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Liqiu Wang - One of the best experts on this subject based on the ideXlab platform.
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thermal wave interference as the origin of the overshooting phenomenon in dual phase lagging Heat Conduction
2011Co-Authors: Jiangfeng Guo, Liqiu Wang, Lin ChengAbstract:In the present work, the overshooting phenomenon is investigated based on the one-dimensional dual-phase-lagging Heat Conduction model. The thermal wave interference is found to trigger the overshooting of temperature field. A condition for the occurrence of overshooting phenomenon is established for the one-dimensional dual-phase-lagging Heat Conduction in a finite medium. According to this condition, the overshooting phenomenon may occur in Heat Conduction across gold films with the thickness ranging from 4.8555 nm to 19.581 μm.
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from boltzmann transport equation to single phase lagging Heat Conduction
2008Co-Authors: Lin Cheng, Liqiu WangAbstract:Abstract In the present work the single-phase-lagging Heat Conduction model is re-derived analytically from the Boltzmann transport equation. In contrast to the Maxwell–Cattaneo law (CV model), it is Galilean invariant in the moving media. Based on this model, the governing equation of the microscale Heat Conduction is established, which is formulated into a delay partial differential equation. The corresponding initial and boundary conditions are prescribed. The thermal oscillation of the single-phase-lagging Heat Conduction is investigated.
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Heat Conduction mathematical models and analytical solutions
2008Co-Authors: Liqiu Wang, Xuesheng Zhou, Xiaohao WeiAbstract:Wave Equations.- Heat-Conduction Equations.- Mixed Problems of Hyperbolic Heat-Conduction Equations.- Cauchy Problems of Hyperbolic Heat-Conduction Equations.- Dual-Phase-Lagging Heat-Conduction Equations.- Potential Equations.
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dual phase lagging Heat Conduction based on boltzmann transport equation
2005Co-Authors: Liqiu WangAbstract:Abstract In this work, the dual-phase-lagging model of the microscale Heat Conduction is re-derived analytically from the Boltzmann transport equation. Based on this model, the delay/advanced partial differential equations governing the microscale Heat Conduction are established. The method of separation of variables is applied to solve such delay/advanced partial differential equations. Finally, the oscillation of the microscale Heat Conduction is investigated.
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well posedness of dual phase lagging Heat Conduction equation higher dimensions
2002Co-Authors: Liqiu WangAbstract:Abstract The dual-phase-lagging Heat Conduction equation is shown to be of one unique solution for a finite region of dimension n ( n ⩾2) under Dirichlet, Neumann or Robin boundary conditions. The solution is also found to be stable with respect to initial conditions. The work is of fundamental importance in applying the dual-phase-lagging model for the microscale Heat Conduction of high-rate Heat flux.
Lin Cheng - One of the best experts on this subject based on the ideXlab platform.
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thermal wave interference as the origin of the overshooting phenomenon in dual phase lagging Heat Conduction
2011Co-Authors: Jiangfeng Guo, Liqiu Wang, Lin ChengAbstract:In the present work, the overshooting phenomenon is investigated based on the one-dimensional dual-phase-lagging Heat Conduction model. The thermal wave interference is found to trigger the overshooting of temperature field. A condition for the occurrence of overshooting phenomenon is established for the one-dimensional dual-phase-lagging Heat Conduction in a finite medium. According to this condition, the overshooting phenomenon may occur in Heat Conduction across gold films with the thickness ranging from 4.8555 nm to 19.581 μm.
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from boltzmann transport equation to single phase lagging Heat Conduction
2008Co-Authors: Lin Cheng, Liqiu WangAbstract:Abstract In the present work the single-phase-lagging Heat Conduction model is re-derived analytically from the Boltzmann transport equation. In contrast to the Maxwell–Cattaneo law (CV model), it is Galilean invariant in the moving media. Based on this model, the governing equation of the microscale Heat Conduction is established, which is formulated into a delay partial differential equation. The corresponding initial and boundary conditions are prescribed. The thermal oscillation of the single-phase-lagging Heat Conduction is investigated.
Gang Chen - One of the best experts on this subject based on the ideXlab platform.
