2.5維非傅立葉法則固體熱傳模擬

Abstract

摘要 本研究為熱傳問題，範圍包跨了傳統傅立葉熱傳及非傅立葉熱傳。隨著科技的進步，電子設備或元件的散熱問題，雷射切割或加熱等精密工業也逐漸受到重視。在某些情況下，傳統熱傳理論已發現不足之處。因此，產生了有別於傳統的非傅立葉熱傳理論。這個理論將熱之傳播考慮成有波動的特性，此特性引起了本研究的動機。經常需接觸地表震動模擬問題的土木系，對於波傳問題已經有很多相當不錯的分析模擬數值方法。為此，有鑑於非傅立葉熱傳的波傳特性，本研究即謀運用波傳的方法，分析熱傳問題。 本文援用了由Yang 和Hung(2001a)所提出的土壤與結構互制之數值分析方法，將之應用於熱傳分析上。首先對熱傳理論部分做充分探討，並提出熱傳無限元素的假設，和其他文獻作比較。接著採用一較簡單的彈性半無限域問題的解析解(洪，2000)，和其他文獻的2維熱傳分析結果作比較，證實此方法經過修正之後，是可以達到相同的結果。隨後模擬了單一移動熱載，將3維問題以2.5維解析解方法處理，藉改變熱載移動速度與熱傳播速度之比，可得出許多不一樣的結果。同時也依據2.5維有限元素與無限元素混和分析法(Yang and Hung 2001a)，將熱傳2.5維的矩陣公式給架構出來。最後根據本文各章節模擬的結果，提出一些結論，同時附上建議與不足之處。

Abstract Temperature is an important factor in engineering applications. To solve the temperature distribution of solids or structures, heat transfer analysis based on Fourier’s law has frequently been adopted. With the development of science and technology, heating technologies are applied more widely and more precisely, for example in problems involving laser beams and welding. However, it was found that, in some practical applications such as laser beams with short pulse or heat loads with rapid changes, heat transfer analysis using the traditional Fourier heat equation can result in large errors. Therefore, it was suggested that the traditional Fourier heat equation should be replaced with a non-Fourier heat equation to account for the finite thermal propagation speed. In this study, we will use the 2.5D finite/infinite element procedure (Yang and Hung, 2001a) for dealing with non-Fourier heat conduction problems. Originally, the 2.5D finite/infinite element procedure was proposed for dealing with ground vibrations induced by moving loads. At a first glance, there is no relationship between the mechanics and thermal problems. In fact, ground vibrations are the cause of traditional wave propagation problems, while the non-Fourier heat conduction is governed by the hyperbolic equation, which exhibits wave-like behavior. Thus, the two types of problems share similar nature, and can be treated by similar means. Finally, we will show the analysis results obtained by the model used, along with some conclusions and recommendations.