Emergence of non-Fourier hierarchies

Abstract

The non-Fourier heat conduction phenomenon on room temperature is analyzed from various aspects. The first one shows its experimental side, in what form it occurs and how we treated it. It is demonstrated that the Guyer-Krumhansl equation can be the next appropriate extension of Fourier's law for room temperature phenomena in modeling of heterogeneous materials. The second approach provides an interpretation of generalized heat conduction equations using a simple thermomechanical background. Here, Fourier heat conduction is coupled to elasticity via thermal expansion, resulting in a particular generalized heat equation for the temperature field. Both of the aforementioned approaches show the size dependency of non-Fourier heat conduction. Finally, a third approach is presented, called pseudo-temperature modeling. It is shown that non-Fourier temperature history can be produced by mixing different solutions of Fourier's law. That kind of explanation indicates the interpretation of underlying heat conduction mechanics behind non-Fourier phenomena.

References in corpus (12)

• Generalized heat conduction in heat pulse experiments
• Universal heat conduction -- the thermodynamics of some weakly nonlocal theories
• Deviation from the Fourier law in room-temperature heat pulse experiments
• Guyer-Krumhansl-type heat conduction at room temperature
• Weakly nonlocal irreversible thermodynamics - the Guyer-Krumhansl and the Cahn-Hilliard equations
• Thermodynamical consistency of the Dual Phase Lag heat conduction equation
• Models of ballistic propagation of heat at low temperatures
• Generalized heat-transport equations: Parabolic and hyperbolic models
• Thermodynamic hierarchies of evolution equations
• Kinematic quantities of finite elastic and plastic deformation
• Objective thermomechanics
• Elastic, thermal expansion, plastic and rheological processes - theory and experiment

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• On the rarefied gas experiments
• Novel evaluation method for non-Fourier effects in heat pulse experiments
• A case study of non-Fourier heat conduction using Internal Variables and GENERIC
• Size effects and beyond-Fourier heat conduction in room-temperature experiments
• Continuum modeling perspectives of non-Fourier heat conduction in biological systems