【《导热模型分析综述》1900字】

导热模型分析综述目录TOC\o"1-3"\h\u21712导热模型分析综述 1254311.1Matthiessen’srule模型 110681.2Fourier-Biot模型 2216681.3Boltzmanntransport模型 2168361.4Percolation模型 3144531.5Maxwell-Eucken模型 3对于碳材料的热导率是由自由电子和声子决定的，而电绝缘材料如氮化硼的热导率完全由声子决定。通过将热导率的本质进一步的探究，有声子化出发建立的一系列导热模型，可以深入地阐释导热机理。1.1Matthiessen’srule模型许多研究者考察了晶界声子散射（GBs）对多晶材料热传导的影响。SoodA等人报道，利用空间分辨时域热反射（TDTR）测量和电子背散射衍射（EBSD）相结合的方法，对掺硼聚晶金刚石中单个晶界范围内进行了局部化测量，并基于单个晶粒内部局部热导率空间变化的概念，建立了一个理论建模框架ADDINEN.CITE<EndNote><Cite><Author>Sood</Author><Year>2018</Year><RecNum>77</RecNum><DisplayText><styleface="superscript">[41]</style></DisplayText><record><rec-number>77</rec-number><foreign-keys><keyapp="EN"db-id="0tdetzpzm5dtavevrs4vd2zzwzdd0aew5vdd"timestamp="1621144911">77</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Sood,A.</author><author>Cheaito,R.</author><author>Bai,T.</author><author>Kwon,H.</author><author>Wang,Y.</author><author>Li,C.</author><author>Yates,L.</author><author>Bougher,T.</author><author>Graham,S.</author><author>Asheghi,M.</author></authors></contributors><titles><title>DirectVisualizationofThermalConductivitySuppressionDuetoEnhancedPhononScatteringNearIndividualGrainBoundaries</title><secondary-title>NanoLetters</secondary-title></titles><periodical><full-title>NanoLetters</full-title></periodical><pages>acs.nanolett.8b00534</pages><dates><year>2018</year></dates><urls></urls></record></Cite></EndNote>[41]。在距GBs距离x的点上的局域声子MFP(Λloc)可以用Matthiessen规则写成如下：Λlocx其中Λbulk是由于晶体中声子-声子散射而产生的本征MFP，Λdef对应于点缺陷（如掺杂剂）处的声子散射，Λbdry对应于GBs处的声子散射。晶粒内的局部热导率与局部MFP有关，klocx=Fxkbulk1.2Fourier-Biot模型通过一阶Fourier-Biot方程确定，即稳态下在单位时间∆t内，在截面面积为A的样品内通过∆x的距离，产生κ=设热扩散率α为温度差∆T∂T(r,t)∂t热导率与热扩散率存在以下关系：κ=αρc其中κ为热导率，α为热扩散率，ρ为材料密度，cp图1.7热传递示意图1.3Boltzmanntransport模型自由电子不仅可以传递电流，还可以传递热能，因此金属材料的热导率和电导率基本相同。然而，导电性和导热性的这个广义关系并不适用于非金属材料，这是由于在非金属中主要通过声载子传递热量。声子作为一种准粒子，是晶格振动模量子化的描述方式。对于由沿4个方向的温度梯度引起的声子输运，可以写出声子布居偏离平衡的表达式ADDINEN.CITE<EndNote><Cite><Author>Liang</Author><Year>2000</Year><RecNum>78</RecNum><DisplayText><styleface="superscript">[42]</style></DisplayText><record><rec-number>78</rec-number><foreign-keys><keyapp="EN"db-id="0tdetzpzm5dtavevrs4vd2zzwzdd0aew5vdd"timestamp="1621145029">78</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Liang,X.G.</author><author>Ji,X.</author></authors></contributors><titles><title>Thermalconductanceofrandomlyorientedcompositesofthinlayers</title><secondary-title>InternationalJournalofHeatandMassTransfer</secondary-title></titles><periodical><full-title>InternationalJournalofHeatandMassTransfer</full-title></periodical><pages>3633-3640</pages><volume>43</volume><number>19</number><dates><year>2000</year></dates><urls></urls></record></Cite></EndNote>[42]：v∂T其中g=f−fBE，式中，v是声子群速度，τ是单模弛豫时间，fBE是玻色-爱因斯坦分布函数。一般来说，g是x和zgx在此，hBN的晶体结构保持不变，与彼此接触的hBN相关的Λbdry1.4Percolation模型目前许多学者通过将逾渗模型引入到热管理领域中来预测填充型导热聚合物的热导率ADDINEN.CITE<EndNote><Cite><Author>Devpura</Author><Year>2000</Year><RecNum>79</RecNum><DisplayText><styleface="superscript">[43,44]</style></DisplayText><record><rec-number>79</rec-number><foreign-keys><keyapp="EN"db-id="0tdetzpzm5dtavevrs4vd2zzwzdd0aew5vdd"timestamp="1621145070">79</key></foreign-keys><ref-typename="ConferenceProceedings">10</ref-type><contributors><authors><author>Devpura,Amit</author><author>Phelan,PatrickE.</author><author>Prasher,RaviS.