In the present study, authors are conceptually showing that the classically considered time limit to use the semi-infinite approximate solutions is highly conservative, particularly at the internal location(s) inside the finite heat conduction medium. Accordingly, a new length scale, which accounts the heat propagation from the far-field boundary condition as well, is proposed to ascertain the prolonged time limit. The proposed time limit is obtained by comparing the temperature distribution in a finite heat conduction problem with its equivalent semi-infinite model. Overall, three standard one-dimensional heat conduction problems are analysed and the proposed time limit is found to be valid in all three problems. The new time limit will certainly boost the utility of the semi-infinite solutions and rejuvenate the interest of the scientific community in such solutions.

中文翻译：

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使用半无限传热解决方案的时间限制：一种新颖的方法

在本研究中，作者从概念上表明，传统上考虑使用半无限近似解的时限是高度保守的，尤其是在有限导热介质内部的位置。因此，提出了一种新的长度标尺，该标尺也考虑了来自远场边界条件的热传播，以确定延长的时限。通过将有限热传导问题中的温度分布与其等效的半无限模型进行比较，可以得出建议的时限。总体上，分析了三个标准的一维热传导问题，发现提出的时限在所有三个问题中均有效。