Legitimacy of the Local Thermal Equilibrium Hypothesis in Porous Media: A Comprehensive Review

Gazy F Al-Sumaily,Mark C Thompson,Hayder A Dhahad,Amged Al Ezzi,Talal Yusaf

doi:10.3390/en14238114

Abstract

Local thermal equilibrium (LTE) is a frequently-employed hypothesis when analysing convection heat transfer in porous media. However, investigation of the non-equilibrium phenomenon exhibits that such hypothesis is typically not true for many circumstances such as rapid cooling or heating, and in industrial applications involving immediate transient thermal response, leading to a lack of local thermal equilibrium (LTE). Therefore, for the sake of appropriately conduct the technological process, it has become necessary to examine the validity of the LTE assumption before deciding which energy model should be used. Indeed, the legitimacy of the LTE hypothesis has been widely investigated in different applications and different modes of heat transfer, and many criteria have been developed. This paper summarises the studies that investigated this hypothesis in forced, free, and mixed convection, and presents the appropriate circumstances that can make the LTE hypothesis to be valid. For example, in forced convection, the literature shows that this hypothesis is valid for lower Darcy number, lower Reynolds number, lower Prandtl number, and/or lower solid phase thermal conductivity; however, it becomes invalid for higher effective fluid thermal conductivity and/or lower interstitial heat transfer coefficient.

Highlights

Porous media appeared as a persuasive passive cooling improver in several engineering applications such as chemical and catalytic packed beds, particle-bed reactors, packed-bed regenerators, solid-matrix heat exchangers, and fixed-bed nuclear propulsion systems
The basic approach commonly used in modelling convection heat transfer in porous media is that assuming local thermal equilibrium LTE amongst the involved phases at every instant of time
The local thermal equilibrium (LTE) condition assumes that the local temperature difference between the fluid and solid phases of the porous system is negligible at any location within the bulk porous medium, which means that both fluid and solid phases have the same temperature at any location

Summary

Introduction

Porous media appeared as a persuasive passive cooling improver in several engineering applications such as chemical and catalytic packed beds, particle-bed reactors, packed-bed regenerators, solid-matrix heat exchangers, and fixed-bed nuclear propulsion systems. In spite of the study of hydrodynamic characteristics in porous media is an old topic in fluid mechanics, see for example Gadomski [1] and Hilfer [2], the convection heat transport within porous media has arisen relatively as a contemporary subject owing to new technologies, see Santamaria-Holek et al [3] In this context, the basic approach commonly used in modelling convection heat transfer in porous media is that assuming local thermal equilibrium LTE amongst the involved phases at every instant of time. The LTE assumption can be generally valid only when the thermal communication between the fluid and the solid phases is effective enough so that the local temperature difference between them is negligibly small. This is an attempt to draw a clear green zone for researchers who will have an attention to use the LTE approach in accurate and realistic circumstances

In Forced Convection

In Free Convection

In Mixed Convection

Findings

Conclusions