均溫板的理論分析與參數討論

Abstract

本研究針對五層結構、一面受熱、另一面對流冷卻之均溫板建構兩個極端數學模型，以了解並預測均溫板之極限熱傳性能與內部流場特徵。其中金屬壁乃配合非均勻加熱條件求解三維溫度場，液體與蒸氣層之流場皆假設為二維，根據介面熱通量計算得相變化質量通量後，再求得相關壓力場及速度場。本文提出之模型分別稱之為完全均溫模型與完全非均溫模型，其差別在於假設蒸氣是否在蒸氣區域充分混和，並使用商業軟體ANSYS驗證簡化的合理性與數學推導過程的正確性。最後將模型預測與實驗數據比較，發現大多數的預測值與實驗值皆落於25%以內。 本研究接著利用數學模型探討各項因子對均溫板性能的影響。研究發現，在固定均溫板面積與熱源功率下，當熱源面積越來越大時，熱阻會越來越低，並且在熱源面積和均溫板面積相等時，兩種模型會獲得相同數值；在不同長寬比下，隨著長寬比逐漸加大時，此二種模型呈現相反趨勢，當長寬比較小時且蒸氣區域之蒸氣能達到均溫混和時，均溫板反應出更優良的性能。當環境熱對流係數與毛細組織等效熱傳導係數逐漸上升時，熱阻的降低幅度與總流路壓降的上升幅度逐漸不明顯。本研究還比較四種工作流體（水、甲醇、乙醇、丙酮）的毛細極限，其中水作為工作流體的均溫板具有最高的極限熱通量，而後依序為甲醇、丙酮及乙醇，此結果與文獻中觀察到的現象吻合。

In this study, two mathematical models were constructed to predict the thermal performance and internal flow characteristics of a five-layer structure vapor chamber in two limiting cases, fully uniform and fully nonuniform, where the chamber is heated on one side and convectively cooled on the other side. The three-dimensional temperature fields of copper plates under non-uniform heating conditions were solved first. The flow fields in the liquid and vapor core regions are assumed to be two-dimensional. Mass fluxes due to phase change are computed according to the interface heat flux, and used for solving the pressure and velocity fields. The main difference between the two models lies in the assumption whether heat is fully mixed or completely unmixed in the vapor core region. The commercial software ANSYS is used to examine the rationality of some assumptions and most of all the accuracy of the mathematic derivations. The model predictions were finally compared with experimental measured. It is found that the relative error falls within 25%. The mathematical models were then employed to investigate the influence of various factors on the thermal performance of the vapor chamber. The results show that under a fixed vapor chamber cross-sectional area and heat source power, the thermal resistance decreases with increasing heating area. Both models reach the same value when the heating area is equal to the vapor chamber cross-sectional area. As the aspect ratio of the vapor chamber increases, the two models yield opposite results. When vapor is uniformly mixed in the vapor core, a smaller aspect ratio leads to a better performance. When the environmental heat transfer coefficient and effective thermal conductivity of the capillary structure increase, the reduction in thermal resistance and the increase of pressure drop become less significant. This work also compares the capillary limits of four working fluids: water, methanol, ethanol, and acetone. The result shows that water has the highest maximum heat flux, followed by methanol, acetone, and ethanol, which is consistent with the research results mentioned in the literature.