Numerical simulation of low temperature thermal conductance of corrugated nanofibers
Numerical simulation of low temperature thermal conductance of corrugated nanofibers
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发表时间：
2010
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通讯作者：
T. Puurtinen
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作者：
T. Puurtinen
Puurtinen，Tuomas Numerical simulation of low temperature thermal conductivity of corrugated nanofibers于韦斯屈莱：于韦斯屈莱大学，2010年，114页（于韦斯屈莱Studies in Computing ISSN 1456-5390; 123）ISBN 978-951-39-4094-2 Finnish summary Diss.在目前的工作中，对介电弹性纳米纤维的低温热传导进行了数值模拟。在纤维边界上形成一个特殊的光滑圆柱形或椭圆形的界面，通过反射低能声子来降低热导率。在T = 0.1 - 10 K的温度范围内，热能主要由弯曲波、扭转波和纵波携带，在这里用1D和3D模型进行了模拟。利用有限元法求解了周期纤维的频谱和波通过有限个局部周期纤维的散射矩阵。Landauer公式被用来计算导热系数。以硅纳米纤维为典型算例进行数值计算。研究发现，轴对称周期振荡的三维频谱可以近似为由某些简单微分方程得到的一维频谱。通过模拟多种边界形状，对一维模型给出可靠结果的参数范围提出了建议。结果表明，一维模型可以用来可靠地计算低能声子的透射几率曲线。最后，设计了一个特殊的啁啾圆-椭圆形的反射器，在T = 0.1 − 1 K的范围内将热导率降低了90%。
Puurtinen, Tuomas Numerical simulation of low temperature thermal conductance of corrugated nanofibers Jyväskylä: University of Jyväskylä, 2010, 114 p. (Jyväskylä Studies in Computing ISSN 1456-5390; 123) ISBN 978-951-39-4094-2 Finnish summary Diss. In the present work the low temperature thermal conductance of dielectric elastic nanofibers was numerically simulated. A special smooth cylindrical or elliptical corrugation was shaped on the fiber boundary in order to lower the thermal conductance by reflecting low energy phonons. On temperature range T = 0.1− 10K thermal energy is carried mainly by flexural, torsional and longitudinal waves, which were simulated here with 1D and 3D models. Finite element method was used to solve frequency spectrum of periodical fibers and scattering matrix for the waves through a finite locally periodical fibers. Landauer formalism was then used to calculate the thermal conductance. For numerical calculation there were taken silicon nanofibers as typical examples. It was found that 3D frequency spectrum of axially symmetrical periodical corrugation can be approximated with 1D frequency spectra obtained from certain simple differential equations. By simulating numerous boundary shapes, suggestions were made about the parameter range where 1D models give reliable results. It was concluded that 1D models can be used to reliably calculate transmission probability curves for low energy phonons. Finally, a special chirped circular-elliptical corrugation was designed to decrease the thermal conductance by 90% on range T = 0.1 − 1K.