A Well-Posed Problem for the Dual-Phase-Lag Heat Conduction

2008 ◽  
Vol 31 (3) ◽  
pp. 260-269 ◽  
Author(s):  
Ramon Quintanilla
Keyword(s):  
Heat Conduction ◽  
Phase Lag ◽  
Dual Phase ◽  
Well Posed

scholarly journals Qualitative aspects in dual-phase-lag heat conduction

2006 ◽  
Vol 463 (2079) ◽  
pp. 659-674 ◽  
Author(s):  
Ramón Quintanilla ◽  
Reinhard Racke
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Uniqueness Result ◽  
Phase Lag ◽  
Dual Phase ◽  
Natural Property ◽  
Unbounded Solutions ◽  
Decay Of Solutions ◽  
Exponentially Stable ◽  
Well Posed

We investigate the equation of the dual-phase-lag heat conduction proposed by Tzou. To describe this equation, we use the phase lag of the heat flux and the phase lag of the gradient of the temperature. We analyse the basic properties of the solutions of this problem. First, we prove that when both parameters are positive, the problem is well posed and the spatial decay of solutions is controlled by an exponential of the distance. When the phase lag of the gradient of the temperature is bigger than the phase lag of the heat flux, the problem is exponentially stable (which is a natural property to expect for a heat equation) and the spatial behaviour is controlled by an exponential of the square of the distance. Also, a uniqueness result for unbounded solutions is proved in this case.

Thermoelastic damping in the size-dependent micro/nanobeam resonator with nonlocal dual-phase-lag heat conduction

2021 ◽  
Vol 169 ◽  
pp. 108437
Author(s):  
Hongyue Zhou ◽  
Haobin Jiang ◽  
Pu Li ◽  
Hongtao Xue ◽  
Billy Bo
Keyword(s):  
Heat Conduction ◽  
Phase Lag ◽  
Dual Phase ◽  
Thermoelastic Damping ◽  
Size Dependent
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