Creating materials in which heat propagates along a line: theory and numerical results

TL;DR

This paper develops a theoretical and numerical framework for designing materials that direct heat along a specific line, enabling heat-based information transfer, which is a novel concept in thermal management.

Contribution

It introduces a new method to construct potentials for heat equations that guide heat propagation along a line, combining theory and numerical techniques.

Findings

Successful theoretical formulation of heat-guiding materials.

Numerical method for constructing the guiding potential.

Potential for heat-based information transfer applications.

Abstract

In this paper the theory is developed for creating a material in which the heat is transmitted along a given line. This gives a possibility to transfer information using heat signals. This seems to be a novel idea. The technical part of the theory is the construction of the potential $q(x)$. This potential describes the heat equation $u_t = \Delta u - q(x)u$ in the limiting medium which is obtained after the small impedance particles are distributed in a given domain. A numerical method is also established to construct numerically such a potential.