  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.

Applied Physics