Emergence of Non-Fourier Hierarchies

Area of Science:

• Thermodynamics and Heat Transfer
• Materials Science

Background:

• Fourier's law of heat conduction is insufficient for room-temperature phenomena in heterogeneous materials.
• Non-Fourier heat conduction exhibits size-dependent behavior.
• Generalized heat conduction equations require a thermo-mechanical interpretation.

Purpose of the Study:

• To analyze non-Fourier heat conduction at room temperature from experimental and theoretical perspectives.
• To demonstrate the applicability of the Guyer-Krumhansl equation for modeling heterogeneous materials.
• To interpret generalized heat conduction using a thermo-mechanical background and introduce pseudo-temperature modeling.

Main Methods:

• Experimental observation of non-Fourier heat conduction.
• Application of the Guyer-Krumhansl equation for heterogeneous materials.
• Development of a thermo-mechanical model coupling Fourier heat conduction with elasticity.
• Introduction of pseudo-temperature modeling to explain non-Fourier temperature history.

Main Results:

• The Guyer-Krumhansl equation is a suitable extension of Fourier's law for room-temperature phenomena in heterogeneous materials.
• A generalized heat equation for the temperature field is derived by coupling Fourier heat conduction with elasticity.
• Both approaches highlight the size dependency of non-Fourier heat conduction.
• Pseudo-temperature modeling explains non-Fourier temperature history by mixing Fourier's law solutions.

Conclusions:

• Non-Fourier heat conduction at room temperature can be effectively modeled using the Guyer-Krumhansl equation and pseudo-temperature modeling.
• Size dependency is a critical factor in non-Fourier heat conduction phenomena.
• A thermo-mechanical interpretation provides a deeper understanding of generalized heat conduction equations.