在體外組織內圓柱型發熱源附近之二維非穩態溫度分佈

Two-Dimensional Unsteady-State Temperature Profiles around a Cylindrical Heat Source in an in vitro Tissue

林紀廷(Chi-ting Lin)

指導教授 ： 洪賑城

大同大學/工程學院/化學工程學系所/碩士(2011年)

摘要

本研究探討在體外組織內圓柱型發熱源附近之二維非穩態溫度分佈。分別探討以下三種情形: (1)單一圓柱型發熱源之熱傳遞；(2)兩個平行圓柱型發熱源之間熱傳遞；以及(3)單一圓柱型發熱源和平行血管間之熱傳遞。
針對上述三種狀況，本研究分別建立一個二維非穩態溫度分佈之數學模式。先利用四階有限差分法將偏微分方程式轉換為聯立常微分方程式，再利用四階Predictor-Corrector Method及自行發展之Fortran程式解出二維之溫度分佈隨時間變化之關係。
從模擬結果發現，組織之溫度隨r之增加而快速下降，此乃組織內溫度上升主要靠熱傳導，而組織之導熱度卻很小所致。二維的溫度分佈在徑向(r方向)之結果與一維的溫度分佈相似，但在軸向(z方向)則有顯著之差別。當發熱源之熱通量在軸向之分佈均勻時，二維模式之模擬結果顯示軸向的溫度分佈為中央凸起之曲線，此乃熱量在組織邊緣散失至空氣而導致溫度下降所致。若發熱源之熱通量分佈為中間凸起且兩邊對稱時，軸向的中點溫度更明顯得高於邊緣溫度；而當熱通量分佈為中間凹下且兩邊對稱時，軸向的溫度分佈則較均勻。再者，當溫度越高時，軸向之不均勻度越大，意指高溫時一維模式(假設軸向溫度均一)有相當的誤差。

關鍵字

熱療 ； 溫度分佈 ； 電腦模擬 ； 熱傳

並列摘要

Two-dimensional (2D) unsteady-state temperature profiles around a cylindrical heat source in an in vitro tissue have been studied. Comparison of the temperature profiles between the results of this study and that of previous one-dimensional (1D) unsteady-state model has also been investigated. Three heat transfer cases have been studied, including (1) heat transfer around a single cylindrical heat source, (2) heat transfer between two cylindrical heat sources, and heat transfer between a single cylindrical heat source and a parallel blood vessel.
A two-dimensional unsteady-state mathematical model has been developed for each of the above-mentioned case. Fourth-order finite difference was used to transfer the governing partial differential equation to simultaneous ordinary differential equations. Fourth-order Predictor- Corrector Method and Fortran program developed in this laboratory were then used to solve the 2D temperature profiles as function of time.
It has been found from the simulation results that the temperature decreases rapidly along the radial direction, due that the temperature increase in the tissue is resulted from heat conduction and the heat conductivity of the tissue is small. Temperature profiles of 2D model are similar to that of 1D model in radial direction. However, significant difference in axial temperature profiles is found between 1D and 2D models. When heat flux of the heat source is flat in axial direction, 2D simulation results show that temperature profiles are convex in axial direction, due to heat loss at the boundary. When heat flux is convex in axial direction, the temperature at the center point of heat source is even higher. However, when heat flux is concave in axial direction, the temperature profile becomes uniform. In addition, non-uniformity of temperature profile along axial coordinate increases with increasing temperature, indicating 1D model, which assumes uniform temperature in axial direction, might have significant error at high temperature.

並列關鍵字

heat transfer ； temperature profile ； thermal therapy ； computer simulation

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