Hamilton–Jacobi and quantum theory formulations of thermal-wave propagation under the dual-phase lagging model of heat conduction

2010 ◽  
Vol 51 (2) ◽  
pp. 023506
Author(s):  
J. Ordonez-Miranda ◽  
Miguel A. Zambrano-Arjona ◽  
J. J. Alvarado-Gil
Keyword(s):  
Wave Propagation ◽  
Quantum Theory ◽  
Heat Conduction ◽  
Thermal Wave ◽  
Dual Phase

On the Wave Theory in Heat Conduction

1994 ◽  
Vol 116 (3) ◽  
pp. 526-535 ◽  
Author(s):  
M. N. O¨zis¸ik ◽  
D. Y. Tzou
Keyword(s):  
Wave Propagation ◽  
Thermal Wave ◽  
Wave Model ◽  
Wave Theory ◽  
Resonance Phenomenon ◽  
Phase Lag ◽  
Dual Phase ◽  
Material Interface ◽  
Step Model ◽  
Rate Effects

This work contains three major components: a thorough review on the research emphasizing engineering applications of the thermal wave theory, special features in thermal wave propagation, and the thermal wave model in relation to the microscopic two-step model. For the sake of convenience, the research works are classified according to their individual emphases. Special features in thermal wave propagation include the sharp wavefront and rate effects, the thermal shock phenomenon, the thermal resonance phenomenon, and reflections and refractions of thermal waves across a material interface. By employing the dual-phase-lag concept, we show that the energy equation may be reduced to that governing the heat transport through the metal lattice in the microscopic two-step model. The dual-phase-lag concept can thus capture the microscopic mechanisms in some limiting cases.

Nanofluids: Synthesis, Heat Conduction, and Extension

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
Liqiu Wang ◽  
Xiaohao Wei
Keyword(s):  
Heat Conduction ◽  
Olive Oil ◽  
Thermal Wave ◽  
Thermal Waves ◽  
Water Conductivity ◽  
Conductivity Enhancement ◽  
Chemical Solution Method ◽  
New Type ◽  
Fourier Heat Conduction ◽  
Two Phases

We synthesize eight kinds of nanofluids with controllable microstructures by a chemical solution method (CSM) and develop a theory of macroscale heat conduction in nanofluids. By the CSM, we can easily vary and manipulate nanofluid microstructures through adjusting synthesis parameters. Our theory shows that heat conduction in nanofluids is of a dual-phase-lagging type instead of the postulated and commonly used Fourier heat conduction. Due to the coupled conduction of the two phases, thermal waves and possibly resonance may appear in nanofluid heat conduction. Such waves and resonance are responsible for the conductivity enhancement. Our theory also generalizes nanofluids into thermal-wave fluids in which heat conduction can support thermal waves. We emulsify olive oil into distilled water to form a new type of thermal-wave fluids that can support much stronger thermal waves and resonance than all reported nanofluids, and consequently extraordinary water conductivity enhancement (up to 153.3%) by adding some olive oil that has a much lower conductivity than water.

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