雙層平板內具熱傳導及熱輻射效應之複合逆向熱傳問題

Abstract

本論文主要討論雙層平板內具熱傳導及熱輻射效應之複合逆向熱傳問題，並使用可求解逆向複合熱傳問題的空間推移(space-marching)法，利用物體內之溫度探測器所得內部兩點位置的溫度變化歷程，反算出邊界熱通量、內部溫度分佈及輻射熱傳量。考慮系統為雙層一維雙平行漫射灰體，且表面間具吸收放射與等向性散射灰體介質。 結果顯示本研究所使用之空間推移法能準確的利用半透明物體內部兩點的真實或具量測誤差的溫度歷程反算單層或雙層平板的邊界熱通量及內部溫度分佈等，且其準確度並不會因為量測點之不同而有明顯的改變。本文所採用的逆向方法在固定時間間距下，格點數會有一個最佳值。在此值之下，格點數增加則逆算結果對量測誤差的敏感度將降低，解析能力亦同時降低；但若在最佳值之上，格點數增加將增強逆算結果對量測誤差的敏感度且降低其解析能力。在相同格點數之下，輻射為主的熱傳模式逆向解會較純熱傳導精確，但對量測誤差的靈敏度則幾乎是相同的。

This study presents a systematic analysis of an inverse heat conduction-radiation problem in a two-layer planar medium by applying the space-marching technique. The use of this inverse technique allows for the estimation of the internal radiation fluxes, temperature distributions, and the surface heat flux histories, from transient temperature measurements within the semitransparent layers at two positions. The present analysis considers an absorbing, emitting, isotropically scattering and gray two-layer planar medium bounded by infinite opaque, diffusely absorbing, and diffusely reflecting surfaces. The results showed that the DDO approximation method was a precision and stable method to solve both direct and inverse combined conduction and radiation problem. Moreover, the modified space-marching technique could accurately estimate the surface fluxes and temperature histories of a inverse heat conduction-radiation problem in a semitransparent single-layer or two-layer planar medium from two internal temperature measurements with exact data (predicted values) and simulated experimental data, and the accuracy wasn’t significantly influenced by the sensor locations. The performance of the presented inverse method for a given time step was investigated. Furthermore, there exists an optimal value of grid number to obtain the minimum standard deviation. For a fixed number of grid points, the inverse solutions for the radiation dominant cases are more accurate than that of the pure conduction cases, but the sensitivity to measurement errors was almost the same.