A hierarchy of heat conduction laws
Filippo Dell'Oro, Vittorino Pata
TL;DR
This paper develops a hierarchy of heat conduction equations by progressively approximating Fourier's law through memory effects and integral perturbations, aiming to better model temperature evolution in rigid conductors.
Contribution
It introduces a new family of heat conduction models based on successive approximations of Fourier's law incorporating memory and perturbations.
Findings
Derived a hierarchy of heat conduction equations
Demonstrated improved modeling of temperature evolution
Provided mathematical framework for successive approximations
Abstract
The purpose of this work is to produce a family of equations describing the evolution of the temperature in a rigid heat conductor. This is obtained by means of successive approximations of the Fourier law, via memory relaxations and integral perturbations.
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Taxonomy
TopicsThermoelastic and Magnetoelastic Phenomena · Numerical methods in inverse problems · Advanced Mathematical Modeling in Engineering