112年 - 112 中央警察大學_碩士班入學考試試題_消防科學研究所：火災科學#147976

(一)y''+λy=0, y(0)=0, y(10)=0 (12 分)

(二)(y'/x)'+(λ+1)y/x3=0, y(1)=0, y(eπ )=0 (13 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. \[ u(t) = \begin{cases} 0 & \text{if } -L < t < 0 \\ E \sin \omega t & \text{if } 0 < t < L \end{cases} \quad p = 2L = \frac{2\pi}{\omega} \]

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)。

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。

火災科學 1
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 plume
fluid in stratified ambient (m)

火災科學 2