Numerical investigation of coupled anomalous diffusion and heat transfer during thermal displacement process in porous media under local thermal equilibrium

2021 ◽  
Author(s):  
Abiola Obembe ◽  
Sidqi A. Abu-Khamsin ◽  
M. Enamul Hossain
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Numerical Investigation ◽  
Anomalous Diffusion ◽  
Thermal Equilibrium ◽  
Local Thermal Equilibrium ◽  
Thermal Displacement

Nanofluid Suspensions as Derivative of Interface Heat Transfer Modeling in Porous Media

2009 ◽  
Author(s):  
Peter Vadasz
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Porous Media ◽  
Heat Conduction ◽  
Thermal Equilibrium ◽  
Local Thermal Equilibrium ◽  
Interface Heat Transfer ◽  
Wire Method ◽  
Special Case ◽  
Heat Conduction Process

Spectacular heat transfer enhancement has been measured in nanofluid suspensions. Attempts in explaining these experimental results did not yield yet a definite answer. Modeling the heat conduction process in nanofluid suspensions is being shown to be a special case of heat conduction in porous media subject to Lack of Local thermal equilibrium (LaLotheq). The topic of heat conduction in porous media subject to Lack of Local thermal equilibrium (LaLotheq) is reviewed, introducing one of the most accurate methods of measuring the thermal conductivity, the transient hot wire method, and discusses its possible application to dual-phase systems. Maxwell’s concept of effective thermal conductivity is then introduced and theoretical results applicable for nanofluid suspensions are compared with published experimental data.

A Paradox of Heat Conduction in Porous Media Subject to Lack of Local Thermal Equilibrium

2006 ◽  
Author(s):  
Peter Vadasz
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Heat Conduction ◽  
Boundary Conditions ◽  
Constant Temperature ◽  
Thermal Equilibrium ◽  
Local Thermal Equilibrium ◽  
Apparent Paradox

Based on the traditional formulation of heat transfer in porous media it is demonstrated that Local Thermal Equilibrium (Lotheq) applies generally for any boundary conditions that are a combination of constant temperature and insulation. The resulting consequences raising an apparent paradox are being analyzed and discussed.

Simulation of heat transfer in a closed-cell porous media under local thermal non-equilibrium condition

2019 ◽  
Vol 29 (8) ◽  
pp. 2478-2500 ◽  
Author(s):  
Chunyang Wang ◽  
Moghtada Mobedi ◽  
Fujio Kuwahara
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Thermal Equilibrium ◽  
Heat Transfer Process ◽  
Local Thermal Equilibrium ◽  
Pore Scale ◽  
Unsteady Heat Transfer ◽  
Content Type ◽  
Closed Cell ◽  
Non Equilibrium

Purpose The purpose of this study is to validate whether the local thermal equilibrium for unsteady state is an appropriate assumption for the porous media with closed pores. It also compares the transient temperatures between the pore scale and volume averaged approaches to prove that the volume averaged method is an appropriate technique for the heat transfer in closed-cell porous media. The interfacial heat transfer coefficient for the closed-cell porous media is also discussed in details. Design/methodology/approach The governing equations for the pore scale and continuum domains are given. They are solved numerically for the pore scale and volume-averaged domains. The results are compared and discussion was done. The performed discussions and explanations are supported with figure and graphics. Findings A local thermal non-equilibrium exits for the closed-cell porous media in which voids are filled with water during the unsteady heat transfer process. Local thermal non-equilibrium condition exists in the cells under high temperature gradient and it disappears when the heat transfer process becomes steady-state. Although a local thermal equilibrium exists in the porous media in which the voids are filled with air, a finite value for heat transfer coefficient is found. The thermal diffusivity of air and solid phase are close to each other and hence a local thermal equilibrium exists. Research limitations/implications The study is done only for the closed-cell porous media and for Rayleigh number till 105. Two common working fluids as water and air are considered. Practical implications There are many applications of porous media with closed pores particularly in the industry, such as the closed-cell metal foam or the closed cells in porous materials such as foods and plastic-based insulation material. The obtained results are important for transient heat transfer in closed-cell porous materials. Social implications The obtained results are important from the transient application of heat transfer in the closed-cell material existing in nature and industry. Originality/value The authors’ literature survey shows that it is the first time the closed-cell porous media is discussed from local thermal non-equilibrium point of view and it is proved that the local thermal non-equilibrium can exist in the closed-cell porous media. Hence, two equations as solid and fluid equations should be used for unsteady heat transfer in a closed-cell porous medium.

Determination of Flow and Heat-Transfer Parameters in Porous Media With Consideration of Density Variation of Working Fluid

2000 ◽  
Author(s):  
W. H. Hsieh ◽  
W. T. Wu
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Equilibrium Model ◽  
Thermal Equilibrium ◽  
Density Variation ◽  
Local Thermal Equilibrium ◽  
Working Fluid ◽  
Flow And Heat Transfer ◽  
Non Local ◽  
Transfer Parameters

Abstract An experimental investigation is conducted to determine the flow and heat-transfer parameters of porous media with the consideration of density-variation effect of the working fluid. The permeability (K), inertial coefficient (F), and local convective heat transfer coefficient (hloc) are determined for two types of metal screens at Reynolds numbers ranging from 20 to 400. A single-blow transient technique combined with a compressible non-local-thermal-equilibrium model determines the hloc. The compressible non-local-thermal-equilibrium model is also adopted in a Levenberg-Marquardt optimization technique for deducing the K and F from measured steady-state pressure drops at different flow rates. Results show that the permeability increases with the increase of the porosity. A set of empirical correlations is obtained for calculating the Nusselt number. Results also show that, under the test condition of this study, consideration of the density-variation effect would improve the accuracy in deducing the K, F, and hloc.

