Cosmological analogies, Lagrangians, and symmetries for convective-radiative heat transfer

TL;DR

This paper explores a formal analogy between cosmological equations and heat transfer models, revealing underlying Lagrangians, symmetries, and mathematical properties that connect these physical systems.

Contribution

It introduces a novel analogy linking cosmology and heat transfer, emphasizing the Lagrangian and symmetry structures of cooling laws.

Findings

Identifies a formal analogy between Friedmann equations and cooling models.

Highlights the role of Lagrangians and symmetries in heat transfer laws.

Provides mathematical insights into the solutions of cooling equations.

Abstract

A formal analogy between the Friedmann equation of relativistic cosmology and models of convective-radiative cooling/heating of a body (including Newton's, Dulong-Petit's, Newton-Stefan's laws, and a generalization) is discussed. The analogy highlights Lagrangians, symmetries, and mathematical properties of the solutions of these cooling laws.