[Paper Review] The boundary and continual transfer phenomena in fluids and flows

S. L. Arsenjev, I. B. Lozovitski+1 more|ArXiv.org|Apr 7, 2003

Geotechnical and Geomechanical Engineering3 citations

TL;DR

This paper proposes a revised framework for modeling thermal conductivity, viscosity, and diffusion in fluids by incorporating wave-like energy and mass transfer in thermally nonequilibrium, heterogeneous continua. It demonstrates that classical expressions overestimate transfer intensity under non-equilibrium conditions and introduces a corrected quantitative model applicable to non-stationary heat exchange in natural and technical flows.

ABSTRACT

The clearing up of a wave nature of the energy and mass transfer phenomena in classical expressions of the molecular-kinetic theory has allowed to find a quantitative measure of intensity of processes of a thermal conductivity, viscosity and diffusion in conditions of a thermally nonequilibrium and heterogeneous composition continuum. It is rotined that the appearance of a temperature drop in fluid stipulates the appearance of the continuum stratification and formation of the flowing bodies interacting among themselves. It is rotined that the known expressions for a thermal conductivity, viscosity, diffusion and heat convection had been obtained for a thermally equilibrium and homogeneous continuum and produce a maximum quantity of intensity of the transfer processes. The introduced expression is usable for a quantitative estimation of intensity of the transfer processes in fluid and its streams in conditions of the non-stationary heat exchange in natural conditions and technical problems.

Motivation & Objective

• To address the limitations of classical transport equations in thermally nonequilibrium and heterogeneous fluid continua.
• To identify the root cause of overestimation in standard expressions for thermal conductivity, viscosity, and diffusion.
• To develop a corrected quantitative model for transfer intensity that accounts for continuum stratification and wave-like phenomena.
• To enable accurate estimation of transfer processes in non-stationary heat exchange scenarios in natural and technical environments.

Proposed method

• Analyzes the wave nature of energy and mass transfer within the molecular-kinetic theory framework.
• Derives corrected expressions for thermal conductivity, viscosity, and diffusion by accounting for thermodynamic nonequilibrium and heterogeneity.
• Introduces a new formulation that reflects the actual intensity of transfer processes under non-equilibrium conditions.
• Validates the model by showing that classical expressions assume thermal equilibrium and homogeneity, leading to maximum intensity estimates.
• Applies the corrected model to non-stationary heat exchange in natural and technical fluid flows.
• Uses a continuum model with stratification and interacting flowing bodies to represent real fluid behavior under nonequilibrium conditions.

Experimental results

Research questions

• RQ1 Why do classical expressions for thermal conductivity, viscosity, and diffusion overestimate transfer intensity in real fluid systems?
• RQ2 How does the wave nature of energy and mass transfer affect transport phenomena in nonequilibrium fluid continua?
• RQ3 What is the quantitative impact of continuum stratification and non-equilibrium conditions on transport intensity?
• RQ4 How can existing transport equations be corrected to reflect actual transfer intensity in non-stationary heat exchange?
• RQ5 In what ways do boundary effects and flowing body interactions influence the overall transfer process in heterogeneous fluids?

Key findings

• Classical expressions for thermal conductivity, viscosity, and diffusion are valid only for thermally equilibrium and homogeneous continua, where they yield maximum transfer intensity.
• The appearance of a temperature gradient in a fluid leads to continuum stratification and the formation of interacting flowing bodies.
• The wave nature of energy and mass transfer is fundamental and must be accounted for in nonequilibrium conditions to avoid overestimation.
• The proposed corrected expression provides a more accurate quantitative measure of transfer intensity in non-stationary heat exchange scenarios.
• The model is applicable to both natural fluid systems and technical problems involving non-equilibrium heat transfer.
• The study reveals that the standard formulations fail to represent real fluid behavior under non-equilibrium conditions, necessitating a revised theoretical framework.