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首页> 外文期刊>International Journal of Heat and Mass Transfer >Imaginary Eigenvalues in Multilayer One-Dimensional Thermal Conduction Problem with Linear Temperature-Dependent Heat Generation
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Imaginary Eigenvalues in Multilayer One-Dimensional Thermal Conduction Problem with Linear Temperature-Dependent Heat Generation

机译：具有线性温度依赖性发热的多层一维热传导问题中的虚构特征值

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摘要

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.
机译：在多层体中的扩散是热量和传质中的常见问题，在多个工程系统中的应用，例如在多层体中发生的锂离子电池组和一阶化学反应。在这种系统中描述扩散的分析模型的开发是有助于热量和传质。本文解决了多层一维扩散问题，其中，每层的生成/消耗与局部温度/浓度成比例。例如，这可能发生由于与一阶化学反应相关的温度依赖性发热或物种产生/消耗。结果表明，在两个不同的条件下，该问题的特征值可能变得虚构。讨论了对这些条件的物理解释，衍生出存在假想的数学要求。讨论了虚拟值和各种非维度问题参数之间的关系。还表明，即使某些特征值可能变为虚构，多层体中的计算温度也仍然是真实的。因此，所有特征值，是否必须在温度计算中占真实或虚构。虽然在传热的背景下呈现，但这些结果也适用于由于化学反应而涉及物种产生/消耗的多层传质问题。在对多个工程过程和系统相关的条件下，这项工作提高了多层体中扩散的理论理解。

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