Temperature gradient and Fourier's law in gradient-mass harmonic systems
K.V. Reich
TL;DR
This paper investigates heat transfer in a 1D harmonic lattice with position-dependent masses, demonstrating that a temperature gradient can form and Fourier's law can hold under certain conditions.
Contribution
It introduces a model of a gradient-mass harmonic system showing how Fourier's law can emerge in such non-uniform lattices.
Findings
Temperature gradient can form in a gradient-mass harmonic lattice.
Fourier's law can be obeyed in these systems.
The study provides analytical results in the thermodynamic limit.
Abstract
Heat flow and thermal profile in a 1D harmonic lattice with coordinate-dependent masses has been calculated in the thermodynamic limit. It is shown in the particular example of a 1D harmonic lattice with linearly increasing masses that in standard Langevin conditions of contact, a temperature gradient can form, and Fourier's law can be obeyed.
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