Abstract

A variational model describing a one-dimensional mechanical system in which heat conduction phenomena occur is consistently formulated. Lagrangian variational perspective, too often limited to the study of mechanical phenomena, is extended to study linear irreversible processes, where dissipation and heat production may occur, by generalizing the fundamental ideas and results by Biot (“Linear thermodynamics and the mechanics of solids,” 1958). It is proven here that Cattaneo’s law for heat conduction can be deduced via a variational argument together with the Lord–Shulman model.

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