模拟传热的罗宾边界条件

IF 2.9 3区 综合性期刊 Q1 MULTIDISCIPLINARY SCIENCES Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2024-03-27 DOI:10.1098/rspa.2023.0850
Eduard Marušić-Paloka, Igor Pažanin
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引用次数: 0

摘要

刚体和流体之间的热交换通常采用罗宾边界条件建模,即通过界面的热通量与两者的温差成正比。这种界面定律只描述单侧热交换。本文的目的是通过严格的数学分析,对罗宾边界条件和传输条件(温度和流量连续性)进行比较。我们的主要结果如下。首先,我们证明了罗宾边界条件的广义版本是合理的。其次,我们证明,如果周围液体的电导率远低于本体的电导率,那么在高对流速度下,用标准罗宾条件取代广义罗宾条件是合理的。另一方面,如果液体的传导性比主体好得多,那么有效边界条件就不是罗宾条件,而是涉及二阶导数。我们坚信,这些发现为热交换过程的物理学带来了新的见解,因此在工程实践中可能会很有用。
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The Robin boundary condition for modelling heat transfer

The heat exchange between a rigid body and a fluid is usually modelled by the Robin boundary condition saying that the heat flux through the interface is proportional to the difference between their temperatures. Such interface law describes only the unilateral heat exchange. The goal of this paper is to compare the Robin boundary condition starting with the transmission condition (the temperature and the flux continuity) using rigorous mathematical analysis. Our main results are the following. We first show that a generalized version of the Robin boundary condition can be justified. Second, we prove that replacing the generalized by the standard Robin condition can be justified for high convection velocity if the conductivity of the surrounding liquid is much lower than that of the body. On the other hand, if the fluid conducts much better than the body, then the effective boundary condition is shown not to be the Robin one, but it involves second-order derivatives. We strongly believe that those findings bring new insights to the physics of the heat exchange processes and, thus, could prove useful in engineering practice.

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来源期刊
CiteScore
6.40
自引率
5.70%
发文量
227
审稿时长
3.0 months
期刊介绍: Proceedings A has an illustrious history of publishing pioneering and influential research articles across the entire range of the physical and mathematical sciences. These have included Maxwell"s electromagnetic theory, the Braggs" first account of X-ray crystallography, Dirac"s relativistic theory of the electron, and Watson and Crick"s detailed description of the structure of DNA.
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