mixed boundary condition problem. Validation of results for θ distribution in a non-Fourier conducting-radiating medium with constant thermal conductivity (γ=0.0) for (d) β=1.0, N=0.25, (e) β=0.1, N=0.25, and (f) β=1.0, N=0.025.

Figure 2

Dimensionless temperature θ distribution in the medium for temperature boundary conduction problem for (a)ω=0.0, (b) ω=0.5, (c) N=2.5, (d) N=0.25, (e) β=0.1, and (f) β=0.5

Figure 3

Dimensionless temperature θ distribution in the medium for mixed boundary conduction problem for (a) ω=0.0, (b) ω=0.5, (c) N=2.5,(d) N=0.25, (e) β=0.1, and (f) β=0.5

Figure 4

Dimensionless temperature θ distribution in the medium for a pulsed internal heat source problem for (a) ω=0.0, (b) ω=0.5, (c) N=2.5, (d) N=0.25, (e) β=0.1, and (f) β=0.5

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