使用聲子波茲曼方程對緊密型奈米尺度複合物之熱傳模擬

Abstract

在巨觀尺度下，熱傳遵守傅立葉熱傳方程式。若尺度縮小到微奈米等級時，傅立葉熱傳方程式在分析模擬上會高估實際的物理量產生熱傳率。所以在微尺度下探討分析真實熱傳導，傅立葉熱傳方程已不適用。半導體或絕緣體材料中，熱是由熱載子(電子、聲子和光子)來傳遞的。在本文中，主要探討聲子在複合材料內的熱傳遞。 聲子輻射熱傳方程式為非線性且含有積分微分的多變數方程式，要直接求解並不容易，若將碰撞項用鬆弛時間近似成BGK方程式 (Bhatnagar-Gross-Krook Equation)來簡化，在數學上會較易處理，本文在方向上使用離散座標法(Discrete Ordinate Method)將方向餘弦離散化，在空間上使用迎風算則( Upwind Scheme)來分析問題。 奈米複合材料在超晶格(superlattice)中，被觀察到有類似熱導率減少及熱電效率增加的現象，這提供了奈米尺度效應在熱電材料中可增加益處的方向。奈米複合材料排列可分成兩種類型，一種為材料以奈米線的樣式嵌入在另一個主要的基質材料，稱為線型(nanowire)，另一種為像棋盤式的緊密混合兩種不同類型的奈米線，稱為緊密型(nanocompacted)。以相同的化學計量下，緊密型混合奈米線的複合材料，因為材料沒有連續相，熱傳導係數會低於將奈米線嵌入一主要基材的類型。 本文利用聲子輻射熱傳方程配分離座標法探討一維界面密度問題，以及二維線型(wire)及緊密型(compacted)的超晶格界面密度的比較，以及在不同溫度下，兩種類型的熱傳導率分佈情況。 最後再與先前論文中利用直接蒙地卡羅(DSMC)模擬的結果做誤差比較，以探討缺失。

The equation of phonon radiative transfer (EPRT) is a nonlinear, integral, differential equation with many variables. It is difficult for us to solve the equation directly. If we simplify the relaxation time of collision term by Bhatnagar- -Gross-Krook Equation. The equation will become easily to cope with. In this paper, we deal with phase space where the discrete ordinate method is used for angular discretization; and using upwind scheme the deal with spatial discretization. Nanocomposites in superlattices are observed that may realize a similar thermal conductivity reduction and thermoelectric efficiency enhancements. So it provides us a way to increase the benefits of the nanoscale effects to thermoelectric materials in bulk form. If there are two species of nanocomposites, one is a material in the form of nanowires embedded in another host matrix material; the other is a discrete mixture of two different kinds of nanowires that are compacted. At the same stoichiometry, a nanocomposite in the form of discrete mixtures of nanowires does not have a continuous phase of material, so its thermal conductivity is lower than composites with nanowires embedded in a host material. In this paper, using EPRT with the discrete ordinate method to investigate simulation about the density of interface of one dimension superlattice, nanocomposites of nanowires embedded in another host matrix material, and nanocomposites of compacted silicon and germanium nanowire mixtures nanocompacted. Results show that the thermal conductivity of composites in the form of compacted silicon and germanium nanowire mixtures is lower than the composites with silicon nanowires embedded in a germanium matrix at the same atomic composition and characteristic size of the nanowires. Finally, we will take our data to compare with the other study which simulation by Direct Monte Carlo Method.