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.