| 摘要: | 本研究是利用數值模擬的程式來分析三維不可壓縮液態水在圓形微管流中的流力與熱傳特性。我們為了方便計算程式的求解過程，將三維的圓形微管流簡化為二維軸對稱x-r方向的平面流場，並求解邊界層方程式。這個邊界層方程式因為具有拋物線型的數學特性，用於計算流道內完全發展後的流力與熱傳特性，能夠提供一個準確又有力的最佳工具，就現今較普遍的電腦硬體設備來說，在模擬分析花費的時間比傳統的Navier-Stokes方程式所需要時間還要快幾百倍以上。
文獻中有學者提到，不同的實驗與數值分析之間往往會造成許多量測取得跟解析上的差異，這主要是由溫度效應、壓縮效應、稀薄效應、黏滯消散效應、電滲效應、壁面粗糙度及實驗誤差因素等所造成。因此，本研究中我們主要是將溫度效應視為重點討論；因為溫度的變化影響，使得流體的基本物理性質，如密度、熱傳導係數與黏滯係數會隨著溫度而改變，並直接影響到流場內有無溫度效應的壓力、速度、溫度之差異。
熱邊界條件上，圓形微管流的管壁有分成等溫壁面與固定熱通量兩種，我們分開討論這兩種熱邊界條件下，流體在管徑中的Nusselt number以及摩擦因子與雷諾數的關係，接著與傳統尺寸之熱傳特性去驗證，在求解出的Nusselt number與f*Re之數據，跟傳統尺寸之經驗公式之間的誤差極小。這驗證動作表示本研究在使用邊界層方程式對圓形微管流的模擬分析上，的確是個準確的數值分析方程式。
在無溫度效應下，Nusselt number與f*Re的值，皆會符合傳統尺寸之微管流的流力與熱傳特性；但若考慮有溫度效應時Nusselt number會高於傳統熱傳特性的值，而f*Re是隨著管徑變大而增加。另外，本研究也探討於有無溫度效應下，不同管徑、不同雷諾數等的條件，對圓形微管流的流力與熱傳特性。
The objective of this research is to use numerical simulation program to analyze fluid mechanics and heat transfer characteristics in three dimensional micro-tubes of incompressible water-liquid. Three dimensional micro-tubes simplified into two dimensional axis-symmetric of x-r plane field is to facilitate the computing process of the program, and then only the boundary-layer equation needs estimating. Because this equation has the character of parabolic type in mathematics, it could provide a very accurate and powerful tool for computing fluid mechanics and heat transfer characteristics in micro-tubes after fully developed region. At the time being, comparing with the general computer devices, simulating the program is much faster than the traditional Navier-Stokes equation hundreds of times.
The scholars in the references said that there are usually some differences in measurement and analysis between different experiments and numerical analysis. All of these main influences are due to temperature effects, compressibility effects, rarefaction effects, viscous dissipation effects, Electro-osmotic effects, channel surface conditions, experiment errors and so on. Therefore, temperature effects are considered the main point in the research. Because of the change of temperature, the basic physical properties in fluid, such as density, conductivity and viscosity, will be affected. If temperature changes, they change, and even directly affect the differences of pressure, velocity and temperature in the flow field by considering temperature effects or not.
For thermal boundary condition, it divides into isothermal wall temperature and constant heat flux on the wall in micro-tubes. Under discussing two parts of thermal boundary condition, to investigate Nusselt number and the relationship between friction factor and Reynolds number first, and then verify with heat transfer characteristics of traditional size. According to the values of Nusselt number and f*Re from the program, the contracting error is very small with experimental formula of traditional size. This verification means that the research in using boundary-layer equation with micro-tubes simulating analysis, is truly an accurate numerical simulation equation.
Without temperature effects, all the values of Nusselt number and f*Re would conform to fluid mechanics and heat transfer characteristics in traditional size; but if considering temperature effects, Nusselt number would be higher than traditional heat transfer characteristics, and f*Re would raise following to the increasing diameter. Besides, this research also discusses the fluid mechanics and heat transfer characteristics in different diameter and Reynolds number in micro-tubes without considering temperature effects. |
