利用後向特徵值快速求解隔熱壁之溫度分佈

A Feasible Backward-Eigenvalue Method to Speedily Access the Thermal Profile on Heat-Insulating Multilayer

何正義(Je-Ee Ho) ； 黃嘉和(Chia-Ho Huang)

《國立宜蘭大學工程學刊》 10期 (2014/12) Pp. 1-12

https://doi.org/10.6176/BCE.2014.10.11

摘要

於本論文中，後向特徵值法將被推導並運用於快速求解隔熱壁之溫度分佈。其中安置於內層壁的薄片金屬將作為熱通量的照射面，而其他熱絕緣的材料則依序緊密地排列成多層壁；至於各層接觸面間所設定之獨立坐標系統則用來建構多層壁熱傳之特徵方程式。依據熱連續及熱通量守恆的原理，相關特徵參數值將靈活地給定；亦即內部各層之特徵參數值柔性地設為π，而滿足邊界條件之非線性特徵參數則歸結於最內與最外層壁；經後向遞迴程序計算後，非線性的特徵值即可順利地解出；而以往求解程過中產生的非線性疊代困擾於此將可完全的排除。於流明強度900~1250 lux照射下，理論計算值解與實驗結果呈現良好的一致性（其最大誤差不超過15%）；換句話說，以更快之計算速度而獲致整體的熱行為模式於此將獲得印證。

關鍵字

特徵值 ； 絕熱材料 ； 後向特徵值法 ； 遞迴法

並列摘要

In this study, a feasible backward-eigenvalue method is introduced to analyze the temperature distribution of heat-insulating multilayer. In which, a thin-metal sheet, mounted as an inner layer, is subjected to heat flux, and separable thermal insulating material ,in the multilayer, is then well compacted subsequently while independent coordinate specified on the each interface of slabs will be used to construct the governing eigen-equations of heat conduction for multilayers. Base on thermal continuity law including temperature as well as heat flux, each eigen-parameter accessed from the corresponding exterior slab might be feasibly set as π, and those at boundary surface could be left to be constrained by boundary conditions. Thus the difficulty encountered in previous method, arisen from iteratively solving nonlinear eigen- function for each slab, could be fully avoided by leaving these troubles on the first layer and which might be easily solved using backward - eigenvalues recurrence. Compared with analytic and experimental results accessed from the irradiation of illumination falling within 900~1250 lux, both are found to behave a good agreement and their maximum relative error will be less than 20% ,i.e., the faster calculating speed to approach overall thermal behaviour has been confirmed in this study.

並列關鍵字

Eigenvalue ； Thermal insulating material ； Backward-eigenvalue method ； Recurrence