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effects of aperiodicity and roughness on coherent Heat Conduction in superlattices
2015Co-Authors: Bo Qiu, Gang Chen, Zhiting TianAbstract:Coherent phonon Heat Conduction has recently been confirmed experimentally in superlattice structures. Such traveling coherent phonon waves in superlattices lead to a linear increase in thermal conductivity as the number of periods increases. For applications such as thermal insulation or thermoelectrics, minimization of the phonon coherent effect is desirable. In this work, we use molecular dynamics simulations to study how to control coherent Heat Conduction in superlattices (SLs). It is found that either aperiodic SLs or SLs with rough interfaces can significantly disrupt coherent Heat Conduction when the interface densities are high. For sample thickness less than 125 nm, aperiodic SLs with perfect interfaces are found to have the lowest thermal conductivity. We use the atomic Green’s function method to examine the phonon dynamics. The impact of either aperiodicity or interface roughness is attributed to reduced transmittance. Such impact diminishes as the interface density reduces.
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disparate quasiballistic Heat Conduction regimes from periodic Heat sources on a substrate
2014Co-Authors: Lingping Zeng, Gang ChenAbstract:We report disparate quasiballistic Heat Conduction trends for periodic nanoscale line Heaters deposited on a substrate, depending upon whether measurements are based on the peak temperature of the Heaters or the temperature difference between the peak and the valley of two neighboring Heaters. The degree of quasiballistic transport is characterized by the effective thermal conductivities of the substrate which are obtained by matching the diffusion solutions to the phonon Boltzmann transport equation results. We find that while the ballistic Heat Conduction effect based on the peak temperature diminishes as the two Heaters become closer, it becomes stronger based on the peak-valley temperature difference. Our results also show that the collective behavior of closely spaced Heaters can counteract the nonlocal effects caused by an isolated nanoscale hot spot. These results are relevant to thermal conductivity spectroscopy techniques under development and also have important implications for understanding nonlocal Heat Conduction in integrated circuits and carbon nanotube array thermal interface materials.
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disparate quasiballistic Heat Conduction regimes from periodic Heat sources on a substrate
2014Co-Authors: Lingping Zeng, Gang ChenAbstract:We report disparate quasiballistic Heat Conduction trends for periodic nanoscale line Heaters deposited on a substrate, depending upon whether measurements are based on the peak temperature of the Heaters or the temperature difference between the peak and the valley of two neighboring Heaters. The degree of quasiballistic transport is characterized by the effective thermal conductivities of the substrate which are obtained by matching the diffusion solutions to the phonon Boltzmann transport equation (BTE) results. We find that while the ballistic Heat Conduction effect based on the peak temperature diminishes as the two Heaters become closer, it becomes stronger based on the peak-valley temperature difference. Our results also show that the collective behavior of closely spaced Heaters can counteract the nonlocal effects caused by an isolated nanoscale hot spot. These results are relevant to thermal conductivity spectroscopy techniques under a) To whom correspondence should be addressed. Electronic mail: gchen2@mit.edu 2 development and also have important implications for understanding nonlocal Heat Conduction in integrated circuits and carbon nanotube array thermal interface materials.
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simulation of nanoscale multidimensional transient Heat Conduction problems using ballistic diffusive equations and phonon boltzmann equation
2005Co-Authors: Ronggui Yang, Gang Chen, Marine Laroche, Yuan TaurAbstract:Heat Conduction. in micro- and nanoscale and in ultrafast processes may deviate from the predictions of the Fourier law, due to boundary and interface scattering, the ballistic nature of the transport, and the finite relaxation time of Heat carriers. The transient ballistic-diffusive Heat Conduction equations (BDE) were developed as an approximation to the phonon Boltzmann equation (BTE) for nanoscale Heat Conduction problems. In this paper, we further develop BDE for multidimensional Heat Conduction, including nanoscale Heat source term and different boundary conditions, and compare the simulation results with those obtained from the phonon BTE and the Fourier law. The numerical solution strategies for multidimensional nanoscale Heat Conduction using BDE are presented. Several two-dimensional cases are simulated and compared to the results of the transient phonon BTE and the Fourier Heat Conduction theory. The transient BTE is solved using the discrete ordinates method with a two Gauss-Legendre quadratures. Special attention has been paid to the boundary conditions. Compared to the cases without internal Heat generation, the difference between the BTE and BDE is larger for the case studied with internal Heat generation due to the nature of the ballistic-diffusive approximation, but the results from BDE are still significantly better than those from the Fourier law. Thus we conclude that BDE captures the characteristics of the phonon BTE with much shorter computational time.
