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Research Papers: Micro/Nanoscale Heat Transfer

Thermal Dispersion in Finite Medium Under Periodic Surface Disturbance Using Dual-Phase-Lag Model

[+] Author and Article Information
Tung T. Lam

Fellow ASME
Spacecraft Thermal Department,
Vehicle Systems Division,
The Aerospace Corporation,
2310 E. El Segundo Blvd.,
El Segundo, CA 90245-4609
e-mail: tung.t.lam@aero.org

Ed Fong

Spacecraft Thermal Department,
Vehicle Systems Division,
The Aerospace Corporation,
2310 E. El Segundo Blvd.,
El Segundo, CA 90245-4609
e-mail: ed.fong@aero.org

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received February 26, 2015; final manuscript received September 21, 2015; published online November 3, 2015. Assoc. Editor: Laurent Pilon.

J. Heat Transfer 138(3), 032401 (Nov 03, 2015) (12 pages) Paper No: HT-15-1148; doi: 10.1115/1.4031732 History: Received February 26, 2015; Revised September 21, 2015

Transient heat conduction in finite thin films subjected to time-varying surface heat flux incidences at both boundaries and internal heat generation is investigated via the dual-phase-lag (DPL) hyperbolic model. Analytical solution of the temperature profiles inside the solid is derived by using the superposition principle and the method of Fourier series expansion in conjunction with the solution structure theorems. For comparison purposes, the classical diffusion, Cattaneo–Vernotte (C–V) model, and simplified thermomass (TM) models are deduced from the generalized DPL model. This is made possible by adjusting the temperature and heat flux relaxation parameters, and offers the opportunity to examine various interconnected non-Fourier conduction heat transfer characteristics including wave and diffusion effects as well as their interrelationship. Details of this process are examined and results are explored in this study.

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Figures

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Fig. 1

Schematic diagram of a thin film subjected to time-varying laser irradiation and internal heat generation

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Fig. 4

Transient surface temperature at x = 0.0 with heating on both sides (qls = qrs = 1) based on the DPL model for various τT/2τq ratios at ω = 0.25

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Fig. 2

Transient surface temperature at x = 0.0 with heating on the left side (qls = 1 and qrs = 0) based on the DPL model for various τT/2τq ratios at (a) ω = 0.25, (b) ω = 0.5, and (c) ω = 1.0

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Fig. 3

(a) Effect of surface temperatures with heating on the left side (qls = 1 and qrs = 0) based on the DPL model for a τT/2τq ratio of 0.1 at ω = 0.25. (b) Magnified view of Fig. 3(a) illustrating surface temperature responses. (c) Effect of surface temperatures with heating on the left side (qls = 1 and qrs = 0) based on the DPL model for a τT/2τq ratio of 2.0 at ω = 0.25.

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Fig. 7

Comparison of the transient surface temperature within the film at t = 0.1 and μ = 10 with qls = qrs = 1 and ω = 0.25 for various models

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Fig. 5

Spatial temperature variation at t = 0.1 with heating on both sides (qls = qrs = 1) based on the DPL model for various τT/2τq ratios at ω = 0.25

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Fig. 6

Comparison of transient surface temperature behavior at x = 0.0 based on the simplified TM, diffusion, DPL (τT/2τq = 0.3), and C–V models with qls = 1 and qrs = 0 and ω = 0.25

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