Chuang Zhang

• Department of Physics
• Professor (Associate) at Hangzhou Dianzi University

Many phonon hydrodynamics phenomena, including heat vortices, wave and parabolic distributions of heat flux, which appear due to sufficient normal process, can also appear when there is insufficient normal process. In other words, a smoking gun of phonon hydrodynamics phenomena at the macroscopic level is still lacking. To find it, transient coolin...

In this paper, a multiscale boundary condition for the discrete unified gas kinetic scheme (DUGKS) is developed for gas flows in all flow regimes. Based on the discrete Maxwell boundary condition (DMBC), this study addresses the limitations of the original DMBC used in DUGKS. Specifically, it is found that the DMBC produces spurious velocity slip a...

Fast and accurate predictions of the spatiotemporal distributions of temperature are crucial to the multi-scale thermal management and safe operation of microelectronic devices. To realize it, an efficient semi-implicit Lax-Wendroff kinetic scheme is developed for numerically solving the transient phonon Boltzmann transport equation (BTE) from the...

Hydrodynamic second sound can be generated by heat pulses when the phonon-phonon interaction is dominantly momentum conserving, and the propagation of the temperature field becomes wavelike rather than diffusive. While the Boltzmann transport equation (BTE) has been widely applied to study phonon dynamics and thermal transport at the nanoscale, mod...

The phonon Boltzmann transport equation (BTE) is widely used for describing multiscale heat conduction (from nm to $\mu$m or mm) in solid materials. Developing numerical approaches to solve this equation is challenging since it is a 7-dimensional integral-differential equation. In this work, we propose Monte Carlo physics-informed neural networks (...

Efficiently capturing the three-dimensional spatiotemporal distributions of temperature is of great significance for alleviating hotspot issues in 3D FinFETs. However, most previous thermal simulations mainly focused on the steady-state problem with continuous heating. Few studies are conducted for the transient thermal conduction in 3D FinFETs wi...

Many macroscopic non-Fourier heat conduction models have been developed in the past decades based on Chapman-Enskog, Hermite, or other small perturbation expansion methods. These macroscopic models have achieved great success in capturing non-Fourier thermal behaviors in solid materials, but most of them are limited by small Knudsen numbers and inc...

Electrons are the carriers of heat and electricity in materials and exhibit abundant transport phenomena such as ballistic, diffusive, and hydrodynamic behaviors in systems with different sizes. The electron Boltzmann transport equation (eBTE) is a reliable model for describing electron transport, but it is a challenging problem to efficiently obta...

A synthetic iterative scheme is developed for thermal applications in hotspot systems with large temperature variance. Different from previous work with linearized equilibrium state and small temperature difference assumption, the phonon equilibrium distribution shows a nonlinear relationship with temperature and mean free path changes with the spa...

Electrons are the carriers of heat and electricity in materials, and exhibit abundant transport phenomena such as ballistic, diffusive, and hydrodynamic behaviors in systems with different sizes. The electron Boltzmann transport equation (eBTE) is a reliable model for describing electron transport, but it is a challenging problem to efficiently obt...

The electron-phonon coupling in ultrafast heating systems is studied within the framework of Boltzmann transport equation (BTE) with coupled electron and phonon transport. To directly solve the BTE, a discrete unified gas kinetic scheme is developed, in which the electron/phonon advection, scattering and electron-phonon interactions are coupled tog...

流体是自然界中十分常见的一种物质。从物理层面上看，它是由大量的粒子构成的一个离散系统。基于不同的观察尺度，流体系统可以分为微观分子模型、介观动理学模型和宏观连续模型。其中，介观动理学模型是描述非平衡态流动的基本控制方程。它通过描述微观分布函数的演化过程，来从中获得宏观流动的物理信息。基于这种模型，许多很好的介观方法，诸如Unified Gas Kinetic Scheme（UGKS），Discrete Unified Gas Kinetic Scheme（DUGKS），在非平衡态流动、跨流域流动的研究中被成功应用。但是，在模拟非平衡态流动中，粒子速度空间的离散加大了对计算机内存的要求。基于目前的计算机配置，应用这些方法去模拟大型的复杂的多尺度、跨流域问题依然是一个巨大的挑战。 针对当前计算机...

The graded thermal conductivity in nanoscale "hot spot" systems is a new phenomenon in nanoscale heat conduction. Graded thermal conductivity, that is, in the nano "hot spot" system, it is found that the thermal conductivity is no longer uniform, and the thermal conductivity gradually increases from the inside to the outside in the radial direction...

Many macroscopic non-Fourier heat conduction models have been developed in the past decades based on Chapman-Enskog, Hermite or other small perturbation expansion methods. These macroscopic models have made great success on capturing non-Fourier thermal behaviors in solid materials, but most of them are limited by small Knudsen numbers and incapabl...

In this work, a steady discrete unified gas kinetic scheme (SDUGKS) is proposed to solve the steady radiative transfer equation (RTE), which is an improvement of the original SDUGKS [X. F. Zhou et al., J. Comput. Phys. 423, 109767 (2020)]. The trapezoidal rule other than the rectangular rule used in the original SDUGKS is adopted in the proposed me...