J J Alvaradogil - One of the best experts on this subject based on the ideXlab platform.
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a constitutive equation for nano to macro scale Heat Conduction based on the boltzmann transport equation
2011Co-Authors: Jose Ordonezmiranda, Ronggui Yang, J J AlvaradogilAbstract:A constitutive equation for Heat Conduction is derived from the exact solution of the Boltzmann transport equation under the relaxation time approximation. This is achieved by a series expansion on multiple space derivatives of the temperature and introducing the concept of thermal multipoles, where the thermal conductivity defined under the framework of the Fourier law of Heat Conduction is just the first thermal pole. It is shown that this equation generalizes the Fourier law and Cattaneo equation of Heat Conduction, and it depends strongly on the relative values of the length and time scales compared with the mean-free path and mean-free time of the energy carriers, respectively. In the limiting case of steady-state Heat Conduction, it is shown that the Heat flux vector depends on a spatial scale ratio whose effects are remarkable in the micro-scale spatial domains. By applying a first-order approximation of the obtained thermal multipole expansion to the problem of transient Heat Conduction across a t...
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a constitutive equation for nano to macro scale Heat Conduction based on the boltzmann transport equation
2011Co-Authors: Jose Ordonezmiranda, Ronggui Yang, J J AlvaradogilAbstract:A constitutive equation for Heat Conduction is derived from the exact solution of the Boltzmann transport equation under the relaxation time approximation. This is achieved by a series expansion on multiple space derivatives of the temperature and introducing the concept of thermal multipoles, where the thermal conductivity defined under the framework of the Fourier law of Heat Conduction is just the first thermal pole. It is shown that this equation generalizes the Fourier law and Cattaneo equation of Heat Conduction, and it depends strongly on the relative values of the length and time scales compared with the mean-free path and mean-free time of the energy carriers, respectively. In the limiting case of steady-state Heat Conduction, it is shown that the Heat flux vector depends on a spatial scale ratio whose effects are remarkable in the micro-scale spatial domains. By applying a first-order approximation of the obtained thermal multipole expansion to the problem of transient Heat Conduction across a thin film and comparing the results with the predictions for the same problem using the Fourier, Cattaneo and Boltzmann transport equations, it is shown that our results could be useful in the study of the Heat transport in short as well as in long scales of space and time. The common and different features of the multipole expansion compared with the Ballistic-diffusive model of Heat Conduction are also discussed. Special emphasis is put to the cases where the physical scales of space and time are comparable to the mean-free path and mean-free time of the energy carriers.
Bingyang Cao - One of the best experts on this subject based on the ideXlab platform.
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fractional order Heat Conduction models from generalized boltzmann transport equation
2020Co-Authors: Bingyang CaoAbstract:The relationship between fractional-order Heat Conduction models and Boltzmann transport equations (BTEs) lacks a detailed investigation. In this paper, the continuity, constitutive and governing e...
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generalized variational principles for Heat Conduction models based on laplace transforms
2016Co-Authors: Bingyang CaoAbstract:Abstract The classical variational principle does not exist for parabolic and hyperbolic Heat Conduction equations, which has led to the demand for special variational methods for Heat Conduction. O’Toole (1967) first used Laplace transforms for the variational principle only for Fourier’s law with the first type of boundary condition. In this paper, the Laplace transform strategy is extended to other parabolic and hyperbolic Heat Conduction models and other types of boundary conditions. Generalized variational principles are given for Heat Conduction models including Fourier’s law, the Cattaneo–Vernotte (CV) model, the Jeffrey model, the two-temperature model and the Guyer–Krumhansl (GK) model, based on Laplace transforms. The Laplace transform method transforms the Heat Conduction equations of these models into linear variational equations whose variational principles are already known. For the three standard types of boundary conditions, these generalized variational principles are strictly equivalent to the Heat Conduction equations for these models. The Laplace transform method has stronger convergence in infinite temporal domain problems. In physics, the Laplace transform method is understood as replacing the time dimension with the frequency of the temperature change and the rate of the entropy change.
