• 作者： Lu, Shih-Yuan
• 中文摘要： 吾人提出一等效粒子模式,用以估算含定向橢圓柱分散系統之有效導熱度。橢圓柱表面可以是與基材完美接觸,存在某接觸熱阻或被覆以一層第三種材料。對於一般橢圓柱情況,發現有效導熱度張量中之平行及垂直分量滿足 Keller倒數定理,而對於被覆橢圓柱情況,一類似於Keller定理的倒數關係可被提出。不同於一般橢圓柱狀況,在接觸熱阻及被覆橢圓柱情況中,橢圓柱可在一方向顯出強化導熱度效應,而在另一方向展現減弱效應。對於一般橢圓柱問題,其無因次有效導熱度被發現是橢圓柱體積分率,橢圓柱軸長比及無因次橢圓柱導熱度之函數。在接觸熱阻問題中,多出一個參數,其為以半主軸長為基準之Biot數,而在被覆橢圓柱問題中,則多出兩個參數,一為相對塗佈厚度,另一為被覆層之無因次導熱度。吾人完整地探討這些參數對無因次有效導熱度之效應。
• 英文摘要： An equivalent inclusion model is proposed to estimate the effective conductivity of dispersions containing aligned long elliptic cylinders. The cylinders are either in perfect contact with the matrix, possessive of certain contact resistance or coated with a confocal elliptic layer of a third material. The parallel and perpendicular components of the effective conductivity tensor for the plain cylinder case are shown to satisfy Keller's reciprocal theorem, while those for the coated cylinder case follow a reciprocal relation similar to Keller's. Unlike the plain cylinder case, the inclusion effect for the contact resistance and coated cylinder cases can be enhancing in one direction, but impairing in the other direction. For the plain cylinder problem, the reduced effective conductivity (.sigma./sub eff/) is found to depend on the cylinder volume fraction (f), cylinder aspect ratio (a/sub 0//b/sub 0/), and reduced cylinder conductivity (.sigma./sub 0/). One more parameter, the semi- major axis based Biot number (Bi), is needed for the contact resistance problem, while two more parameters, the reduced coating layer conductivity(.sigma./sub c/) and the relative coating thickness(. delta./a/sub 0/), appear for the coated cylinder problem. Effects of these parameters on .sigma./sub eff/ are thoroughly investigated.
• 中文關鍵字： 有效熱導度; 橢圓柱; 接觸熱阻; 塗佈; 等效粒子模式
• 英文關鍵字： Effective Conductivity; Elliptic Cylinder; Contact Resistance; Coating; Equivalent Inclusion Method