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Imaginary Eigenvalues in Multilayer One-Dimensional Thermal Conduction Problem with Linear Temperature-Dependent Heat Generation
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DOI：10.1016/j.ijheatmasstransfer.2021.120993.png)
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摘要
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Diffusion in a multi-layer body is a common problem in heat and mass transfer, with applications in multiple engineering systems, such as Li-ion battery packs and first-order chemical reactions occurring in a multilayer body. Development of analytical models to describe diffusion in such systems is helpful for both heat and mass transfer. This paper addresses a multi-layer one-dimensional diffusion problem, in which, generation/consumption in each layer is proportional to the local temperature/concentration. This could occur, for example, due to temperature-dependent heat generation or species generation/consumption associated with a first-order chemical reaction. It is shown that eigenvalues of this problem may become imaginary under two distinct conditions. A physical interpretation of these conditions is discussed, and a mathematical requirement for existence of imaginary eigenvalues is derived. The relationships between imaginary eigenvalues and various non-dimensional problem parameters are discussed. It is also shown that the computed temperature in the multilayer body remains real even if some eigenvalues may become imaginary. Therefore, all eigenvalues, whether real or imaginary must be accounted for in temperature computation. While presented in the context of heat transfer, these results are also valid for multi-layer mass transfer problems involving species generation/consumption due to chemical reaction. This work improves the theoretical understanding of diffusion in a multilayer body under conditions relevant for several engineering processes and systems. (C) 2021 Elsevier Ltd. All rights reserved.
Keyword:
Diffusion
Multilayer Body
Eigenvalues
Imaginary Numbers
Li-ion Cells
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5.8
论文数:
2.6W
被引数:
10.2W
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