一維嵌入式熱切換超材料之分析、驗證與逆向設計

Abstract

在高功率密度電子元件與精密系統的熱管理中，如何於有限尺度內產生方向性導熱差異以實現熱整流，已成為重要研究議題。現有文獻雖已展示特定材料組合下之熱整流效果，然而對於提升熱整流時的材料選擇、幾何參數調整與操作溫度窗改變後之設計規則，仍缺乏系統化整理，使後續研究仍需仰賴大量試誤與參數掃描。基於此，本研究以一維異質材料串聯結構為核心，建立嵌入式熱切換超材料之系統化分析與設計流程，並結合理論推導與數值模擬，發展由目標熱整流率反推材料需求與結構參數之方法。首先，本研究以一維穩態串聯熱阻與溫度位勢為基礎，建立通用理論模型，分析異質材料熱導率k(T)之非線性如何於正向與反向操作下造成總熱阻差異，進而形成熱整流率（Thermal rectification ratio, TRR）。透過長度比最佳化，說明不同材料組合與幾何配置皆存在對應之最大TRR，且其上限會受到操作溫度區間影響。 進一步地，本研究探討嵌入段對熱整流表現之影響。結果顯示，常數熱導嵌入段會使整體TRR下降，且理論與數值模擬誤差小於1%。當嵌入段改為具導熱切換特性之熱切換材料（Thermally switchable material, TSM），並引入切換溫度T_sw與切換模式後，可使正向與反向操作落入不同導熱態，從而提升TRR；其中，平滑切換理論與數值模擬之誤差可控制於0.35%內。最後，本研究整合常數導熱基準模型與雙態TSM嵌入模型，建立目標TRR導向之設計流程，使在給定TRR_target時，得以反推出所需之TSM嵌入位置、厚度與導熱參數範圍，並作為嵌入式熱切換超材料（Thermally switchable metamaterials, TSMM）之設計依據。此流程可作為後續熱整流器分析、材料篩選與結構設計之參考。

In the thermal management of high-power-density electronic devices and precision systems, generating directional differences in heat conduction within a limited length scale to achieve thermal rectification has become an important research topic. Although existing studies have demonstrated thermal rectification effects for specific material combinations, systematic design rules for material selection, geometric parameter adjustment, and changes in the operating temperature window remain insufficiently established. As a result, subsequent studies still largely rely on extensive trial-and-error processes and parameter sweeps. Based on this motivation, this study focuses on a one-dimensional heterogeneous material series structure and establishes a systematic analysis and design framework for embedded thermally switchable metamaterials. By combining theoretical derivation with numerical simulation, a method is developed to inversely determine the required material properties and structural parameters from a target thermal rectification ratio. First, based on the one-dimensional steady-state series thermal resistance model and the temperature-potential method, a general theoretical model is established to analyze how the nonlinear thermal conductivity, k(T), of heterogeneous materials leads to differences in the total thermal resistance under forward and reverse operating conditions, thereby producing a thermal rectification ratio (TRR). Through length-ratio optimization, it is shown that different material combinations and geometric configurations exhibit corresponding maximum TRR values, and that the achievable upper limit is further influenced by the operating temperature window. Furthermore, this study investigates the effect of the embedded segment on thermal rectification performance. The results show that a constant-thermal-conductivity embedded segment decreases the overall TRR, with a discrepancy of less than 1% between theoretical predictions and numerical simulations. When the embedded segment is replaced by a thermally switchable material (TSM) with thermal-conductivity switching behavior, and the switching temperature T_swand switching mode are introduced, the forward and reverse operations can fall into different thermal-conductivity states, thereby enhancing TRR. The discrepancy between the smooth-switching theory and numerical simulation can be controlled within 0.35%. Finally, this study integrates the constant-conductivity baseline model and the two-state embedded TSM model into a target-TRR-oriented design framework. Given a target thermal rectification ratio, TRR_target, the required embedding position, thickness, and thermal-conductivity parameter range of the TSM can be inversely determined. These results serve as design guidelines for embedded thermally switchable metamaterials (TSMMs) and provide a reference for future thermal rectifier analysis, material screening, and structural design.