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.

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.

Absence of Oscillations and Resonance in Porous Media Dual-Phase-Lagging Fourier Heat Conduction

2005 ◽  
Vol 127 (3) ◽  
pp. 307-314 ◽  
Author(s):  
Peter Vadasz
Keyword(s):  
Porous Media ◽  
Heat Conduction ◽  
Thermal Equilibrium ◽  
Local Thermal Equilibrium ◽  
Dual Phase ◽  
Thermal Waves ◽  
Conduction Model ◽  
Physical Conditions ◽  
Fourier Heat Conduction ◽  
Thermal Oscillations

The approximate equivalence between the dual-phase-lagging heat conduction model and the Fourier heat conduction in porous media subject to lack of local thermal equilibrium suggested the possibility of thermal oscillations and resonance. The present investigation demonstrates that the physical conditions necessary for such thermal waves and, possibly resonance, to materialize are not attainable in a porous slab subject to constant temperature conditions applied on the boundaries.

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.

Modeling of Effective Stagnant Thermal Conductivity of Porous Media

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Yasuyuki Takatsu ◽  
Takashi Masuoka ◽  
Takahiro Nomura ◽  
Yuji Yamada
Keyword(s):  
Thermal Conductivity ◽  
Porous Media ◽  
Heat Conduction ◽  
Local Thermal Equilibrium ◽  
Two Phase ◽  
Spatially Periodic ◽  
Phase Systems ◽  
Multi Phase ◽  
Theory And Experiments ◽  
Good Agreement

Based on one-dimensional analysis of heat conduction, a general formula for the effective stagnant thermal conductivity of spatially periodic porous media is derived without assuming local thermal equilibrium. Furthermore, we discuss the contribution of the contact area between particles to the effective stagnant thermal conductivity in detail, and the modification of the formula is proposed to predict the actual effective stagnant thermal conductivity for the porous media. The present results are in good agreement with experimental results of Nozad et al. (1985, “Heat Conduction in Multi-Phase Systems I: Theory and Experiments for Two-Phase Systems,” Chem. Eng. Sci., 40(5), pp. 843–855) for a packed-sphere bed.

Analytical and Numerical Modeling of Conductive and Convective Heat Transfer Through Open-Cell Metal Foams

2012 ◽  
Author(s):  
Mehrdad Taheri ◽  
Sanjeev Chandra ◽  
Javad Mostaghimi
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Numerical Modeling ◽  
Convective Heat Transfer ◽  
Effective Thermal Conductivity ◽  
Convective Heat ◽  
Thermal Equilibrium ◽  
Metal Foams ◽  
Local Thermal Equilibrium ◽  
High Porosity

In this paper, a comprehensive analytical and numerical study of conductive and convective heat transfer through high porosity metal foams is presented. In the first part a novel theoretical model for determination of effective thermal conductivity of metal foams is introduced. This general analysis can be applied to any complex array of interconnected foam cells. Assuming dodecahedron unit cell for modeling the structure of metal foams, an approximate equation for evaluation of effective thermal conductivity of foam with a known porosity is obtained. In this approximation method, unlike the previous two-dimensional (2D) models, porosity is the only geometric input parameter used for evaluation of effective thermal conductivity, while its predictions of effective thermal conductivity are in excellent agreement with the previous models. In the second part a 3D numerical model for conduction in metal foam is constructed. The foam has a square cross section and is exposed to constant temperature at both ends and constant heat flux from the sides. We assume local thermal equilibrium (LTE), i.e., the solid and fluid temperatures are to be locally equal. Comparison of the 3D numerical results to the experiments shows very good agreement. The last part of the study is concerned with the 3D numerical modeling of convective heat transfer through metal foams. Experimentally determined values of permeability and Forchheimer coefficient for 10 pores per inch (PPI) nickel foam are applied to the Brinkman-Forchheimer equation to calculate fluid flow through the foam. Local thermal equilibrium (LTE) and local thermal non-equilibrium (LTNE) methods were both employed for heat transfer simulations. While LTE method resulted in faster calculations and also did not need surface area to volume ratio (αsf) and internal convective coefficient (hsf) as its input, it was not accurate for high temperatures. LTNE should be used to obtain distinct local solid and fluid temperatures.

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