本研究著重在開創新的方法，求得具接觸熱阻(contact resistance)之複合材料有效導熱度。考慮的複合材料含有隨機分佈於基材[連續相(matrix)]中的球型粒子、或無限長圓柱型纖維[分散相(inclusion)]。即是粒子強化型複材與長纖維強化型複材。
在多位先進的努力下，求得複材之有效導熱度的知識已是相當豐富。我們知道在分散相表面具有極薄界面層的接觸熱阻問題中，可藉由無因次群Biot數適當地表現其界面特性。存在一 [critical Biot number] ，界面性質對整體有效導熱度產生中立效應(neutral effect)，使得有效導熱度 = 1。而我們所努力的方向，是建造一模擬的模式，求得隨機分佈之纖維或粒子強化型之有效導熱度。讓後人能夠繼續沿用此模擬方式，求得不規則型的纖維或粒子強化型複材之有效導熱度。

我們假想熱分子，以布朗運動的方式遊走於複合材料之粒子與基材間。Kim和Torquato(1990;1991)提出：當熱分子行走至界面附近時，熱分子能否跨越界面的機率問題與越過界面或折返所花費的時間問題。利用有效率的隨機行走法，可以求得兩相物質以任意比例混合後的有效導熱度。Kim和Torquato推導越過界面的機率與時間問題的過程中，考慮單一粒徑分散相與連續相界面間完美接觸的情況(溫度場分佈連續、正向熱流通量也連續)，對於分散相平衡隨機分佈的有效導熱度之接觸熱阻問題(溫度場分佈不連續、正向熱流通量連續)，並未加以研究。然而，分散相與連續相間存在接觸熱阻是很常見的，且我們發現，當 時，接觸熱阻問題將變成完美接觸的情形，即完美接觸是接觸熱阻問題中之極端的情形。

此創新的方法確能在求得有效導熱度上有所突破。不論對於整齊排列之纖維或粒子強化型複材之有效導熱度之計算，均有令人滿意結果。隨機分佈之完美接觸複材，亦得到預期中的結果。並且再次驗證了Bi確為一重要的參數。在Bi > ，我們觀察到了界面性質對整體有效導熱度產生增強效應(enhancing effect)；在Bi < ，產生減損效應(impairing effect)。此外，並驗證了我們的分散相系統是相當地隨機分佈。

Our research emphasizes on developing new methods to simulate the effective conductivities of the composites possessive of contact resistance. We concern composites with inclusions dispersed randomly in the matrix. The inclusions can be spherical particles, or infinitely long fibers. They are named particulate-reinforced composite and long-fiber-reinforced composites , respectively.
There is an abundant knowledge about how to obtain the effective conductivities of composites. The critical Biot number, , gives “neutral effect.” That is, we can neglect interface properties while we treat composites’ effective conductivities. We focus on construction of a simulation model, that can be used to calculate the effective conductivities of the composites with any size or any irregular type inclusions dispersed randomly in the matrix.

We image that thermal molecules do random walks among inclusions and matrix. Kim and Torquato (1990,1991) brought up the ideas whether the test thermal molecules will walk across the interface or not and how much time it will spend on crossing the interface or coming back. They obtained the effective conductivity of two phase composites. However, they considered single-sized inclusions, and a perfect contact with the matrix. (Temperature fields are continuous across the matrix-inclusion, so are the normal heat fluxes). They didn’t work on problems involving poly-dispersed inclusions with contact resistance at the matrix-inclusion interface. (Temperature fields are not continuous, but the normal heat fluxes are continuous.) However, it is common that contact resistance exists between matrix and inclusions. When the Biot number is infinite, contact resistance will disappear. Then, the matrix contacts the inclusions perfectly. Therefore, the contact resistance problem is a limiting case of the contact resistance problems.

The new method is a breakthrough in the area of composites’ effective conductivities. We obtained satisfactory results of the effective conductivities of the fibers and particles arranged regularly in the matrix. Moreover, the effective conductivities of the particulate-reinforced and the fiber-reinforced composites with inclusions randomly distributed are also computed. And we confirm that Biot number is an important parameter again. When Bi is less than the critical Biot number, the combined effect of interface and inclusion is enhancing to the matrix. When Bi is greater than the critical Biot number, the combined effect of interface and inclusion is enhancing to the matrix. We also verify that the inclusions generated are dispersed randomly enough.

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