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

Energies ◽  
2021 ◽  
Vol 14 (23) ◽  
pp. 8114
Author(s):  
Gazy F. Al-Sumaily ◽  
Amged Al Ezzi ◽  
Hayder A. Dhahad ◽  
Mark C. Thompson ◽  
Talal Yusaf
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Porous Media ◽  
Thermal Equilibrium ◽  
Solid Phase ◽  
Convection Heat Transfer ◽  
Thermal Response ◽  
Darcy Number ◽  
Industrial Applications ◽  
Local Thermal Equilibrium

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.

A Correlation for Interfacial Heat Transfer Coefficient for Turbulent Flow Over an Array of Square Rods

2005 ◽  
Vol 128 (5) ◽  
pp. 444-452 ◽  
Author(s):  
Marcelo B. Saito ◽  
Marcelo J. S. de Lemos
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Heat Transfer Coefficient ◽  
Turbulent Flow ◽  
Transfer Coefficient ◽  
Energy Equation ◽  
Local Thermal Equilibrium ◽  
Equation Modeling ◽  
Interfacial Heat Transfer Coefficient ◽  
Interfacial Heat Transfer

Interfacial heat transfer coefficients in a porous medium modeled as a staggered array of square rods are numerically determined. High and low Reynolds k-ϵ turbulence models are used in conjunction of a two-energy equation model, which includes distinct transport equations for the fluid and the solid phases. The literature has documented proposals for macroscopic energy equation modeling for porous media considering the local thermal equilibrium hypothesis and laminar flow. In addition, two-energy equation models have been proposed for conduction and laminar convection in packed beds. With the aim of contributing to new developments, this work treats turbulent heat transport modeling in porous media under the local thermal nonequilibrium assumption. Macroscopic time-average equations for continuity, momentum, and energy are presented based on the recently established double decomposition concept (spatial deviations and temporal fluctuations of flow properties). The numerical technique employed for discretizing the governing equations is the control volume method. Turbulent flow results for the macroscopic heat transfer coefficient, between the fluid and solid phase in a periodic cell, are presented.

scholarly journals Numerical investigation of porous stack for a solar-powered thermoacoustic refrigerator

2020 ◽  
Vol 12 (6) ◽  
pp. 168781402093084
Author(s):  
Oumayma Miled ◽  
Hacen Dhahri ◽  
Abdallah Mhimid
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Lattice Boltzmann ◽  
Equation System ◽  
Local Thermal Equilibrium ◽  
Dissipation Term ◽  
Solar Powered ◽  
Boltzmann Method ◽  
Media Form ◽  
Thermoacoustic Refrigerator

This article proposes a numerical analysis for performance improvement of the stack, which represents a crucial element on the solar-powered thermoacoustic refrigerator. The stack is considered as a saturated parallelepiped homogeneous porous media. Numerical simulation of the flow and the heat transfer in the thermoacoustic refrigerator is carried out. The physical flow is governed by the modified Darcy–Brinkmann–Forchheimer model. The governing equations are solved numerically using the lattice Boltzmann method. Furthermore, the local thermal equilibrium assumption is applied to examine heat transfer. Particular attention is paid a new form of the lattice Boltzmann equation system describing the flow and the heat transfer in porous media and fluid regions. The effects of several parameters characterizing the thermal behaviour in the porous medium are studied. The parametric results lead to the optimization of the porous media form. The presence of the viscous dissipation term in the heat transfer formulation within the thermoacoustic system is particularly highlighted, due to its significant effects introduced by the Eckert number.

Heat-Transfer Study of Aluminum-Foam Heat Sink for Electronic Cooling

Volume 4 ◽  
2004 ◽  
Author(s):  
W. H. Hsieh ◽  
J. Y. Wu ◽  
W. H. Shih ◽  
W. C. Chiu
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Temperature Difference ◽  
Heat Sink ◽  
Thermal Equilibrium ◽  
Aluminum Foam ◽  
Local Thermal Equilibrium ◽  
Pore Density ◽  
Gas Phases ◽  
Non Local

The demand of high speed and miniaturization of electronic components results in increased power dissipation requirement for thermal management. In this work, the effects of porosity (ε), pore density (PPI) and air velocity on the heat-transfer characteristics of aluminum-foam heat sinks are investigated experimentally. The phenomenon of non-local thermal equilibrium (NLTE) is also observed and reported. Results show that the Nu increases as the pore density increases, due to the fact that aluminum foam with a larger pore density has a larger heat-transfer area. The Nusselt number also increases with the increase of porosity due to the same reason. It is noted that temperatures of the solid and gas phases of the aluminum foam decrease as Reynolds number increases, caused by the increased convective heat-transfer rate at higher Reynolds number. The deduced temperature difference between solid and gas phases clearly indicates the existence of non-local thermal equilibrium condition within the aluminum-foam heat sink. The increase of the porosity and the pore density enhances the phenomenon of non-local thermal equilibrium. The temperature difference increases with the decrease of Reynolds number and the distance away from the heat source.

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