文獻中所提出的熱對流遮罩受限於達西定律的適用範圍以及圓形的幾何形狀，因而限制了材料的選擇性和其他幾何形狀的應用，本研究基於熱對流雙層理論中的雙層結構，應用多變數優化法至熱對流隱形問題之中，透過數值方法模擬布林克曼方程式和熱對流方程式，計算出外層材料參數以設計熱對流遮罩，可以適用於較高滲透係數的材料和較高速度的流場分布，同時也能應用於圓形以外的幾何形狀，達成了多孔介質中的熱對流隱形。本文透過對不同的流場和溫度場背景分布狀況和三種幾何形狀進行遮罩隱形效能的探討，結果指出在較高的雷諾數與佩克萊數的背景分布下，遮罩的隱形效果會降低，在遮罩的幾何結構方面，對於圓形遮罩而言，根據不同的背景分布條件所計算出的最佳外層材料參數並沒有明顯的變化，非圓形遮罩的幾何形狀、厚度和擺放角度，對於遮罩的隱形效能和計算出的最佳外層材料參數皆有顯著的影響。因此，透過此方法，在工程應用上可以根據優化結果分析並修改遮罩的幾何參數以提升隱形效能。

Convection cloaking in porous media proposed in recent years applies to Darcy’s law and circular geometry, thus restricting the use of materials with higher permeability, the application to flow fields at higher Reynolds numbers, and effective space utilization. This study proposes a numerical method, based on multivariable optimization, to design a bilayer convection cloak with irregular shape that can be applied to materials with higher permeability and flow fields at higher Reynolds number. The proposed method solves the Stokes-Brinkman equation and energy equation and calculates the optimal outer-layer effective thermal conductivity and permeability of the bilayer convection cloak to achieve the best thermal cloaking effects. Cloaking performance for different convective background and three geometric shapes of the convection cloak is investigated. The numerical results demonstrate the effect of the background field distributions and cloak geometries on the cloaking performance. For circular cloak, the orientation between the flow and heat flux direction has little impact on the optimal solution. For geometrically anisotropic cloaks, orientation and thickness of the outer-layer are shown to have significant impact. Thus, for engineering application, this method can be used to improve cloaking performance by refining the geometrical parameters of the cloak based on analyses of the optimal results.

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