线源传导辐射问题的边界追踪精确解

Q1 Mathematics

Partial Differential Equations in Applied Mathematics Pub Date : 2024-12-01 DOI:10.1016/j.padiff.2024.101009

Conway Li , Brendan J. Florio , Neville Fowkes , Miccal Matthews

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引用次数: 0

摘要

边界跟踪是一种利用已知域的边值问题的精确解来生成承认相同解的备选域的技术。在这里，我们使用拉普拉斯方程的线源解来产生新的领域中传导辐射问题的精确解，例如带突出的圆形区域和带短尾或长尾的泪滴形区域。所得到的形状和尺寸是实用的，可用于新型散热器的设计。

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Exact solutions of line-source conduction–radiation problems via boundary tracing

Boundary tracing is a technique whereby exact solutions to boundary value problems in known domains are used to generate alternate domains admitting the same solution. Here we use line-source solutions of Laplace’s equation to produce exact solutions to the conduction–radiation problem in novel domains, such as circular regions with protrusions and teardrop-shaped regions with short or long tails. The shapes and sizes obtained are practical and could be used for novel radiator design.

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