The propagation of heat in the transient thermal grating geometry is studied based on the phonon Boltzmann transport equation (BTE) in different phonon transport regimes. Our analytical and numerical results show that the phonon dispersion relation and temperature govern the emergence of heat waves. For the frequency-independent BTE, a heat wave ma...

Transient heat dissipation in close-packed quasi-two-dimensional nanoline and three-dimensional nanocuboid hotspot systems is studied based on the phonon Boltzmann transport equation. It is found that, counterintuitively, the heat dissipation efficiency is not a monotonic function of the distance between adjacent nanoscale heat sources but reaches...

The phonon Boltzmann transport equation with dual relaxation times is often used to describe the heat conduction in semiconductor materials when the classical Fourier's law is no longer valid. For practical engineering designs, accurate and efficient numerical methods are highly demanded to solve the equation efficiently and accurately. At a large...

We revisit the recent work from Beardo et al. \cite{beardo2021observation} wherein the observation of second sound in germanium is claimed. We review the requirements imposed on the collision operator (or equivalently, the full scattering matrix) of the linearized phonon Boltzmann transport equation (LBTE) for the observation of driftless second so...

This paper is a continuation of our work on the transient hydrodynamic phonon transport from three-dimensional to two-dimensional materials. In the previous work [Zhang \textit{et al.}, Int. J. Heat Mass Transfer 181, 121847 (2021)], a transient heat conduction phenomenon proving the existence and uniqueness of hydrodynamic phonon transport in thre...

Transient heat dissipation in close-packed quasi-2D nanoline and 3D nanocuboid hotspot systems is studied based on phonon Boltzmann transport equation. Different from previous intuitive understanding of micro/nano scale heat conduction, it is found that the heat dissipation efficiency is not monotonic when the distance between adjacent nanoscale he...

The propagation of heat in the transient thermal grating geometry is studied based on phonon Boltzmann transport equation (BTE) in different phonon transport regimes. Our analytical and numerical results show that the phonon dispersion relation and temperature play a significant role in the emergence of heat wave. For the frequency-independent BTE,...

Hotspot is a ubiquitous phenomenon in micro/nanoscale chips. Here, it is found that the thermal conductivity is not a constant in such a homogeneous system. The hotspots in homogeneous 2D disk/3D sphere and graphene disk are studied based on phonon Boltzmann transport equation. Instead a constant value, a graded thermal conductivity is observed eve...

Previous studies have predicted the failure of Fourier’s law of thermal conduction due to the existence of wave like propagation of heat with finite propagation speed. This non-Fourier thermal transport phenomenon can appear in both the hydrodynamic and (quasi) ballistic regimes. Hence, it is not easy to clearly distinguish these two non-Fourier re...

Heat conduction in solid materials may behave like fluid dynamics when normal (N) scattering dominates phonon transport. In this hydrodynamic regime, the heat vortices have been predicted with frequency-independent relaxation time. So can this phenomena appear in other regimes? And what are the differences? In order to answer these questions, in th...

The heat transfer in solid materials at the micro- and nano-scale can be described by the mesoscopic phonon Boltzmann transport equation (BTE), rather than the macroscopic Fourier’s heat conduction equation that works only in the diffusive regime. The implicit discrete ordinate method (DOM) is efficient to find steady-state solutions to the BTE for...

随着电子产品的几何尺寸不断减小和封装集成度逐渐增加，器件的功率密度急剧上升，热管理成为一个巨大的挑战。 在微纳尺度下的散热原理与在宏观尺度下存在巨大的差异，经典的傅里叶导热定律不再适用，因此理解微纳尺度下的热输运现象及机理变得尤为重要。 目前已发现大量非傅里叶导热现象，例如声子水动力学、尺寸效应、热整流、声子局域化等。 为研究非傅里叶导热问题，许多物理模型和方法得到了充分发展，其中玻尔兹曼输运方程（Boltzmann transport equation，BTE）在多个时间和空间尺度上均成立，可以描述微纳尺度下的热输运现象，因此成为研究非傅里叶导热问题一个重要的工具。 本文以声子BTE为主，首先提出了一种求解该稳态方程的高效的介观数值方法，然后应用该方法并结合理论分析，研究了热流涡、梯度热导...

Many studies have predicted the failure of Fourier's law of thermal conduction due to the existence of wave like propagation of heat with finite propagation speed. This non-Fourier thermal transport phenomenon can appear in both the hydrodynamic and (quasi) ballistic regimes. Hence, it is not easy to clearly distinguish these two non-Fourier regime...

Abstract In this work, a discrete unified gas kinetic scheme (DUGKS) is developed for radiative transfer in anisotropic scattering media. The method is an extension of a previous one for isotropic radiation problems [1]. The present scheme is a finite-volume discretization of the anisotropic gray radiation equation, where the anisotropic scattering...

