2.5D無限元素非傅立葉熱傳法則模擬

A 2.5D infinite element approach for modeling non-Fourier heat conduction subjected to moving heat sources

邱重凱(Chong-Kai Chiu)

指導教授 ： 楊永斌

國立臺灣大學/工學院/土木工程學研究所/碩士(2014年)

https://doi.org/10.6342/NTU.2014.02084

摘要

本研究旨在分析非傅立葉熱傳問題，對於一般情況下的熱傳問題，使用傳統的傅立葉熱傳理論，即可達到良好的結果。然而，當涉及到極端條件的熱傳問題時，如溫度急遽變化或極高(低)溫度等情形，傅立葉熱傳無法精確模擬，是以出現了有別於傳統的非傅立葉熱傳理論。在傅立葉熱傳中，熱的傳播速度為無限大，不符合實際物理情形；在非傅立葉熱傳中，因考慮熱的波動特性，熱係以有限的速度傳遞。
本文援用了由Yang 和Hung (2001)所提出的土壤與結構互制之分析方法，將之用於熱傳分析中。首先介紹非傅立葉熱傳的基本特性，並透過傅立葉轉換推導2維解析解，由此探討各物理參數對溫度反應的影響。數值解的部分採用有限/無限元素混和分析法，利用動態無限元素模擬半無限域。隨後分析單一移動熱荷載作用於半無限域之問題，將3維問題以2.5維方法作分析，討論不考慮自振頻率荷載及考慮自振頻率荷載兩種情況，針對兩者的差異修正無限元素參數，最後經由數值解與解析解的結果，吾人作了一些結論與討論。

關鍵字

有限元素分析 ； 傅立葉熱傳 ； 非傅立葉熱傳 ； 無限元素 ； 自振頻率 ； 2.5維有限/無限元素混和分析法

並列摘要

Heat transfer analysis based on Fourier’s law has often been adopted to analyze the general heat conduction problem. However, it was found that the Fourier model fails to predict the temperature under some extreme conditions, such as rapid changes in temperature or extremely high or low temperatures. The Fourier heat equation implies that the propagation speed is infinite, while the non-Fourier heat equation is governed by the hyperbolic equation, which implies the propagation speed of heat waves is finite. Therefore, it was suggested that the traditional Fourier heat equation should be replaced with the non-Fourier heat equation to account for the finite thermal propagation speed.
In this study, the analytical solution of the governing equation is solved by the Fourier transform. The effects of some physical parameters on the temperature response are presented. The 2.5D finite/infinite element procedure proposed by Yang and Hung (2001) is adopted to deal with the non-Fourier heat conduction problems. The unbounded properties of the semi-infinite domain are simulated by infinite elements. The responses of a semi-infinite field subjected to a moving heat load, both with and without a self-oscillation frequency, are investigated. Finally, by comparing the results obtained with the corresponding analytical solutions, some conclusions are made along with discussions.

並列關鍵字

finite element analysis ； Fourier heat conduction ； non-Fourier heat conduction ； infinite element ； self-oscillation frequency ； 2.5D analysis

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