This study introduces an analysis of high-order dual-phase-lag (DPL) heat transfer equation and its thermodynamic consistency. The frameworks of extended irreversible thermodynamics (EIT) and traditional second law are employed to investigate the compatibility of DPL model by evaluating the entropy production rates (EPR). Applying an analytical approach showed that both the first- and second-order approximations of the DPL model are compatible with the traditional second law of thermodynamics under certain circumstances. If the heat flux is the cause of temperature gradient in the medium (over diffused or flux precedence (FP) heat flow), the DPL model is compatible with the traditional second law without any constraints. Otherwise, when the temperature gradient is the cause of heat flux (gradient precedence (GP) heat flow), the conditions of stable solution of the DPL heat transfer equation should be considered to obtain compatible solution with the local equilibrium thermodynamics. Finally, an insight inspection has been presented to declare precisely the influence of high-order terms on the EPRs.

References

References
1.
Antaki
,
P. J.
,
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
.
2.
Tzou
,
D. Y.
,
1995
, “
A Unified Field Approach for Heat Conduction From Macro- to Micro-Scales
,”
ASME J. Heat Transfer
,
117
(
1
), pp.
8
16
.
3.
Tzou
,
D. Y.
,
2015
,
Macro- to Microscale Heat Transfer: The Lagging Behavior
,
2nd ed.
, Wiley, Hoboken, NJ.
4.
Antaki
,
P. J.
,
2005
, “
New Interpretation of Non-Fourier Heat Conduction in Processed Meat
,”
ASME J. Heat Transfer
,
127
(
2
), pp.
189
193
.
5.
Xu
,
F.
,
Seffen
,
K. A.
, and
Lu
,
T. J.
,
2008
, “
Non-Fourier Analysis of Skin Biothermomechanics
,”
Int. J. Heat Mass Transfer
,
51
(
9–10
), pp.
2237
2259
.
6.
Fu
,
J. W.
,
Chen
,
Z. T.
, and
Qian
,
L. F.
,
2015
, “
Coupled Thermoelastic Analysis of a Multi-Layered Hollow Cylinder Based on the C-T Theory and Its Application on Functionally Graded Materials
,”
Compos. Struct.
,
131
, pp.
139
150
.
7.
Yang
,
Y.-C.
,
Wang
,
S.
, and
Lin
,
S.-C.
,
2016
, “
Dual-Phase-Lag Heat Conduction in a Furnace Wall Made of Functionally Graded Materials
,”
Int. Commun. Heat Mass Transfer
,
74
, pp.
76
81
.
8.
Zhang
,
Y.
,
2009
, “
Generalized Dual-Phase Lag Bioheat Equations Based on Nonequilibrium Heat Transfer in Living Biological Tissues
,”
Int. J. Heat Mass Transfer
,
52
(
21–22
), pp.
4829
4834
.
9.
Liu
,
K.-C.
,
2015
, “
Analysis for High-Order Effects in Thermal Lagging to Thermal Responses in Biological Tissue
,”
Int. J. Heat Mass Transfer
,
81
, pp.
347
354
.
10.
Askarizadeh
,
H.
, and
Ahmadikia
,
H.
,
2015
, “
Analytical Study on the Transient Heating of a Two-Dimensional Skin Tissue Using Parabolic and Hyperbolic Bioheat Transfer Equations
,”
Appl. Math. Model.
,
39
(
13
), pp.
3704
3720
.
11.
Ghazanfarian
,
J.
, and
Shomali
,
Z.
,
2012
, “
Investigation of Dual-Phase-Lag Heat Conduction Model in a Nanoscale Metal-Oxide-Semiconductor Field-Effect Transistor
,”
Int. J. Heat Mass Transfer
,
55
(
21–22
), pp.
6231
6237
.
12.
Dai
,
W.
,
Han
,
F.
, and
Sun
,
Z.
,
2013
, “
Accurate Numerical Method for Solving Dual-Phase-Lagging Equation With Temperature Jump Boundary Condition in Nano Heat Conduction
,”
Int. J. Heat Mass Transfer
,
64
, pp.
966
975
.
13.
Tzou
,
D. Y.
, and
Chiu
,
K. S.
,
2001
, “
Temperature-Dependent Thermal Lagging in Ultrafast Laser Heating
,”
Int. J. Heat Mass Transfer
,
44
(
9
), pp.
1725
1734
.
14.
Askarizadeh
,
H.
, and
Ahmadikia
,
H.
,
2016
, “
Dual-Phase-Lag Heat Conduction in Finite Slabs With Arbitrary Time-Dependent Boundary Heat Flux
,”
Heat Transfer Eng.
,
37
(
12
), pp.
1038
1049
.
15.
Kumar
,
S.
,
Bag
,
S.
, and
Baruah
,
M.
,
2016
, “
Finite Element Model for Femtosecond Laser Pulse Heating Using Dual Phase Lag Effect
,”
J. Laser Appl.
,
28
(
3
), p.
32008
.
16.
Khayat
,
R. E.
,
DeBruyn
,
J.
,
Niknami
,
M.
,
Stranges
,
D. F.
, and
Khorasany
,
R. M. H.
,
2015
, “
Non-Fourier Effects in Macro- and Micro-Scale Non-Isothermal Flow of Liquids and Gases. Review
,”
Int. J. Therm. Sci.
,
97
, pp.
