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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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References

Fourier, J. B. , 1822, Théorie Analytique de la Chaleur, Paris, (English translation by Freeman, A., 1955, The Analytical Theory of Heat, Dover Publications, New York).
Yeung, W. K. , and Lam, T. T. , 1999, “ Thermal Analysis of Anisotropic Thin-Film Superconductors,” Adv. Electron. Packag., 26(2), pp. 1261–1268.
Fan, J. , and Wang, L. Q. , 2011, “ Analytical Theory of Bioheat Transport,” J. Appl. Phys. 109(10), p. 104702. [CrossRef]
Chang, C. W. , Okawa, D. , Garcia, H. , Majumdar, A. , and Zettl, A. , 2008, “ Breakdown of Fourier's Law in Nanotube Thermal Conductors,” Phys. Rev. Lett., 101(7), p. 075903. [CrossRef] [PubMed]
Lam, T. T. , 2014, “ A Generalized Heat Conduction Solution for Ultrafast Laser Heating in Metallic Films,” Int. J. Heat Mass Transfer, 73, pp. 330–339. [CrossRef]
Shen, B. , and Zhang, P. , 2008, “ Notable Physical Anomalies Manifested in Non-Fourier Heat Conduction Model Under the Dual-Phase-Lag Model,” Int. J. Heat Mass Transfer, 51, pp. 1713–1727. [CrossRef]
Chen, J. K. , Beraun, J. E. , and Tzou, D. Y. , 2000, “ A Dual-Phase-Lag Diffusion Model for Predicting Thin-Film Growth,” Semicond. Sci. Technol., 15(3), pp. 235–241. [CrossRef]
Chen, J. K. , Beraun, J. E. , and Tzou, D. Y. , 2005, “ Numerical Investigation of Ultrashort Laser Damage in Semiconductors,” Int. J. Heat Mass Transfer, 48(3–4), pp. 501–509.
Morse, P. M. , and Feshbach, H. , 1953, Methods of Theoretical Physics, McGraw-Hill, New York.
Cattaneo, C. , 1958, “ Sur Uneforme de I'Equation de la Chaleurelinant le Paradoxed'une Propagation Instantance,” C. R. Acad. Sci. Paris, 247, pp. 431–433.
Vernotte, M. P. , 1958, “ Les Paradoxes de la Theorie Continue de I'equation de la Chaleur,” C. R. Acad. Sci. Paris, 246, pp. 3154–3155.
Tzou, D. Y. , 1997, Macro- to Microscale Heat Transfer: The Lagging Behavior, Taylor & Francis, Washington, DC.
Tzou, D. Y. , 1995, “ Experimental Support for the Lagging Behavior in Heat Propagation,” AIAA J. Thermophys. Heat Transfer, 9(4), pp. 686–693. [CrossRef]
Tzou, D. Y. , 1995, “ A Unified Field Approach for Heat Conduction From Micro- to Macro-Scales,” ASME J. Heat Transfer, 117(1), pp. 8–16. [CrossRef]
Tzou, D. Y. , 1995, “ The Generalized Lagging Response in Small-Scales and High-Rate Heating,” Int. J. Heat Mass Transfer, 38(17), pp. 3231–3240. [CrossRef]
Lam, T. T. , 2013, “ A Unified Solution of Several Heat Conduction Models,” Int. J. Heat Mass Transfer, 56, pp. 653–666. [CrossRef]
Antaki, P. , 1998, “ Solution for Non-Fourier Dual Phase Lag Heat Conduction in a Semi-Infinite Slab With Surface Heat Flux,” Int. J. Heat Mass Transfer, 41(14), pp. 2253–2258. [CrossRef]
Tang, D. W. , and Araki, N. , 1999, “ Wavy, Wavelike, Diffusive Thermal Responses of Finite Rigid Slabs to High-Speed Heating of Laser-Pulses,” Int. J. Heat Mass Transfer, 42(5), pp. 855–860. [CrossRef]
Tang, D. W. , and Araki, N. , 2000, “ Non-Fourier Heat Conduction Behavior in a Finite Mediums Under Pulse Surface Heating,” Mater. Sci. Eng., 292(2), pp. 173–178. [CrossRef]
Wang, L. Q. , Xu, M. T. , and Zhou, X. S. , 2001, “ Well-Posedness and Solution Structure of Dual-Phase-Lagging Heat Conduction,” Int. J. Heat Mass Transfer, 44(9), pp. 1659–1669. [CrossRef]
Dai, W. Z. , and Nassar, R. , 2002, “ An Approximate Analytic Method for Solving 1D Dual-Phase-Lagging Heat Transport Equations,” Int. J. Heat Mass Transfer, 45(8), pp. 1585–1593. [CrossRef]
Al-Khairy, R. T. , 2009, “ Analytical Solution of Non-Fourier Temperature Response in a Finite Medium Symmetrically Heated on Both Sides,” Phys. Wave Phenom., 17(4), pp. 277–285. [CrossRef]
