熱波效應對於含傳導與輻射交互作用熱傳問題之影響

Abstract

複合式熱傳遞相關的問題在過去有相當多的學者研究過，然而絕大部分的研究其熱傳導方面皆是以傅利葉熱傳導定律來處理，亦即熱是以擴散的模式來傳遞。此定律意味著當我們對一介質施加一溫度梯度時，瞬間在此介質內部均會有其相對應的熱通量產生。換句話說，就是熱傳遞的速度為無限大。但是一些學者發現傳統的傅利葉定律在某些情況下並不成立，例如在溫度非常低，接近絕對零度、極短暫的時間、溫度或熱通量變化極快速。在上述的情況下熱是以波的形式來傳遞，其速度為有限值且對整個系統的熱傳具有重大的影響。 本篇論文的重點在研究熱波對於單層薄膜介質其傳導與輻射熱傳的影響。本文首先應用修正型的熱通量模式，亦即非傅利葉定律，來處理傳導方面的熱傳。在這裡考慮的是一維系統，並假設兩邊界為不透明、漫射性的放射與反射且為定溫。其中輻射熱傳方程式乃應用P3近似法來求解，非傅利葉及能量方程式則是用MacCormack的顯性預測修正法來處理。探討傳導對輻射參數 N，散射比參數 ，介質的光學厚度 ，這三個參數對介質的影響。結果顯示出，N 比 或 對於介質溫度有更優勢性的影響，且改變 對於介質溫度大小的變化趨勢與改變N 造成的結果相反。 其次本文以實驗的方法來量測一些生物組織的穿透率與反射率，並應用比爾定率(Beer's law)來求其消散係數(Extinction coefficient)頻譜。最後再對這消散係數頻譜取羅斯蘭平均(Rossland mean)，然後應用所得的羅斯蘭消散係數、光學厚度和生物組織的一些物理性質來預測這些生物組織內的熱傳現象。所得到的結果可以提供給在研究生物熱傳學方面的人仕一些參考。

Fourier's law of heat conduction, which is the classical theory of diffusion, postulates a heat flux to be directly proportional to a temperature gradient in a medium. In other words, heat propagates at an infinite speed. However, traditional Fourier's law breaks down under some situations, such as conditions at very low temperature near absolute zero, an extremely short transient duration, and an extremely high rate of change of temperature or heat flux. Some investigators found that the heat propagation velocity of such situations becomes finite and dominant. This study presents an analysis of the combined conduction and radiation heat transfer in a participating, one layer medium to investigate the wave effect on the thermal performance of the medium. The modified heat flux model, which is called non-Fourier law, is employed to treat the conductive heat transfer. Consideration is given to a one-dimensional system with two opaque, diffusely emitting, diffusely reflecting, and isothermal boundary surfaces. P3 approximation method is employed to solve the equation of radiative heat transfer while the MacCormack's explicit predictor-corrector scheme is used to obtain the solutions of hyperbolic heat conduction equation. Three parameters: conduction-to-radiation parameter, the scattering albedo, and the optical thickness of the medium are examined. The results show that N has more dominant influence than or does, and has the inverse trend with N to influence temperature. An experiment is also carried out in the present study to measure the total transmittance and total reflectance of biological bodies. Beer's law is then employed to calculate the spectral extinction coefficient. Finally, taking Rossland mean of these spectral extinction coefficients, and then substituting the Rossland mean extinction coefficient and other properties into our analysis to predict thermal performance in the biological bodies. The results can be contributed as a reference to the researchers in the field of bioheat transfer.