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首页> 外文期刊>International Journal of Refrigeration >Improvement of the exact analytical solutions for combined heat and mass transfer problems obtained with the Fourier method
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Improvement of the exact analytical solutions for combined heat and mass transfer problems obtained with the Fourier method

机译：傅立叶方法获得的传热和传质联合问题的精确解析解的改进

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摘要

Grigor'eva and Nakoryakov presented an analytical solution for combined heat and mass transfer in laminar falling films by means of the Fourier method. The obtained solutions exhibited mathematical instabilities for small flow length, such as oscillations in the mass fraction profile and a mismatch of the inlet temperature. Grigor'eva and Nakoryakov explained these instabilities with the inconsistency of the inlet and boundary conditions and therefore an additional short term solution was introduced. In the present study the established tangent function, that is used to determine the eigenvalues within the Fourier method, is rearranged to a term without domain restrictions. Consequently, more eigenvalues are found, leading to a physical valid solution even for small flow lengths, matching the results of the short term solution perfectly.
机译：Grigor'eva和Nakoryakov提出了一种通过傅立叶方法对层流降膜中的传热传质进行综合分析的解决方案。对于小流量，所获得的解决方案表现出数学上的不稳定性，例如质量分数曲线中的振荡和入口温度的不匹配。 Grigor'eva和Nakoryakov用入口条件和边界条件的不一致解释了这些不稳定性，因此引入了另一种短期解决方案。在本研究中，已建立的切线函数（用于确定傅里叶方法中的特征值）被重新排列为没有域限制的项。因此，发现了更多的特征值，即使对于较小的流量，也得出了物理上有效的解决方案，与短期解决方案的结果完美匹配。

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