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.

References

References
1.
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).
2.
Yeung
,
W. K.
, and
Lam
,
T. T.
,
1999
, “
Thermal Analysis of Anisotropic Thin-Film Superconductors
,”
Adv. Electron. Packag.
,
26
(
2
), pp.
1261
1268
.
3.
Fan
,
J.
, and
Wang
,
L. Q.
,
2011
, “
Analytical Theory of Bioheat Transport
,”
J. Appl. Phys.
109
(
10
), p.
104702
.
4.
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
.
5.
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
.
6.
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
.
7.
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
.
8.
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
.
9.
Morse
,
P. M.
, and
Feshbach
,
H.
,
1953
,
Methods of Theoretical Physics
,
McGraw-Hill
,
New York
.
10.
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
.
11.
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
.
12.
Tzou
,
D. Y.
,
1997
,
Macro- to Microscale Heat Transfer: The Lagging Behavior
,
Taylor & Francis
,
Washington, DC
.
13.
Tzou
,
D. Y.
,
1995
, “
Experimental Support for the Lagging Behavior in Heat Propagation
,”
AIAA J. Thermophys. Heat Transfer
,
9
(
4
), pp.
686
693
.
14.
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
.
15.
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
.
16.
Lam
,
T. T.
,
2013
, “
A Unified Solution of Several Heat Conduction Models
,”
Int. J. Heat Mass Transfer
,
56
, pp.
653
666
.
17.
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
.
18.
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
.
19.
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
.
20.
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
.
21.
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
.
22.
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
.
23.
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
.
24.
Lam
,
T. T.
,
2010
, “
Thermal Propagation in Solids Due to Surface Laser Pulsation and Oscillation
,”
Int. J. Therm. Sci.
,
49
(
9
), pp.
1639
1648
.
25.
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
.
26.
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
.
27.
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
.
28.
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
.
29.
Wang
,
L. Q.
,
Zhou
,
X. S.
, and
Wei
,
X. H.
,
2008
,
Heat Conduction: Mathematical Models and Analytical Solutions
,
Springer-Verlag
,
Heidelberg, Germany
.
30.
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
.
31.
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
.
32.
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
.
33.
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
.
34.
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
.
35.
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
.
36.
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
.
37.
Myers
,
G. E.
,
1998
,
Analytical Methods in Conduction Heat Transfer
,
2nd ed.
,
AMCHT Publications
,
Madison, WI
, pp.
141
148
.
38.
Wang
,
L. Q.
,
2000
, “
Solution Structure of Hyperbolic Heat Conduction Equation
,”
Int. J. Heat Mass Transfer
,
43
(
21
), pp.
365
373
.
39.
Guo
,
Z.-Y.
, and
Hou
,
Q.-W.
,
2010
, “
Thermal Wave Based on the Thermomass Model
,”
ASME J. Heat Transfer
,
132
(
7
), p.
072403
.
40.
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
.
41.
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
.
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