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首页> 外文期刊>International Journal of Heat and Mass Transfer >The time fractional approach for the modeling of thermal therapies: Temperature analysis in laser irradiation
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The time fractional approach for the modeling of thermal therapies: Temperature analysis in laser irradiation

机译：热疗法建模的时间分数方法：激光照射温度分析

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摘要

In this study we assessed the use of the fractional derivative formulation of the heat transmission equation (FDHTE) as an alternative to the classical or parabolic heat transfer equation (PHTE) in the mathematical modeling of some thermal therapy processes. We obtained the FDHTE analytical solutions in two cases: a general case of heat transfer in a finite bar with different and constant temperature in its extremes (without heat source), and the heating by a laser source of a semi-infinite medium which includes a heat source and it was considered in thermal therapies to destroy or alter biological tissue. Both solutions were obtained analytically and compared with the PHTE results. We also compared the FDHTE solution with the results of the hyperbolic heat transfer equation (HHTE), which is another alternative to the PHTE, but is only used for problems in which intense heat is applied to materials for very short times. The results show that the FDHTE can be used as an alternative to the PHTE in thermal therapy processes in which the PHTE theoretical models underestimate or overestimate the temperatures achieved in tissue. Unlike the HHTE, the FDHTE is not restricted to special problems only. We have thus laid the groundwork for the analytical resolution of the problems considered by the FDHTE.
机译：在该研究中，我们评估了传热方程（Fdhte）的分数衍生物制剂作为一些热疗过程的数学建模中的经典或抛物线传热方程（PHTE）的替代方案。我们在两种情况下获得了FDHTE分析解决方案：在其极端（没有热源）中的有限杆中的有限杆中的传热的一般情况，以及由包含a的半无限介质的激光源加热。热源和它被认为是热疗法以破坏或改变生物组织。两种溶液分析并与PHTE结果进行比较。我们还将FDHTE解决方案与双曲传热方程（HHTE）的结果进行了比较，这是PHTE的另一种替代物，但仅用于将强热量应用于非常短的材料的问题。结果表明，FDHTE可以用作热疗过程中PHTE的替代方法，其中PHTE理论模型低估或高估组织中所达到的温度。与HHTE不同，FDHTE仅限于特殊问题。因此，我们为FDHTE考虑的问题的分析解决方案奠定了基础。

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