微細雙層圓管的熱傳分析

Abstract

本論文係針對一在軸向無限延長，而外徑為a、內徑為b之圓柱圓管的熱傳導係數進行詳細分析。考慮之材料為介電材質，且為等向對稱之量子井，即不考慮電子對熱傳導的貢獻，晶體中熱傳導主要依靠聲子來完成。我們考慮材料為自由邊界，即邊界介於彈性材料及空氣中，因此兩個邊界上之正向應力張量為零。針對上述材料之幾何圖形，我們探討其對聲子頻譜之影響。 此外，我們也對灰體介電材質雙層微細圓管研究其在內部及交界面的熱傳效應。當圓管為兩層相疊，內外管皆會受到彼此對方來自內外邊界及其來源項的影響，且在交界面會造成反射及折射。我們探討交界面不同反射率薄膜厚度、曲率及內外層不同厚度差等材料參數對雙層微細圓管內熱傳導之效應，另外，針對 之實際雙層材質之例子分析內部之熱傳特性。結果顯示，微管內能量分布決定於外壁激發的聲子能量及在交界面之反射率，因此，微管外壁溫度及材質的反射率影響其內部溫度分布甚鉅。除了微管管壁厚度外，微管的曲率也是影響熱通量及等效熱傳導係數的重要參數。

A cylindrical dielectric tube of infinite length in the longitudinal direction with inner radius a and outer radius b is considered. Free boundaries are assumed, that is, boundary between an elastic material and vacuum is considered, where the normal components of the stress tensor are zero and the displacement is unrestricted. We investigate the geometric figure of material to understand the effect of phonon frequency spectrum. In this thesis, we also study the effect of various geometrical and thermophysical parameters as well as the interface on the heat conduction in a two-layer microtube of gray body. Results indicate that the energy distribution in the annulus is dominated by phonons excited by outer surfaces. Consequently, the temperature is considerably affected by the temperature of outer surfaces and the reflectivity of the interface. In addition to tube wall thickness, which was usually considered as the size effect on heat conduction, the curvature effect would significantly change the heat flux across the tube wall .