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

Eur Phys J C Part Fields. 2020;80(8):706. doi: 10.1140/epjc/s10052-020-8292-0. Epub 2020 Aug 6.

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.