| With the decreasing of the geometrical size of the electronic products and the gradual increase of packaging integration,the power density of devices increases dramatically,and thermal management becomes a huge challenge.There is a huge difference between the principle of heat dissipation at micro/nano scale and that at macro scale,and the classical Fourier's law of thermal conduction is no longer applicable.Therefore,it is important to understand the thermal transport phenomena and mechanisms at micro/nano scale.At present,a large number of non-Fourier heat conduction phenomena have been found,such as phonon hydrodynamics,size effects,thermal rectification,phonon localization and so on.In order to study the non-Fourier heat conduction problems,many physical models and methods have been fully developed.Among them,the Boltzmann transport equation(BTE)is valid on multiple temporal and spatial scales,and can describe the thermal transport phenomena at micro/nano scale.Therefore,it has become an important tool in the study of non-Fourier heat conduction.Based on the phonon BTE,an efficient mesoscopic numerical method is proposed to solve the stationary equation in this thesis.Then,the phenomena and mechanisms of the heat vortices,graded thermal conductivity and thermal rectification are studied by using the numerical method combined with theoretical analysis.The main results are highlighted as follows:1.A synthetic iterative acceleration method for fast solution of stationary phonon BTE is proposed.In this method,a macroscopic equation is introduced on the basis of phonon BTE,and the microscopic and macroscopic equations are solved iteratively and alternately,which realizing the efficient convergence at different scales.The results show that this method can accurately predict the non-Fourier heat conduction problems and is 1-3 orders of magnitude faster than the implicit discrete ordinate method at low Knudsen numbers.2.A new phonon hydrodynamic phenomenon——heat vortices,is predicted,and the occurrence conditions and parameter range of this phenomenon are analyzed.The variation of heat vortices with length is analyzed in ribbon structure.The critical parameters about when the heat vortices disappear are given in porous structure.The results show that the heat vortices can appear in the ballistic and phonon hydrodynamics regimes,but disappear in the diffusive regime.3.The phenomenon and mechanisms of the graded thermal conductivity in radial homogeneous structures are studied,and the effects of phonon scattering on the graded thermal conductivity are analyzed.The spatial distributions of the temperature and thermal conductivity are derived analytically based on phonon BTE in the phonon hydrodynamics,diffusive and ballistic limits.The results find that in a homogeneous structure with a fixed size and a hotspot at the center,when the phonon scattering is not sufficient,the graded thermal conductivity appears.That is,the thermal conductivity increases from inside to outside along the radial direction.4.Based on the perturbation method,an analytical formula to describe the thermal rectification phenomenon is presented,and the physical relationships among the thermal rectification coefficient,temperature difference,system length and effective thermal conductivity are established.This theory proves that the thermal rectification coefficient is proportional to the temperature difference but nonlinear to the effective thermal conductivity.When the effective thermal conductivity and the central position of the system are independent of the system length,the thermal rectification coefficient is proportional to the system length.The theory is applied to explain the previous experimental and simulation results.The results of this thesis provide an effective tool for simulating engineering heat dissipation problems,deepen the understanding of the mechanism of non-Fourier heat conduction,and provide theoretical support for thermal management and engineering thermal design at micro/nano scale. |
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