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Multilayer one-dimensional Convection-Diffusion-Reaction (CDR) problem: Analytical solution and imaginary eigenvalue analysis
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DOI：10.1016/j.ijheatmasstransfer.2021.121465.png)
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摘要
En 中文
This paper presents a theoretical analysis of a one-dimensional multilayer heat transfer problem with diffusion, advection and linear temperature-dependent heat generation occurring in each layer. A general solution of the problem is derived. Orthogonality of eigenfunctions is proved, and an explicit expression for the eigenequation is derived. The special case of a two-layer body is discussed. It is shown that, un-der specific conditions, this problem admits two types of imaginary eigenvalues, one of which is related to divergence of temperature at large times, corresponding to the thermal runaway phenomenon in bat-teries. The impact of various problem parameters related to diffusion, advection and heat generation on the appearance of imaginary eigenvalues is discussed. Specifically, due to the directional nature of fluid flow, advection in each layer of a two-layer body has opposing impact on the occurrence of imaginary eigenvalues. It is also shown that a balance between heat generation, diffusion and advection determines whether an imaginary eigenvalue is encountered, and consequently, whether thermal runaway occurs. Results presented here expand the theoretical understanding of multilayer heat transfer, and may also contribute towards improved thermal design of multilayer engineering systems such as flow batteries. (c) 2021 Elsevier Ltd. All rights reserved.
Keyword:
Convection-Diffusion-Reaction (CDR)
equation
Multilayer body
Eigenvalues
Imaginary numbers
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IF:
5.8
论文数:
2.6W
被引数:
10.2W
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