163
177
.
17.
Tzou
,
D. Y.
, and
Dai
,
W.
,
2009
, “
Thermal Lagging in Multi-Carrier Systems
,”
Int. J. Heat Mass Transfer
,
52
(
5–6
), pp.
1206
1213
.
18.
Lam
,
T. T.
, and
Fong
,
E.
,
2015
, “
Thermal Dispersion in Finite Medium Under Periodic Surface Disturbance Using Dual-Phase-Lag Model
,”
ASME J. Heat Transfer
,
138
(
3
), p.
032401
.
19.
Mukhopadhyay
,
S.
,
Kothari
,
S.
, and
Kumar
,
R.
,
2014
, “
Dual Phase-Lag Thermoelasticity
,”
Encyclopedia of Thermal Stresses
,
R. B.
Hetnarski
, ed.,
Springer
,
Dordrecht, The Netherlands
, pp.
1003
1019
.
20.
Chirita
,
S.
,
Ciarletta
,
M.
, and
Tibullo
,
V.
,
2015
, “
On the Wave Propagation in the Time Differential Dual-Phase-Lag Thermoelastic Model
,”
Proc. R. Soc. A
,
471
(
2183
), p. 20150400.
21.
Barletta
,
A.
, and
Zanchini
,
E.
,
1997
, “
Hyperbolic Heat Conduction and Local Equilibrium: A Second Law Analysis
,”
Int. J. Heat Mass Transfer
,
40
(
5
), pp.
1007
1016
.
22.
Ahmadikia
,
H.
, and
Rismanian
,
M.
,
2011
, “
Analytical Solution of Non-Fourier Heat Conduction Problem on a Fin Under Periodic Boundary Conditions
,”
J. Mech. Sci. Technol.
,
25
(
11
), pp.
2919
2926
.
23.
Askarizadeh
,
H.
, and
Ahmadikia
,
H.
,
2016
, “
Periodic Heat Transfer in Convective Fins Based on Dual-Phase-Lag Theory
,”
J. Thermophys. Heat Transfer
,
30
(
2
), pp.
359
368
.
24.
Tzou
,
D. Y.
,
1995
, “
Experimental Support for the Lagging Behavior in Heat Propagation
,”
J. Thermophys. Heat Transfer
,
9
(
4
), pp.
686
693
.
25.
Mitra
,
K.
,
Kumar
,
S.
,
Vedevarz
,
A.
, and
Moallemi
,
M. K.
,
1995
, “
Experimental Evidence of Hyperbolic Heat Conduction in Processed Meat
,”
ASME J. Heat Transfer
,
117
(
3
), pp. 568–573.
26.
Kaminski
,
W.
,
1990
, “
Hyperbolic Heat Conduction Equation for Materials With a Nonhomogeneous Inner Structure
,”
ASME J. Heat Transfer
,
112
(
3
), pp.
555
560
.
27.
Askarizadeh
,
H.
,
Baniasadi
,
E.
, and
Ahmadikia
,
H.
,
2017
, “
Equilibrium and Non-Equilibrium Thermodynamic Analysis of High-Order Dual-Phase-Lag Heat Conduction
,”
Int. J. Heat Mass Transfer
,
104
, pp.
301
309
.
28.
Al-Nimr
,
M. A.
,
Naji
,
M.
, and
Arbaci
,
V. S.
,
2000
, “
Nonequilibrium Entropy Production Under the Effect of the Dual-Phase-Lag Heat Conduction Model
,”
ASME J. Heat Transfer
,
122
(
2
), pp.
217
223
.
29.
Rukolaine
,
S. A.
,
2017
, “
Unphysical Effects of the Dual-Phase-Lag Model of Heat Conduction: Higher-Order Approximations
,”
Int. J. Therm. Sci.
,
113
, pp.
83
88
.
30.
Fabrizio
,
M.
, and
Lazzari
,
B.
,
2014
, “
Stability and Second Law of Thermodynamics in Dual-Phase-Lag Heat Conduction
,”
Int. J. Heat Mass Transfer
,
74
, pp.
484
489
.
31.
Rukolaine
,
S. A.
,
2014
, “
Unphysical Effects of the Dual-Phase-Lag Model of Heat Conduction
,”
Int. J. Heat Mass Transfer
,
78
, pp.
58
63
.
32.
Sahoo
,
N.
,
Ghosh
,
S.
,
Narasimhan
,
A.
, and
Das
,
S. K.
,
2014
, “
Investigation of Non-Fourier Effects in Bio-Tissues During Laser Assisted Photothermal Therapy
,”
Int. J. Therm. Sci.
,
76
, pp.
208
220
.
33.
Askarizadeh
,
H.
, and
Ahmadikia
,
H.
,
2014
, “
Analytical Analysis of the Dual-Phase-Lag Model of Bioheat Transfer Equation During Transient Heating of Skin Tissue
,”
Heat Mass Transfer
,
50
(
12
), pp.
1673
1684
.
34.
Bergman
,
T. L.
,
Incropera
,
F. P.
, and
Lavine
,
A. S.
,
2011
,
Fundamentals of Heat and Mass Transfer
,
Wiley
, Hoboken, NJ.
35.
Jou
,
D.
,
Casas-Vázquez
,
J.
, and
Lebon
,
G.
,
1996
,
Extended Irreversible Thermodynamics
,
Springer
, Berlin.
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