Transient non-Fourier behavior of large surface bodies

TL;DR

This paper develops a two-dimensional analytical model for large heterogeneous bodies to analyze transient non-Fourier heat conduction, aiding thermal characterization and validation of numerical methods for complex materials.

Contribution

It extends previous one-dimensional non-Fourier heat conduction analysis to two dimensions for large bodies with complex structures.

Findings

Derived steady-state and transient temperature distributions.

Provided heat flux profiles for space-dependent sources.

Validated analytical solutions for complex material analysis.

Abstract

The variety and complexity of heterogeneous materials in the engineering practice are continuously increasing, open-cell metal foams filled with phase change materials are typical examples. These are also having an impact on the recent developments in the energy industry. Earlier room temperature heat pulse experiments on macroscale foam samples showed non-Fourier over-diffusive behavior on a particular time scale. Since there is a need to investigate such complex structures on larger spatial scales and extend the one-dimensional analysis on two-, and three-dimensional settings, here we develop a two-dimensional analytical solution for the Guyer-Krumhansl and Jeffreys-type heat equations in cylindrical coordinates to investigate the transient thermal behavior of large bodies. We provide the steady-state and transient temperature and heat flux distributions for a space-dependent heat source. The solutions presented here will be helpful for the thermal characterization of complex materials and for the validation of numerical methods.