Al-Khairy, R. T. , 2011, “ Thermal Wave Propagation in a Finite Medium Irradiated by a Heat Source With Gaussian Distribution in Both the Temporal and Spatial Domain,” Int. J. Therm. Sci., 50(8), pp. 1369–1373. [CrossRef]
Lam, T. T. , 2010, “ Thermal Propagation in Solids Due to Surface Laser Pulsation and Oscillation,” Int. J. Therm. Sci., 49(9), pp. 1639–1648. [CrossRef]
Torii, S. , and Yang, W.-J. , 2005, “ Heat Transfer Mechanisms in Thin Film With Laser Heat Source,” Int. J. Heat Mass Transfer, 48(3–4), pp. 537–544. [CrossRef]
Zhang, M.-K. , Cao, B.-Y. , and Guo, Y.-C. , 2013, “ Numerical Studies on Dispersion of Thermal Waves,” Int. J. Heat Mass Transfer, 67, pp. 1072–1082. [CrossRef]
Mishra, T. N. , Sarkar, S. , and Rai, K. N. , 2014, “ Numerical Solution of Dual-Phase-Lagging Heat Conduction Model for Analyzing Overshooting Phenomenon,” Appl. Math. Comp., 236, pp. 693–708. [CrossRef]
Wang, B. L. , Han, J. C. , and Sun, Y. G. , 2012, “ A Finite Element/Finite Difference Scheme for the Non-Classical Heat Conduction and Associated Thermal Stresses,” Finite Elem. Anal. Des., 50, pp. 201–206. [CrossRef]
Wang, L. Q. , Zhou, X. S. , and Wei, X. H. , 2008, Heat Conduction: Mathematical Models and Analytical Solutions, Springer-Verlag, Heidelberg, Germany.
Tang, D. W. , and Araki, N. , 1996, “ Non-Fourier Heat Conduction in a Finite Medium Under Periodic Surface Thermal Disturbance,” Int. J. Heat Mass Transfer, 39(8), pp. 1585–1590. [CrossRef]
Lewandowska, M. , and Malinowski, L. , 2006, “ An Analytical Solution of the Hyperbolic Heat Conduction Equation for the Case of a Finite Medium Symmetrically Heated on Both Side,” Int. Commun. Heat Mass Transfer, 33(1), pp. 61–69. [CrossRef]
Hays-Stang, K. J. , and Haji-Sheikh, A. , 1999, “ A Unified Solution for Heat Conduction in Thin Films,” Int. J. Heat Mass Transfer, 42(3), pp. 455–465. [CrossRef]
Lam, T. T. , and Fong, E. , 2011, “ Application of Solution Structure Theorem to Non-Fourier Heat Conduction Problems: Analytical Approach,” Int. J. Heat Mass Transfer, 54(23–24), pp. 4796–4806. [CrossRef]
Lam, T. T. , and Fong, E. , 2011, “ Heat Diffusion vs. Wave Propagation in Solids Subjected to Exponentially-Decaying Heat Source: Analytical Solution,” Int. J. Therm. Sci., 50(10), pp. 2104–2116. [CrossRef]
Lam, T. T. , and Fong, E. , 2013, “ Application of Solution Structure Theorems to Cattaneo–Vernotte Heat Conduction Equation With Non-Homogeneous Boundary Conditions,” Heat Mass Transfer, 49(4), pp. 509–519. [CrossRef]
Fong, E. , and Lam, T. T. , 2014, “ Asymmetrical Collision of Thermal Waves in Thin Films: An Analytical Solution,” Int. J. Therm. Sci., 77, pp. 55–65. [CrossRef]
Myers, G. E. , 1998, Analytical Methods in Conduction Heat Transfer, 2nd ed., AMCHT Publications, Madison, WI, pp. 141–148.
Wang, L. Q. , 2000, “ Solution Structure of Hyperbolic Heat Conduction Equation,” Int. J. Heat Mass Transfer, 43(21), pp. 365–373. [CrossRef]
Guo, Z.-Y. , and Hou, Q.-W. , 2010, “ Thermal Wave Based on the Thermomass Model,” ASME J. Heat Transfer, 132(7), p. 072403. [CrossRef]
Tan, Z.-M. , and Yang, W.-J. , 1997, “ Heat Transfer During Asymmetrical Collision of Thermal Waves in a Thin Film,” Int. J. Heat Mass Transfer, 40(17), pp. 3999–4006. [CrossRef]
Tan, Z.-M. , and Yang, W.-J. , 1997, “ Non-Fourier Heat Conduction in a Thin Film Subjected to a Sudden Temperature Change on Two Sides,” J. Nonequilib. Thermodyn., 22, pp. 75–87. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

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

Grahic Jump Location
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

Grahic Jump Location
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.

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
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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