| Summary: | 博士 === 國立中正大學 === 機械系 === 92 === With the increasing applications of lasers with ultrashort pulse duration, picosecond or femtosecond, heat transfer at short time scales has drawn many research interests. As the device size becomes comparable to the mean free path of heat transfer carrier, the microscale effect in space needs to be further accommodated. In both situations, the Fourier’s law, used for macroscale heat conduction, breaks down. To model the microscale events, various microscale heat transfer models have been proposed. However, some of these models possess unusual features, others may predict controversial results. To have a more comprehensive understanding to these issues, the present study examines two most often discussed macroscopic models, the Cattaneo-Vernotte model and the dual-phase-lag model, from the fundamental phonon Boltzmann transport equation.
In this study, several numerical schemes based on the lattice Boltzmann method are developed. With suitable modification on the source term, the macroscopic classical heat diffusion equation, hyperbolic heat conduction equation and dual-phase-lag based heat conduction equation can be obtained from the lattice Boltzmann equation. This demonstrates the ability of solving partial differential equations by the LB method. The Chapman-Enskog expansion technique has demonstrated both the classical heat conduction equation and the phonon thermal wave equation can be retrieved at the macroscopic limit from the phonon Boltzmann equation. Verification of the proposed numerical schemes is accomplished through comparing numerical values with the available results in the literature. Illustrative examples include the hyperbolic Stefan problem, energy heat transfer at interface of dissimilar materials and phonon heat conduction in a bending nanoduct.
Comparing the two wave models that are respectively based on hyperbolic heat condition and dual-phase-lag model, the present proposed lattice Boltzmann scheme demonstrate several special phenomena occurring as an pulsed thermal energy passing the interface of a two-layered structure within the frame of the dual-phase-lag model. Study of phonon heat conduction in a free standing, bent duct with characteristic dimension down to the nanoscale shows the size effect depends strongly on the Knudsen number. For large Knudsen number, transport of heat is mainly dominated by ballistic that results in strong size effect, and vice versa. Although the specular boundary scattering introduces no change in the bulk distribution for a straight duct, it, however, brings in the geometric influence as the duct is bended. Comparing to the straight duct, the bent duct has the supremacy in conducting heat as the Knudsen number is small. Conversely straight duct presents higher conductivity as Knudsen number is large.
Comparing with the dual-phase-lag based thermal wave equation, the phonon thermal wave equation obtained from the macroscopic limit of the phonon Boltzmann eqaution has an additional 4th-ordered spatial derivative term. Fundamental difference between the two models is discussed through examining a propagating thermal pulse in a single-phased medium and transient and steady-state transport phenomena on a two-layered structure. Results show transport phenomena are pretty different between the two models. Several phenomena predicted based on the dual-phase-lag model are incompatible with any microscopic phonon propagating modes. With the intrinsic compatibility to microscopic state, discontinuous quantity, such as jump of temperature at boundary or at interface, can be calculated naturally and straightforwardly by the present lattice Boltzmann method. Finally, the Cattaneo-Vernotte model is reexamined based on the Boltzmann transport equation. It is demonstrated the assumption on which the Cattaneo-Vernotte model based leads to a steady-state energy equation. This aspect might help to explain some unreal phenomena predicted by the hyperbolic heat conduction equation.
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