Lagrangian based heat conduction

TL;DR

This paper introduces a Hamiltonian framework for Fourier heat conduction based on a Lagrangian description, allowing for solutions to thermal propagation problems including the Maxwell-Cattaneo-Vernotte model with initial and boundary conditions.

Contribution

It presents a novel Hamiltonian approach to heat conduction derived from a Lagrangian perspective, enabling new solutions to PDEs involving thermal propagation.

Findings

Provides a new solution method for Fourier heat conduction equations.

Extends the approach to Maxwell-Cattaneo-Vernotte type heat transfer.

Offers a framework that incorporates initial and boundary conditions effectively.

Abstract

Based on the Lagrangian description of the dissipative oscillator, the Hamiltonian description of Fourier heat conduction is treated here. The method enables us to calculate the solution of thermal propagation involving the Maxwell-Cattaneo-Vernotte (MCV) telegrapher type also, in which both the initial and the boundary conditions are taken into account. The presented study offers a new kind of solution to certain partial differential equations.