</author></authors></contributors><titles><title>Percolationtheoryappliedtotheanalysisofthermalinterfacematerialsinflip-chiptechnology</title><secondary-title>ThermalandThermomechanicalPhenomenainElectronicSystems,2000.ITHERM2000.TheSeventhIntersocietyConferenceon</secondary-title></titles><dates><year>2000</year></dates><urls></urls></record></Cite><Cite><Author>Maxwell</Author><RecNum>80</RecNum><record><rec-number>80</rec-number><foreign-keys><keyapp="EN"db-id="0tdetzpzm5dtavevrs4vd2zzwzdd0aew5vdd"timestamp="1621145096">80</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Maxwell,Jca</author></authors></contributors><titles><title>ATreatiseOnElectricityandMagnetism</title><secondary-title>Nature</secondary-title></titles><periodical><full-title>Nature</full-title></periodical><pages>478-480</pages><volume>7</volume><number>182</number><dates></dates><urls></urls></record></Cite></EndNote>[43,44]。在复合材料中，当导热填料的体积分数超过某一数值之后，填料相互接触并在高分子材料中形成有效的导热通道，而这个体积分数的值就被称为逾渗临界值（VC）。Percolation模型形式如下：λcPercolation模型只针对于球形粒子，且只有在填料体积分数接近逾渗临界值时才能预测得比较准确。1.5Maxwell-Eucken模型Maxwell使用连续相电阻率作为远场电阻率，导出基于满足拉普拉斯方程的电位理论的包含N个球形粒子的球体的有效电阻率。通过将N个球的系统的电阻率视为具有单个球的等效电阻率，并且从电势和稳定传导的温度之间的类比，获得复合材料的有效导热率。MaxwellADDINEN.CITE<EndNote><Cite><Author>Kumlutas</Author><Year>2003</Year><RecNum>81</RecNum><DisplayText><styleface="superscript">[45]</style></DisplayText><record><rec-number>81</rec-number><foreign-keys><keyapp="EN"db-id="0tdetzpzm5dtavevrs4vd2zzwzdd0aew5vdd"timestamp="1621145135">81</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Kumlutas,D.</author><author>Tavman,I.H.</author><author>Coban,MTurhan</author></authors></contributors><titles><title>Thermalconductivityofparticlefilledpolyethylenecompositematerials</title><secondary-title>COMPOSITESSCIENCEANDTECHNOLOGY</secondary-title></titles><periodical><full-title>COMPOSITESSCIENCEANDTECHNOLOGY</full-title></periodical><dates><year>2003</year></dates><urls></urls></record></Cite></EndNote>[45]导出基于满足拉普拉斯方程的电位理论的包含N个球形粒子的球体的有效电阻率σ的计算公式为：σc其中V是球形粒子的体积分数，σc,σ1,σ2分别是复合材料，聚合物基体，填料的电导率。Eucken将电导率换为导热系数，得到Maxwell-Eucken模型：λc其中V是球形粒子的体积分数，λc,λ1,λ2分别是复合材料，聚合物基体，填料的导热系数。方程式（1.8）发现只有当填料粒子在复合材料中的含量极低时，复合材料的有效热导率的实验结果才与式（1.8）计算结果相一致ADDINEN.CITE<EndNote><Cite><Author>Sundstrom</Author><Year>2010</Year><RecNum>82</RecNum><DisplayText><styleface="superscript">[46,47]</style></DisplayText><record><rec-number>82</rec-number><foreign-keys><keyapp="EN"db-id="0tdetzpzm5dtavevrs4vd2zzwzdd0aew5vdd"timestamp="1621145169">82</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Sundstrom,D.W.</author><author>Yu〥erLee</author></authors></contributors><titles><title>Thermalconductivityofpolymersfilledwithparticulatesolids</title><secondary-title>JournalofAppliedPolymerScience</secondary-title></titles><periodical><full-title>JournalofAppliedPolymerScience</full-title></periodical><pages>3159-3167</pages><volume>16</volume><number>12</number><dates><year>2010</year></dates><urls></urls></record></Cite><Cite><Author>Bernardino-Nicanor</Author><Year>2017</Year><RecNum>83</RecNum><record><rec-number>83</rec-number><foreign-keys><keyapp="EN"db-id="0tdetzpzm5dtavevrs4vd2zzwzdd0aew5vdd"timestamp="1621145198">83</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Bernardino-Nicanor,A.</author><author>GAcosta-García</author><author>NGüemes-Vera</author><author>Monta?Ez-Soto,J.L.</author><author>VVMaría</author><author>LGonzález-Cruz</author></authors></contributors><titles><title>Fouriertransforminfrareda