本文提出以混合拉氏轉換法並配合特徵函數或傅立葉餘弦積分轉換法來解析非傅立葉熱傳導問題及具有熱波效應之生物熱傳問題。本文乃先以特徵函數展開法或傅立葉餘弦積分轉換法將二維統御方程式簡化成一維方程式。而後再以拉氏轉換法、控制體積法與雙曲線形狀函數之混合數值方法來解析簡化後之方程式。此方法之特點為運算過程簡單又能求得精確的數值解。
為了驗證本文方法之有效性與精確性，本文將例舉各種不同型式之問題。文中並探討血流灌注率及加熱功率對生物組織內部溫度分佈的影響，結果顯示本文之數值結果頗吻合其它文獻之結果。二維生物熱傳之熱波問題中統御方程式含有時變量之加熱源，亦能得到合理物理現象下之溫度分佈。

The present study proposes the hybrid technique of the Laplace transform and the Eigenfunction expansion or Fourier-cosine integral transform method to analyze the two-dimensional non-Fourier heat conduction problems and bioheat transfer problems with the wave phenomenon. Due to the application of Eigenfunction expansion method, the two-dimensional governing differential equation is simplified as an one-dimensional partial differential equation, which are then solved efficiently in conjunction with the Laplace transform, control volume method and hyperbolic shape function in order to suppress numerical oscillation due to the wave front discontinue vicinity.
To validate the efficiency and accuracy of the present proposed method, the comparison among the present numerical results, analytical solution and the previous results will be made. The results shows that the estimations solved by the proposed Eigenfunction expansion method were numerically stable, even in the case of two-dimensional hyperbolic bioheat transfer problems with time dependent heat source considered.

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