Thermal diffusion in branched structures: Metric graph based approach

TL;DR

This paper models heat diffusion in branched structures using metric graphs, providing explicit solutions for linear cases and exploring nonlinear regimes, revealing increased heat transfer intensity.

Contribution

It introduces an analytical approach to heat diffusion on metric graphs and extends it to nonlinear regimes, highlighting differences from linear behavior.

Findings

Explicit solutions for linear heat diffusion on metric graphs

Nonlinear regime shows more intensive heat transfer

Extension of the model to nonlinear heat equations

Abstract

We consider the problem of heat diffusion in branched systems and networks on the basis of a model described in terms of heat equation on metric graphs. Using the explicit analytical solutions of the latter, evolution of the temperature profile and heat flow on each branch are computed. Extension of the study for nonlinear regime is considered using a nonlinear heat equation on metric graphs. It is found that in nonlinear regime is more intensive than that in linear case.