Multiscale Modeling Of Micro-nanoscale Thermal Conduction And Research On Phonon Hydrodynamics In Low-dimensional Materials

With the rapid development of microelectromechanical systems and nanotechnology,thermal transport at micro-nano scale has attracted extensive attention.Under the micro-nano scale condition,the classical Fourier law is no longer valid.As the main heat carrier of most semiconductors,phonon and its transport behavior play a significant role in micro-nanoscale thermal conduction.The phonon Boltzmann equation is one of the most popular theoretical models for phonon thermal conduction in finite-size micro-nano structures.Since the mean free path and relaxation time of phonons of different frequencies in materials usually differ by several orders of magnitude,phonon transport is essentially a multiscale problem.Up to now,most numerical methods for solving the phonon Boltzmann equation are single-scale methods,and the calculation parameters have to be adjusted according to the calculation conditions.In addition,most of the previous focus ballistic-diffusive conduction,and the research on phonon hydrodynamics in low-dimensional materials is not mature yet.In this thesis,we obtain analytical solutions and direct numerical solutions to phonon ballistic-hydrodynamic-diffusive transport problem,and study steady-state and transient phonon hydrodynamic conduction in low-dimensional materials,including steady-state phenomena(e.g.phonon Poiseuille flow,super-ballistic effect,heat vortex and negative nonlocal effect,etc)and transient phenomenon(second sound effect and its dynamics).Phonon ballistic-diffusive conduction can be described by the phonon Boltzmann equation under single-mode relaxation time approximation.In this thesis,we first improve the traditional discrete ordinate method(DOM)for the phonon Boltzmann equation and develop a DOM with streaming and collision processes for gray transport model.Furthermore,a discrete unified gas kinetic scheme accounting for phonon frequency and polarization is also developed.Compared to traditional numerical methods,these two multiscale methods have asympotic-preserving property and release the limitation of phonon relaxation time to the time step,and also can accurately capture the heat transfer characteristics in different transport regimes.Phonon ballistic-hydrodynamic-diffusive conduction can be described by the phonon Boltzmann equation under Callaway's dual relaxation model.For phonon hydrodynamic heat conduction in simple geometry,we derive analytical solutions for in-plane and cross-plane phonon hydrodynamic conduction and steady-state thermal grating.These analytical solutions are compatible with 2D materials and 3D materials.With analytical method,we discuss the phonon Knudsen minimum in in-plane heat conduction,nonlinear effect of temperature distribution in cross-plane heat conduction and super-ballistic effect in steady-state thermal grating.To solve phonon hydrodynamic conduction in complex cases,we develop a discrete unified gas kinetic scheme for the transient phonon Boltzmann equation under Callaway's dual relaxation model.The proposed method is self-consistent in solving thermal conduction in ballistic regime,diffusive regime,hydrodynamic regime and their transitions with fixed mesh size and time step.By direct numerical modeling,we study thermal wave(second sound)in low-dimensional materials.We find that ambient temperature,isotopic abundance and size of graphene ribbon have important influence on the dynamic properties of second sound.Phonon resistive scattering reduce the second sound speed up to 20% within the window condition of second sound.Finally,we study the phonon hydrodynamic conduction in finite-size micro-nano structures by directly solving the steady-state phonon Boltzmann equation under Callaway's dual relaxation model and find a number of new and counterintuitive phenomena including heat vortex and negative nonlocal thermal response in both rectangular ribbon and porous ribbon of graphene.In addition,we reveal the effect of ambient temperature,isotopic abundance and geometrical parameters on heat vortex and negative nonlocal thermal response.The multiscale numerical method and the analytical method for phonon transport developed in this thesis provide an efficient,reliable and powerful theoretical tool for the future study of phonon thermal conductio n.On the other hand,the research results in this thesis also provide theoretical guidance and support in both the future experimental detection of phonon hydrodynamic phenomena and micro-nano scale thermal design and management in electronic devices.