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四、請針對以下火羽在溫度層化環境下(Plumes in Temperature - Stratified Ambients)的描述,解讀附圖的物理現象。原文:When a buoyant, turbulent plume rises, it cools by entrainment of ambient air. If the ambient air increases in temperature with height, which is normal in buildings, and the fire source is weak, the temperature difference between the plume and the ambient, which gives the plume buoyancy, may vanish and actually reverse in sign. Eventually the plume ceases to rise.Figure: Theoretical behavior of centerline plume variables in linearly temperature-stratified ambients. Curve A: ratio of temperature rises (stratified versus unstratified), Curve B: ratio of axial velocities. Curve C: ratio of plume radii. Curve D: ratio of volumetric species concentrations. Where z: height above top of combustible (m) and Zm: maximum vertical penetration of plumefluid in stratified ambient (m)

三、請以史帝芬-波茲曼(Stefan-Boltzmann)公式,說明幅射熱熱傳特性(10 分),並針對設備測試、系統功能及性能設計方面,提出 3 種 在防火工程(Fire Safety Engineering)上的運用情境(15 分)。

二、A sinusoidal voltage \( E \sin \omega t \), where \( t \) is time, is passed through a half-wave rectifier that clips the negative portion of the wave. Find the Fourier series of the resulting period function. \[ u(t) = \begin{cases} 0 & \text{if } -L < t < 0 \\ E \sin \omega t & \text{if } 0 < t < L \end{cases} \quad p = 2L = \frac{2\pi}{\omega} \]

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