非平板系統中微觀熱傳之分析

Abstract

本文應用微觀熱傳理論來探討微小尺寸系統內熱傳導現象。理論模式採用聲子輻射熱傳方程式來分析二維圓柱形微管及一維微圓球中熱傳問題。在數值方法上，本研究採用Discrete ordinate method來求解聲子輻射熱傳方程式。本文主要是針對溫度分布及等效熱傳導係數，討論在不同物理參數及邊界條件下所造成的影響。其中，聲子輻射熱傳模式在兩個邊界上會有溫度落差產生，當圓管的厚度或高度非常小時，熱傳會形成一種穿透現象( Ballistic transport )。相反的，圓管的厚度或高度非常大時，熱會以類似擴散的現象傳遞。方程式中最為重要的參數是圓管的厚度或高度與聲子平均自由路徑的比較，當厚度或高度達到100倍聲子平均自由路徑時，聲子輻射熱傳模式與傅立葉熱傳導定律的結果相當接近。在等效熱傳導係數的部分，圓管及圓球的等效熱傳導係數會隨著厚度或高度的縮小而降低，且圓球等效熱傳導係數會隨著曲率的增加而上升。

This study discusses conductive heat transfer for non-planar micro system from micrpscopic point of view. Equation of phonon radiatve transfer is used to analyze heat conduction in two-dimensional cylindrical micro tube and one-dimensional micro sphere. Discrete ordinate method is used to solve the equation of phonon radiative transfer. This study discusses the response of the temperature distribution and effective thermal conductivity for a variety of physical properties and boundary conditions. It is noticed that temperature jumps at the boundaries are found. When the tube thickness and height is very thin, the temperature profile presents the ballistic behavior. Otherwise, the tube thickness and height is very thick, the temperature profile presents the Diffuse-like behavior. The most important parameter in phonon radiative transfer model is the ratio between the tube thickness or height and the phonon mean free path. The results show that phonon radiative transfer model approaches to Fourier’s law of heat conduction when the tube thickness and height is about 100 times of phonon mean free path. The results show that the reduction of thickness or height of the tube and the sphere will reduce the effective thermal conductivity of the tube and the sphere. The effective thermal conductivity of the sphere increases as the curvature increases.