本論文分析一充滿流體的多孔介質中對流熱傳穩定性。考慮多孔介質固體與流體間的熱傳影響，因此使用熱不平衡模型來描述固體與液體的溫度分布。應用Galerkin方法至多孔介質中的流場與溫度分布，可推得一組五維非線性動力方程式來描述流線與溫度分布的振幅隨時間之運動。研究中詳細分析並討論修正後多孔性傳導係數、固液間熱傳係數H與擴散係數比等對於多孔介質中之臨界熱對流之影響。根據穩定性分析顯示，介面熱傳係數 H傾向於延緩熱對流的發生。然而，在熱對流中的臨界Darcy-Rayleigh常數卻隨著修正後多孔性傳導係數而降低。雖然臨界對流的發生與擴散係數比是無關的，本研究中發現擴散係數比對穩態對流的穩定性之影響。

Stability of thermal convection in a fluid-saturated porous medium was analyzed by using a thermal non-equilibrium model to take account of the interphase heat transfer between the fluid and the solid. The study is based on the five dimensional nonlinear dynamical system deduced by applying the truncated Galerkin expansion to the momentum and heat transfer equations. The effects of the porosity-modified conductivity ratio λ , interphase heat transfer H, and the ratio of diffusivity α , on the onset of convection and the first transition of the convection in a porous medium were analyzed and discussed. The stability analysis revealed that the interphase heat transfer H tends to retard the onset of thermal convection. However, the critical Darcy-Rayleigh number of onset of convection decreases with the porosity-modified conductivity ratio, λ . Even though the onset of convection is independent of α , it is shown the first transition of convection is a strong function of α .

摘 要 英文摘要 目 錄 圖 目 錄 符號說明 第一章 簡介 1.1 研究背景 1.2 文獻回顧 1.3 研究目的與方法 第二章 物理與數學模式 第三章 系統之特性與穩定性分析 第四章 數值結果 4.1 S1之穩定性 (臨界對流) 4.2 S2,3之穩定性(穩態對流之初次轉變) 第五章 結 論 參考文獻

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