scholarly journals Thermodynamical consistency of the dual-phase-lag heat conduction equation

2017 ◽  
Vol 30 (6) ◽  
pp. 1223-1230 ◽  
Author(s):  
Róbert Kovács ◽  
Péter Ván
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Equation ◽  
Conduction Equation ◽  
Phase Lag ◽  
Dual Phase ◽  
Thermodynamical Consistency

Time fractional dual-phase-lag heat conduction equation

2015 ◽  
Vol 24 (3) ◽  
pp. 034401 ◽  
Author(s):  
Huan-Ying Xu ◽  
Xiao-Yun Jiang
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Equation ◽  
Conduction Equation ◽  
Phase Lag ◽  
Dual Phase

Assessment of Models for Extracting Thermal Conductivity From Frequency Domain Thermoreflectance Experiments

2020 ◽  
Author(s):  
Siddharth Saurav ◽  
Sandip Mazumder
Keyword(s):  
Thermal Conductivity ◽  
Heat Conduction ◽  
Boundary Conditions ◽  
Frequency Domain ◽  
Heat Conduction Equation ◽  
Conduction Equation ◽  
Hyperbolic Heat Conduction ◽  
Phase Lag ◽  
Computational Domain ◽  
Fourier Heat Conduction

Abstract The Fourier heat conduction and the hyperbolic heat conduction equations were solved numerically to simulate a frequency-domain thermoreflectance (FDTR) experimental setup. Numerical solutions enable use of realistic boundary conditions, such as convective cooling from the various surfaces of the substrate and transducer. The equations were solved in time domain and the phase lag between the temperature at the center of the transducer and the modulated pump laser signal were computed for a modulation frequency range of 200 kHz to 200 MHz. It was found that the numerical predictions fit the experimentally measured phase lag better than analytical frequency-domain solutions of the Fourier heat equation based on Hankel transforms. The effects of boundary conditions were investigated and it was found that if the substrate (computational domain) is sufficiently large, the far-field boundary conditions have no effect on the computed phase lag. The interface conductance between the transducer and the substrate was also treated as a parameter, and was found to have some effect on the predicted thermal conductivity, but only in certain regimes. The hyperbolic heat conduction equation yielded identical results as the Fourier heat conduction equation for the particular case studied. The thermal conductivity value (best fit) for the silicon substrate considered in this study was found to be 108 W/m/K, which is slightly different from previously reported values for the same experimental data.

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