本研究旨在建立一個假頻譜元素法結合直接施力邊界沉浸法來模擬強迫對流、自然對流熱傳的問題。本研究將被加熱處於高溫且等溫的圓柱利用直接施力邊界沉浸法建模，並使用假頻譜法離散統御方程式來模擬，因此此研究案例皆藉由高溫圓柱在低溫環境下的溫度差進行熱傳分析。在第一個案例中，本篇研究了當雷諾數為40時，流體經過加熱等溫圓柱的強迫對流熱傳分析。在第二個案例中，本篇研究了當瑞利數分別為 10^4、10^5 與 10^6 時，在一個方形封閉空間的中心放置加熱等溫圓柱的自然對流熱傳分析。利用基本的強迫與對流熱傳問題驗證了此方法所獲的的結果。

A pseudospectral matrix element method (PSME) coupled with a direct-forcing immersed boundary method (DFIB) has been utilized to simulate forced convection and natural convection. The direct-forcing immersed boundary method is adopted to model the heated circular cylinder and the governing equations are discretized by the PSME method. Numerical calculations are performed for all of the cases induced by a temperature difference between a cold outer square cylinder and a hot inner circular cylinder. In the first case, forced convection over a heated circular cylinder with an
isothermal surface was investigated with the Reynolds number Re = 40. The second case, natural convection in a square enclosure with a heated circular cylinder placed at the center of the square enclosure was carried out for three different Rayleigh numbers (Ra = 10^4, 10^5 and 10^6). The results obtained are validated using a number of benchmark forced and natural convection problems.

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