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Numerical study of dual-phase-lag heat conduction in a thermal barrier coating with a hybrid method

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Abstract

In this study, the dual-phase-lag (DPL) heat conduction model is applied to study the non-Fourier heat transfer in a thermal barrier coating (TBC) structure subjected to heat flux on the exterior of the coating. An efficient numerical scheme involving the hybrid application of the Laplace transform and control volume methods in conjunction with hyperbolic shape functions is used to solve the hyperbolic heat conduction equations in the linearized form of DPL model. The transformed nodal temperatures are inverted to the physical quantities using numerical inversion of the Laplace transform. Parametric studies of properties of the substrate and the coating on the temperature distributions in the TBC are performed. A comparison between the present study and other work in the literature using the thermal wave model is also made. The results also show that the phase lag of heat flux tends to induce thermal waves with sharp wave fronts separating heated and unheated zones in the structure, while the phase lag of temperature gradient results in non-Fourier diffusion-like conduction and smooths the sharp wave fronts by promoting conduction into the medium.

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Abbreviations

c :

Specific heat (J kg−1 K−1)

k :

Thermal conductivity (W m−1 K−1)

\(L_{1}\) :

Domain extent for the substrate (m)

\(L_{2}\) :

Domain extent for the TBC (m)

l :

Dimensionless distance between two neighboring nodes

m :

Node number at the interface

Q :

Dimensionless heat flux defined in Eq. (14)

q :

Heat flux (W m−2)

R :

Ratio of thermophysical properties between the substrate and the TBC

r :

Position vector (m)

s :

Laplace transform parameter

T :

Temperature (K)

\(T_{c}\) :

Isothermal boundary condition at the substrate (K)

\(T_{R}\) :

Reference temperature (K)

\(T_{0}\) :

Initial temperature (K)

t :

Time (s)

u :

Step function

x :

x-Coordinate (m)

\(\alpha\) :

Thermal diffusivity (m2 s−1)

\(\eta\) :

Dimensionless distance defined in Eq. (14)

\(\theta\) :

Dimensionless temperature defined in Eq. (14)

\(\lambda\) :

Parameter defined in Eq. (26)

\(\rho\) :

Density (kg m−3)

\(\xi\) :

Dimensionless time defined in Eq. (14)

\(\xi_{d}\) :

Dimensionless time of exposure of heat flux on TBC

\(\tau_{q}\) :

Phase lag of the heat flux (s)

\(\tau_{T}\) :

Phase lag of the temperature gradient (s)

i :

Node index

j :

Domain index

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Acknowledgments

This work was supported by the Ministry of Science and Technology, Taiwan, Republic of China, under the Grant Number MOST 103-2221-E-168-004.

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Authors and Affiliations

  1. Clean Energy Center, Department of Mechanical Engineering, Kun Shan University, No. 195, Kun-Da Rd., Yung-Kang Dist., Tainan, 710-03, Taiwan, Republic of China

    Yu-Ching Yang, Wen-Lih Chen, Tzu-Sheng Yeh, Win-Jin Chang & Haw-Long Lee

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  1. Yu-Ching Yang
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  2. Wen-Lih Chen
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  3. Tzu-Sheng Yeh
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  4. Win-Jin Chang
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  5. Haw-Long Lee
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Correspondence to Haw-Long Lee.

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Technical Editor: Francis HR Franca.

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Yang, YC., Chen, WL., Yeh, TS. et al. Numerical study of dual-phase-lag heat conduction in a thermal barrier coating with a hybrid method. J Braz. Soc. Mech. Sci. Eng. 38, 287–296 (2016). https://doi.org/10.1007/s40430-015-0412-7

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  • DOI: https://doi.org/10.1007/s40430-015-0412-7

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