A revised exposition of the Green-Naghdi theory of heat propagation

TL;DR

This paper revises and critically examines the Green-Naghdi heat propagation theories from 1992-3, which incorporate thermal displacement and heat waves, contrasting them with Fourier's classical theory and discussing their applications and limitations.

Contribution

It provides a detailed critique of the Green-Naghdi theories, clarifies their formulation, and suggests directions for future reconsideration and application.

Findings

Green-Naghdi theories incorporate heat waves and thermal displacement.

Criticisms highlight limitations and assumptions in the theories.

The paper encourages re-evaluation of applications and further development.

Abstract

We offer a revised exposition of the three types of heat-propagation theories proposed by Green and Naghdi, in the form they were given in 1992-3. Those theories, which make use of the notion of thermal displacement and allow for heat waves, are at variance with the standard Fourier theory; they have attracted considerable interest, and have been applied in a number of disparate physical circumstances, where heat propagation is coupled with elasticity, viscous flows, etc. However, their derivation is not exempt from criticisms, that we here detail, in hopes of opening the way to reconsideration of old applications and proposition of new ones.