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Research Papers: Conduction

Effective Thermal Properties of Layered Systems Under the Parabolic and Hyperbolic Heat Conduction Models Using Pulsed Heat Sources

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

e-mail: jjag@mda.cinvestav.mx Departamento de Física Aplicada,  Centro de Investigación y de Estudios Avanzados del I.P.N.-Unidad Mérida, Carretera Antigua a Progreso km. 6, A.P. 73 Cordemex, Mérida, Yucatán, México C.P. 97310

J. J. Alvarado-Gil1

e-mail: jjag@mda.cinvestav.mx Departamento de Física Aplicada,  Centro de Investigación y de Estudios Avanzados del I.P.N.-Unidad Mérida, Carretera Antigua a Progreso km. 6, A.P. 73 Cordemex, Mérida, Yucatán, México C.P. 97310

1

Corresponding Author.

J. Heat Transfer 133(9), 091301 (Jul 08, 2011) (9 pages) doi:10.1115/1.4003814 History: Received May 02, 2010; Revised March 01, 2011; Accepted March 09, 2011; Published July 08, 2011; Online July 08, 2011

In this work, transient heat transport in a flat layered system, with interface thermal resistance, is analyzed, under the approach of the Cattaneo–Vernotte hyperbolic heat conduction model using the thermal quadrupole method. For a single semi-infinite layer, analytical formulas useful in the determination of its thermal relaxation time as well as its thermal effusivity are obtained. For a composite-layered system, in the long time regime and under a Dirichlet boundary condition, the well-known effective thermal resistance formula and a novel expression for the effective thermal relaxation time are derived, while for a Neumann problem, only a heat capacity identity is found. In contrast in the short time regime, under both Dirichlet and Neumann conditions, an expression that involves the effective thermal diffusivity and relaxation time as a function of the time is derived. In this time regime and under the Fourier approach, a formula for the effective thermal diffusivity in terms of the time, the thermal properties of the individual layers and its interface thermal resistance is obtained. It is shown that these results can be useful in the development of experimental methodologies to perform the thermal characterization of materials in the time domain.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

Schematic diagram of the studied layered systems. (a) A semi-infinite layer of thermal conductivity κ, thermal diffusivity α and thermal relaxation time τ. (b) The layer of thermal conductivity ki, thermal diffusivity αi, thermal relaxation time τi, and thickness li is in thermal contact with the layer of conductivity ki+1, diffusivity αi+1, relaxation time τi+1, and thickness li+1; for i=1,2. The third layer is considered as a semi-infinite one (l3→∞).

Grahic Jump Location
Figure 2

Time dependence on the surface temperature at x=0, for an excitation of a (a) Dirac heat pulse and (b) constant heat flux. The solid lines correspond to the hyperbolic model and the dashed lines to the parabolic one.

Grahic Jump Location
Figure 3

Time dependence on the normalized parabolic effective thermal diffusivity, for three values of the (a) ratio ɛ2/ɛ2ɛ1ɛ1 of thermal effusivities with R12=0 and (b) normalized interface thermal resistance r, for a constant ratio ɛ2/ɛ2ɛ1ɛ1=2/323

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