Heat equation on a network using the Fokas method

TL;DR

This paper presents an explicit solution to the heat equation on complex networks of rods using the Fokas method, accommodating arbitrary configurations with continuity conditions at interfaces.

Contribution

It generalizes previous work to handle arbitrary network configurations of rods with continuity conditions, expanding the applicability of the Fokas method.

Findings

Explicit solutions for heat conduction on complex networks

Generalization to arbitrary rod configurations

Applicable to various network topologies

Abstract

The problem of heat conduction on networks of multiply connected rods is solved by providing an explicit solution of the one-dimensional heat equation in each domain. The size and connectivity of the rods is known, but neither temperature nor heat flux are prescribed at the interface. Instead, the physical assumptions of continuity at the interfaces are the only conditions imposed. This work generalizes that of Deconinck, Pelloni, and Sheils, 2014, for heat conduction on a series of one-dimensional rods connected end-to-end to the case of general configurations.