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Research Papers: Heat and Mass Transfer

Extended Irreversible Thermodynamics Versus Second Law Analysis of High-Order Dual-Phase-Lag Heat Transfer

[+] Author and Article Information
Hossein Askarizadeh

Department of Mechanical Engineering,
University of Isfahan,
Isfahan 81746-73441, Iran
e-mail: h.askarizadeh@eng.ui.ac.ir

Hossein Ahmadikia

Department of Mechanical Engineering,
University of Isfahan,
Isfahan 81746-73441, Iran
e-mail: ahmadikia@eng.ui.ac.ir

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received December 19, 2016; final manuscript received November 30, 2017; published online April 19, 2018. Assoc. Editor: Milind A. Jog.

J. Heat Transfer 140(8), 082003 (Apr 19, 2018) (9 pages) Paper No: HT-16-1818; doi: 10.1115/1.4038851 History: Received December 19, 2016; Revised November 30, 2017

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.

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Figures

Grahic Jump Location
Fig. 2

Comparison of spatial distribution of heat flux fields with the study of Al-Nimr et al. [28] (Reprinted with permission from ASME @ 2000)

Grahic Jump Location
Fig. 1

Comparison of spatial temperature distributions with the study of Al-Nimr et al. [28] (Reprinted with permission from ASME @ 2000)

Grahic Jump Location
Fig. 6

Spatial distribution of heat flux field based on the first- and second-order DPL models: FP heat flow regime

Grahic Jump Location
Fig. 7

Effects of heat flux relaxation time on the temperature distribution at η = 1

Grahic Jump Location
Fig. 3

Deviations between the predictions of the first- and second-order DPL models for the temperature distributions: GP heat flow regime

Grahic Jump Location
Fig. 4

Deviations between the predictions of the first- and second-order DPL models for the temperature distributions: FP heat flow regime

Grahic Jump Location
Fig. 5

Spatial distribution of heat flux field based on the first- and second-order DPL models: GP heat flow regime

Grahic Jump Location
Fig. 8

Spatial distribution of the nonequilibrium EPR based on the first- and second-order approximations of the DPL model: FP heat flow regime

Grahic Jump Location
Fig. 9

Predictions of the first- and second-order DPL models for EPRs based on LTE in different dimensionless times

Grahic Jump Location
Fig. 10

Spatial distribution of EPRs based on EIT in different dimensionless times. Comparison between the first- and second-order DPL models.

Grahic Jump Location
Fig. 16

Sequence addition of different terms of Eq. (20) to declare which one of them plays a compensative role in EPR based on the second-order DPL model

Grahic Jump Location
Fig. 11

Production of positive and negative EPRs based on the LTE and EIT. Comparison between the first- and second-order DPL models.

Grahic Jump Location
Fig. 12

Analysis of the first-order DPL model when the sharp wavefront causes the negative EPR under the framework of LTE

Grahic Jump Location
Fig. 13

Gradual disappearing of sharp wavefront in the temperature distribution of the first-order DPL model

Grahic Jump Location
Fig. 14

Compatibility of the first-order DPL model with LTE in the presence of a sharp wavefront

Grahic Jump Location
Fig. 15

The role of different terms of Eq. (20) on EPR when a smooth heat wave is present in the medium (Γ=1.0, Λ=2.0) based on the second-order DPL model

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