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Research Papers: Conduction

Single- and Dual-Phase-Lagging Heat Conduction Models in Moving Media

[+] Author and Article Information
Lin Cheng

Institute of Thermal Science and Technology, Shandong University, P.O. Box 88, Jing Shi Road 73, Jinan, Shandong Province 250061, P.R.C.

Mingtian Xu1

Institute of Thermal Science and Technology, Shandong University, P.O. Box 88, Jing Shi Road 73, Jinan, Shandong Province 250061, P.R.C.mingtian@sdu.edu.cn

Liqiu Wang

Department of Mechanical Engineering,  University of Hong Kong, Pokfalum Road, Hong Kong

1

Corresponding author.

J. Heat Transfer 130(12), 121302 (Sep 24, 2008) (6 pages) doi:10.1115/1.2976787 History: Received October 11, 2007; Revised May 24, 2008; Published September 24, 2008

Motivated by the recent work of Christov and Jordan, (“Heat Conduction Paradox Involving Second-Sound Propagation in Moving Media  ,” 2005, Phys. Rev. Lett., 94, p. 154301), we examine the original single- and dual-phase-lagging heat conduction models without Taylor series approximation and their variants in moving media using the Galilean principle of relativity. It is found that the original single- and dual-phase-lagging heat conduction models are Galilean invariant and lead to a single governing equation even for the multidimensional media. However their variants violate the Galilean principle of relativity in the moving media. Although this paradox can be eliminated by replacing the partial time derivatives with the material derivatives, the resulting governing equations cannot be reduced to a single transport equation in the multidimensional media. Therefore we believe that the original single- and dual-phase-lagging heat conduction models are more advantageous in modeling the microscale heat conduction problems.

Copyright © 2008 by American Society of Mechanical Engineers
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