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Analysis of the Thermal Behavior of a Multilayer Slab With Imperfect Contact Using the Dual-Phase-Lag Heat Conduction Model

[+] Author and Article Information
K. Ramadan

Department of Mechanical Engineering, Mu’tah University, P.O. Box 7, Karak 61710, Jordanrkhalid@mutah.edu.jo

M. A. Al-Nimr

Department of Mechanical Engineering, Jordan University of Science and Technology, P.O. Box 3030, Irbid 22110, Jordanmalnimr@just.edu.jo

J. Heat Transfer 130(7), 074501 (May 16, 2008) (5 pages) doi:10.1115/1.2909074 History: Received March 20, 2007; Revised August 09, 2007; Published May 16, 2008

The thermal behavior of a multilayered slab in imperfect contact using the dual-phase-lag heat conduction model is numerically analyzed, considering a range of heat flux-phase lag, temperature gradient-phase lag, and thermal contact resistance. Wave reflections from both insulated boundaries and contact surfaces take place when the phase lag of the temperature gradient is less than the phase lag of the heat flux. Due to the wave nature of energy transport in composite slabs having much less temperature gradient-phase lag than heat flux-phase lag and with a low thermal contact resistance, an initially low-temperature layer can attain a higher temperature than that of the initially high-temperature layer. For composite slabs with temperature gradient-phase lag higher than the heat flux-phase lag and due to the absence of the wave nature of energy transport and the enhancement of heat diffusion, a thermal disturbance is more quickly felt in the whole domain when the temperature gradient-phase lag increases, although in terms of the interfacial temperature difference, the contact surface shows lower response with increasing temperature gradient-phase lag during early stages of the transient energy transport.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Illustration of problem geometry (a), grid numbering in the computational domain (b), and two semi-infinite solids in perfect contact (c)

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Figure 2

Temperature and heat flux distribution at time=1 in two semi-infinite bodies: Acomparison between the exact solution and the DPL model

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Figure 3

Temperature and heat flux distributions at time=0.05 calculated with different grid sizes

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Figure 4

Temperature distribution with different values of the temperature gradient-phase lag

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Figure 5

Variation of the interfacial temperature difference with time for different values of the temperature gradient- and heat flux-phase lags

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Figure 6

Temperature distribution at different times with Rc=5.0 and τq=100τT

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Figure 7

Temperature distribution at different times with Rc=0.01 and τq=100τT

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