摘要

本文的目的為研究在有限平板之雙曲線熱傳導的正、逆算問題受表面輻射的影響。其中，表面溫度的非線性積分方程可用拉氏轉換導出，再以數值方法求解。首先考慮在邊界表面的一端具有脈衝或週期振盪式邊界熱通量的正算問題。以週期振盪式邊界熱通量為例，表面輻射不僅使溫度降低，而且造成表面溫度非對稱振盪。接著利用溫度的積分解，由一邊界的溫度逆算另一邊界的熱通量。發現量測溫度加誤差的逆算結果，隨著時間經過逐漸變差，此量測誤差效應在有表面輻射時更加明顯。本文也探討邊界熱通量週期、振幅和平板厚度對逆算結果的影響。

Abstract

The objective of this work is to investigate the effects of the surface radiation on the direct and inverse problems of the hyperbolic heat conduction in a finite slab. The non-linear integral equation for the surface temperature derived by using the Laplace transform is solved numerically. First, the direct problems with pulse and periodic on-off boundary heat flux at one of the boundary surface are considered. The surface radiation not only lowers the temperature, but also causes the nonsymmetrical oscillation of the surface temperature for a case with periodic on-off boundary heat flux. Next, the integral solution for the temperature is used to estimate the boundary heat flux from the temporal temperature distribution at the other boundary. The inverse results obtained from the measured temperature with error get worse as time passes. The effect of measurement is obvious for the cases with surface radiation. The effects of the period, the amplitude and the thickness are also investigated.

目錄
中文摘要..........................................................................................................I
英文摘要..........................................................................................................II
誌謝..................................................................................................................III
目錄..................................................................................................................IV
圖目錄..............................................................................................................VI
符號說明..........................................................................................................XII
第一章 緒論................................................................................................1
1-1 研究動機及背景.......................................................................................1
1-2 文章架構...................................................................................................3
第二章 熱波傳遞物理模式........................................................................4
2-1 正算模式...................................................................................................4
2-2 逆算模式...................................................................................................5
第三章 正算問題的解及其數值積分........................................................7
3-1 正算問題的無因次化及積分方程式解...................................................7
3-2 數值方法...................................................................................................9
第五章 逆算問題及其數值方法....................................................................13
4-1 逆算問題...................................................................................................13
4-2 數值方法...................................................................................................14
第五章 結果與討論........................................................................................16
5-1 正算問題之結果與討論...........................................................................16
5-2 逆算問題之結果與討論...........................................................................20
第六章 結論....................................................................................................24
參考文獻..........................................................................................................26
附錄..................................................................................................................29
自述..................................................................................................................87

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