熱超材料可透過設計異向性導熱結構操控熱流與溫度場，其中熱隱形斗篷能使目標物在外部熱量測下近似不可偵測。然而既有研究多假設材料界面為完美鍵結，實際上因界面熱阻、鍍層或氧化層等因素，界面不完美效應普遍存在，且隨裝置尺寸縮小而益發顯著。文獻中含不完美界面之熱隱形研究已涵蓋二維穩態、三維穩態與二維暫態等情形，惟三維球型暫態配置之對應條件仍待建立，本論文即以補足此一研究缺口為目標。

本論文結合中性內含物概念與散射消除技術，探討由等向性核心與球型異向性殼層組成之熱斗篷，在完美界面、低導熱型（LC 型）與高導熱型（HC 型）不完美界面下之穩態與暫態隱形條件。穩態部分整理二維圓柱組合（CCA）與三維球組合（CSA）之熱中性條件（強隱形條件），並分析異向性參數與界面參數對核心屏蔽與集中效應之影響。暫態部分為本文主要貢獻：在準靜態近似下，以 spherical Bessel 函數展開各區域溫度場，令最低兩階散射係數 S₀ 與 S₁ 同時為零，推導三維球型暫態弱隱形條件。其中單極約束（S₀ = 0）要求斗篷之體積熱容量與背景介質匹配，為暫態獨有之條件；在準靜態主導階並忽略界面儲熱效應之假設下，此約束不受 LC/HC 型界面傳導參數之直接影響。偶極約束（S₁ = 0）則規範導熱係數之匹配關係，經界面參數修正後與穩態熱中性條件一致。分析顯示，LC 型與 HC 型界面分別呈現串聯型與並聯型之均質化修正特徵，且三維 HC 型修正因球面表面 Laplacian 之幾何效應而多出係數二。

解析結果以 COMSOL 有限元素模擬驗證：穩態模型之異向性殼層以多層等向性材料近似，三維暫態模型則直接設定殼層之徑向與切向導熱係數；不完美界面以有限厚度薄層實作，並以均質背景介質之參考案例比較散射場。在所有測試案例中，數值結果與解析解之誤差率均在百分之零點五以內，且暫態溫度場顯示外部背景擾動可被有效抑制，並隨時間趨近穩態熱中性行為。本文之分析建立於準靜態近似、二維圓柱與三維球型幾何、LC/HC 型界面模型以及忽略界面儲熱效應等假設之下。

總結而言，本論文建立了含 LC 型與 HC 型不完美界面之三維球型暫態弱隱形條件，並釐清其與穩態熱中性條件之對應關係，為不完美界面下之暫態熱超材料設計提供理論依據。

Thermal invisibility cloaks manipulate heat flow so that an embedded object produces little disturbance in the surrounding temperature field. Most analytical designs assume perfectly bonded interfaces, although thermal resistance, coatings, and highly conducting films can modify heat transfer at small scales. This thesis develops steady-state and transient design conditions for thermal cloaks with perfect, low-conductivity (LC-type), and high-conductivity (HC-type) interfaces. The steady analysis organizes thermal-neutrality conditions for two-dimensional composite cylinders and three-dimensional composite spheres. The transient analysis extends the scattering cancellation technique to a three-dimensional spherical cloak. Under the quasi-static approximation, the monopole and dipole scattering coefficients are eliminated simultaneously. The monopole condition requires volumetric heat-capacity matching, whereas the dipole condition gives a conductivity relation that coincides with steady-state thermal neutrality after interface corrections. LC-type and HC-type interfaces enter through series-type and parallel-type homogenization corrections, and the spherical HC-type correction contains an additional factor of two arising from the surface Laplacian. COMSOL simulations verify the analytical conditions. Across the tested cases, numerical and analytical results agree within 0.5%, and the exterior disturbance is strongly suppressed while the solution approaches thermal neutrality at steady state.

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