# Thermal Transport in a Higher-Order Generalized Hydrodynamics

## TL;DR

This paper develops a Higher-Order Generalized Hydrodynamics framework for analyzing thermal transport in classical fluids, incorporating energy density and fluxes of all orders, with implications for technological thermal processes.

## Contribution

It introduces a novel higher-order hydrodynamics model based on kinetic theory, deriving coupled evolution equations and Maxwell times for advanced thermal analysis.

## Key findings

- Derived coupled evolution equations for energy and fluxes.
- Identified Maxwell times as key to motion character.
- Applied order 1 description to thermal prototyping processes.

## Abstract

Thermal transport in classical fluids is analyzed in terms of a Higher-Order Generalized Hydrodynamics (or Mesoscopic Hydro-Thermodynamics), that is, depending on the evolution of the energy density and its fluxes of all orders. It is derived in terms of a Kinetic Theory based on the Non-Equilibrium Statistical Ensemble Formalism. The general system of coupled evolution equations is derived. Maxwell times - which are of large relevance to determine the character of the motion - are derived. They also have a quite important role for the choice of the contraction of description (limitation in the number of fluxes to be retained) in the study of the hydrodynamic motion. In a description of order 1 it is presented an analysis of the technological process of thermal prototyping.