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

2018 ◽  
Vol 140 (8) ◽  
Author(s):  
Hossein Askarizadeh ◽  
Hossein Ahmadikia
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Heat Flow ◽  
Irreversible Thermodynamics ◽  
High Order ◽  
Second Law ◽  
Phase Lag ◽  
Dual Phase ◽  
Heat Transfer Equation ◽  
Extended Irreversible Thermodynamics

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.

scholarly journals Analysis of the dual phase lag bio-heat transfer equation with constant and time-dependent heat flux conditions on skin surface

2016 ◽  
Vol 20 (5) ◽  
pp. 1457-1472 ◽  
Author(s):  
Poor Ziaei ◽  
Hassan Moosavi ◽  
Amir Moradi
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Thermal Wave ◽  
Transfer Equation ◽  
Skin Surface ◽  
Time Dependent ◽  
Skin Tissue ◽  
High Heat Flux ◽  
Phase Lag ◽  
Heat Transfer Equation

This article focuses on temperature response of skin tissue due to time-dependent surface heat fluxes. Analytical solution is constructed for DPL bio-heat transfer equation with constant, periodic and pulse train heat flux conditions on skin surface. Separation of variables and Duhamel?s theorem for a skin tissue as a finite domain are employed. The transient temperature responses for constant and time-dependent boundary conditions are obtained and discussed. The results show that there is major discrepancy between the predicted temperature of parabolic (Pennes bio-heat transfer), hyperbolic (thermal wave) and DPL bio-heat transfer models when high heat flux accidents on the skin surface with a short duration or propagation speed of thermal wave is finite. The results illustrate that the DPL model reduces to the hyperbolic model when ?T approaches zero and the classic Fourier model when both thermal relaxations approach zero. However for ?q = ?T the DPL model anticipates different temperature distribution with that predicted by the Pennes model. Such discrepancy is due to the blood perfusion term in energy equation. It is in contrast to results from the literature for pure conduction material, where the DPL model approaches the Fourier heat conduction model when ?q = ?T . The burn injury is also investigated.

Thermodynamic Basis of Dual-Phase-Lagging Heat Conduction

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
Mingtian Xu
Keyword(s):  
Heat Conduction ◽  
Local Equilibrium ◽  
Second Law Of Thermodynamics ◽  
Maxwell Model ◽  
Irreversible Thermodynamics ◽  
Second Law ◽  
Dual Phase ◽  
Conduction Model ◽  
Extended Irreversible Thermodynamics ◽  
Thermodynamic Basis

The thermal vibration phenomenon occurring in the dual-phase-lagging heat conduction violates the second law of thermodynamics under the local equilibrium assumption. In order to resolve this paradox, two types of the extended irreversible thermodynamics are developed in the present work, which make the dual-phase-lagging heat conduction model compatible with the second law of thermodynamics. It is also shown that these extended irreversible thermodynamics can give rise to the Maxwell model for the viscoelastic fluid flow.

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