In this paper, a perturbation theory of thermal rectification is developed for a thermal system where an effective thermal conductivity throughout the system can be identified and changes smoothly and slightly. This theory provides an analytical formula of the thermal rectification ratio with rigorous mathematical derivations and physical assumptio...

In this work, the heat vortexes in two-dimensional porous or ribbon structures are investigated based on the phonon Boltzmann transport equation (BTE) under the Callaway model. First, the separate thermal effects of normal (N) scattering and resistive (R) scattering are investigated with frequency-independent assumptions. And then the heat vortexes...

Hotspot is a ubiquitous phenomenon in microdevices/chips. In homogeneous nanoscale graphene disk with a hotspot, a graded thermal conductivity is observed previously even when the system size is fixed. However, the underlying physical mechanism is not clear. In this work, the hotspots in homogeneous 2D disk/3D ball and graphene disk are studied bas...

Hotspot is a ubiquitous phenomenon in microdevices/chips. In homogeneous nanoscale graphene disk with a hotspot, a graded thermal conductivity is observed previously even when the system size is fixed. However, the underlying physical mechanism is not clear. In this work, the hotspots in homogeneous 2D disk/3D ball and graphene disk are studied bas...

Thermal rectification which is a diode-like behavior of heat flux has been studied over a long time. However, a universal and systematic physical description is still lacking. {\color{red}{In this letter, a perturbation theory of thermal rectification is developed, which provides an analytical formula of the thermal rectification ratio. It reveals...

In this work, the radial thermal rectification in concentric silicon ring is studied based on the phonon Boltzmann transport equation. In the ballistic and diffusive limits, the analytical solutions reveal no thermal rectification. In the ballistic-diffusive regime, numerical results show that the thermal conductivity is a nonseparable function of...

We study hydrodynamic phonon heat transport in two-dimensional (2D) materials. Starting from the Peierls-Boltzmann equation with the Callaway model approximation, we derive a 2D Guyer-Krumhansl-like equation describing hydrodynamic phonon transport, taking into account the quadratic dispersion of flexural phonons. In addition to Poiseuille flow, se...

The radial thermal rectification in the concentric silicon ring from ballistic to diffusive regime is investigated based on the phonon Boltzmann transport equation. In the ballistic and diffusive limits, the analytical solutions prove that there is no thermal rectification. In the ballistic-diffusive regime, the heat flux prefers to flow from the i...

A novel non-homogeneous or graded thermal conductivity along the radius direction in a single graphene disk structure has been predicted in previous study by using classical non-equilibrium molecular dynamics method. However, the size of the simulated system was only up to 25 nm due to the limitation of computational method. So whether the graded t...

In this paper, a finite-volume discrete unified gas kinetic scheme (DUGKS) based on the non-gray phonon transport model is developed for multiscale heat transfer problem with arbitrary temperature difference. Under large temperature difference, the phonon Boltzmann transport equation (BTE) is essentially multiscale, not only in the frequency space,...

An efficient implicit kinetic scheme is developed to solve the stationary phonon Boltzmann transport equation (BTE) based on the non-gray model with the consideration of phonon dispersion and polarization. Due to the wide range of the dispersed phonon mean free paths, the phonon transport under the non-gray model is essentially multiscale, and has...

The heat transfer in solid materials at the micro-and nano-scale can be described by the mesoscopic phonon Boltzmann transport equation (BTE), rather than the macroscopic Fourier's heat conduction equation that works only in the diffusive regime. The implicit discrete ordinate method (DOM) is efficient to find the steady-state solutions of the BTE...

In this paper, a fast synthetic iterative scheme is developed to accelerate convergence for the implicit DOM based on the stationary phonon BTE. The key innovative point of the present scheme is the introduction of the macroscopic synthetic diffusion equation for the temperature, which is obtained from the zero- and first-order moment equations of...

In this paper, a finite-volume discrete unified gas kinetic scheme (DUGKS) based on the non-gray phonon transport model is developed for multiscale heat transfer problem with arbitrary temperature difference. Under large temperature difference, the phonon Boltzmann transport equation (BTE) is essentially multiscale, not only in the frequency space,...

An efficient implicit kinetic scheme is developed to solve the stationary phonon Boltzmann transport equation (BTE) based on the non-gray model including the phonon dispersion and polarization. Due to the wide range of the dispersed phonon mean free paths, the phonon transport under the non-gray model is essentially multiscale, and has to be solved...

An implicit kinetic scheme is proposed to solve the stationary phonon Boltzmann transport equation (BTE) for multiscale heat transfer problem. Compared to the conventional discrete ordinate method, the present method employs a macroscopic equation to accelerate the convergence in the diffusive regime. The macroscopic equation can be taken as a mome...

A memory reduction technique is proposed for solving stationary kinetic model equations. As implied by an integral solution of the stationary kinetic equation, a velocity distribution function can be reconstructed from given macroscopic variables. Based on this fact, we propose a technique to reconstruct distribution function at discrete level, and...