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Research Papers: Conduction

Determination of Time-Delay Parameters in the Dual-Phase Lagging Heat Conduction Model

[+] Author and Article Information
J. Ordóñez-Miranda

Department of Applied Physics, Centro de Investigación y de Estudios Avanzados del I.P.N-Unidad Mérida, Carretera Antigua a Progreso kilómetro 6, Apartado Postal 73 Cordemex, Mérida, Yucatán 97310, Méxicoeordonez@mda.cinvestav.mx

J. J. Alvarado-Gil

Department of Applied Physics, Centro de Investigación y de Estudios Avanzados del I.P.N-Unidad Mérida, Carretera Antigua a Progreso kilómetro 6, Apartado Postal 73 Cordemex, Mérida, Yucatán 97310, Méxicojjag@mda.cinvestav.mx

J. Heat Transfer 132(6), 061302 (Mar 25, 2010) (9 pages) doi:10.1115/1.4000748 History: Received May 03, 2009; Revised October 28, 2009; Published March 25, 2010; Online March 25, 2010

The study of thermal transport based on the dual-phase lagging model involves not only the well known thermal properties but also two additional time parameters. Those parameters permit to take into account the thermal inertia and the microstructural interactions of the media in such a way that they establish the nonsimultaneity between temperature changes and heat flux. In the dual-phase lagging model, heat transport phenomena are extremely sensitive not only to the size of each time parameter but also to the relative size of them. In order to obtain useful and reliable results, it is important to develop methodologies for the determination of those time parameters. Additionally it is necessary to count with tools that allow evaluating easily the sensitivity of the temperature and heat to the changes in those time parameters. In this work, a system formed by a semi-infinite layer in thermal contact with a finite one, which is excited by a modulated heat flux, is studied. When the thermal effusivities of the layers are quite different, it is shown that a frequency range can be found in which the normalized amplitude and phase of the spatial component of the oscillatory surface temperature show strong oscillations. This behavior is used to obtain explicit formulas for determining simultaneously the time parameters as well as additional thermal properties of the finite layer, under the framework of the dual-phase lagging model of heat conduction. The limits of the corresponding equations for single-phase lagging models of heat conduction are also discussed.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

Schematic diagram of the analyzed system, with k,α,τq,τT and k0,α0,τq0,τT0 being the thermal conductivity, thermal diffusivity, phase lag of the heat flux vector, and the phase lag of the temperature gradient of the finite and semi-infinite layers, respectively. The excitation heat source is applied at x=0.

Grahic Jump Location
Figure 2

Frequency dependence at x=0 of the normalized phase of the temperature. The dashed line corresponds to the parabolic model and the solid lines to the DPL one, for two pairs of time delays: (τq,τT)1=(1×10−7 s,2×10−8 s) and (τq,τT)2=(5×10−8 s,8×10−9 s).

Grahic Jump Location
Figure 3

Frequency dependence of the dimensionless functions N1(ω), N2(ω), and D(ω), for the time delays τq=1×10−7 s and τT=2×10−8 s

Grahic Jump Location
Figure 4

Frequency dependence at x=0 of the normalized amplitude of the temperature. The dashed line corresponds to the parabolic model and the solid lines to the DPL one, for two pairs of time delays: (τq,τT)1=(1×10−7 s,2×10−8 s) and (τq,τT)2=(5×10−8 s,8×10−9 s).

Grahic Jump Location
Figure 5

Frequency dependence at x=0 of the normalized phase of the temperature. The dashed line corresponds to the parabolic model and the solid lines to the DPL one, for three pairs of phase lags. (a) (τq,τT)1=(7×10−8 s,0), (τq,τT)2=(7×10−8 s,1×10−9 s), and (τq,τT)3=(7×10−8 s,1×10−8 s); and (b) (τq,τT)1=(0,7×10−8 s), (τq,τT)2=(1×10−9 s,7×10−8 s), and (τq,τT)3=(1×10−8 s,7×10−8 s). In both cases the thickness of the finite layer is l=10 μm and its thermal diffusivity is taken as α=1×10−4 m2/s.

Grahic Jump Location
Figure 6

Frequency dependence at x=0 of the normalized amplitude of the temperature. The dashed line corresponds to the parabolic model and the solid lines to the DPL one, for three pairs of phase lags. (a) (τq,τT)1=(7×10−8 s,0), (τq,τT)2=(7×10−8 s,1×10−9 s), and (τq,τT)3=(7×10−8 s,1×10−8 s); and (b) (τq,τT)1=(0,7×10−8 s), (τq,τT)2=(1×10−9 s,7×10−8 s), and (τq,τT)3=(1×10−8 s,7×10−8 s). In both cases the thickness of the finite layer is l=10 μm and its thermal diffusivity is taken as α=1×10−4 m2/s.

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