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.

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.

scholarly journals Thermal non-equilibrium of porous flow in a resting matrix applicable to melt migration: a parametric study

2021 ◽  
Author(s):  
Laure Chevalier ◽  
Harro Schmeling
Keyword(s):  
Heat Transfer ◽  
Parameter Space ◽  
Thermal Equilibrium ◽  
Scaling Laws ◽  
Numerical Solutions ◽  
Local Thermal Equilibrium ◽  
Physical Parameters ◽  
Minor Effect ◽  
Solid Temperature ◽  
Non Equilibrium

Abstract. Fluid flow through rock occurs in many geological settings on different scales, at different temperature conditions and with different flow velocities. Depending on these conditions the fluid will be in local thermal equilibrium with the host rock or not. To explore the physical parameters controlling thermal non-equilibrium the coupled heat equations for fluid and solid phases are formulated for a fluid migrating through a resting porous solid by Darcy flow. By non-dimensionalizing the equations three non-dimensional numbers can be identified controlling thermal non-equilibrium: the Peclet number Pe describing the fluid velocity, the heat transfer number A describing the local interfacial heat transfer from the fluid to the solid, and the porosity ϕ. The equations are solved numerically for the fluid and solid temperature evolution for a simple 1D model setup with constant flow velocity. Three stages are observed: a transient stage followed by a stage with maximum non-equilibrium fluid to solid temperature difference, ∆Tmax, and a stage approaching the steady state. A simplified time-independent ordinary differential equation for depth-dependent (Tf  – Ts) is derived and analytically solved. From these solutions simple scaling laws of the form (Tf  – Ts) = f (Pe, A, ϕ, H), where H is the non-dimensional model height, are derived. The solutions for ∆Tmax and the scaling laws are in good agreement with the numerical solutions. The parameter space Pe, A, ϕ, H is systematically explored. In the Pe – A – parameter space three regimes can be identified: 1) at high Pe (> 1) strong thermal non-equilibrium develops independently of Pe and A; 2) at low Pe (< 1) and low A (< 1) non-equilibrium decreases proportional to decreasing Pe; 3) at low Pe (<1) and large A (>1) non-equilbrium scales with Pe/A and thus becomes unimportant. The porosity ϕ has only a minor effect on thermal non-equilibrium. The time scales for reaching thermal non-equilibrium scale with the advective time-scale in the high Pe-regime and with the interfacial diffusion time in the other two low Pe – regimes. Applying the results to natural magmatic systems such as mid-ocean ridges can be done by estimating appropriate orders of Pe and A. Plotting such typical ranges in the Pe – A regime diagram reveals that a) interstitial melt flow is in thermal equilibrium, b) melt channelling as e.g. revealed by dunite channels may reach moderate thermal non-equilibrium, and c) the dyke regime is at full thermal non-equilibrium.

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.

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.

Multiscale Modeling of Flow and Heat Transfer in Porous Media

2012 ◽  
Author(s):  
Zhenyu Liu ◽  
Huiru Wang ◽  
Yuanpeng Yao ◽  
Huiying Wu
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Multiscale Modeling ◽  
Convection Heat Transfer ◽  
Scale Model ◽  
Convection Heat ◽  
Pore Scale ◽  
Flow And Heat Transfer ◽  
Macro Scale ◽  
Non Equilibrium

A great number of studies have been carried out to provide the macroscopic descriptions of the overall viscous resistance and heat transfer in the porous media. The new numerical study is necessary to be performed to obtain an understanding of the characteristics at macro/pore scale. The multiscale modeling of the flow and heat transfer in the porous media remains difficult with standard one mesh methods due to the heterogeneity in different scales. In this study, the convection heat transfer is simulated using a macro-scale model including the thermal non-equilibrium assumption. The results, which are validated by the predictions in open literature, show that the convection heat transfer in the porous media can be predicted numerically using a thermal non-equilibrium model. To understand the heat transfer characteristics between the fluid and the solid in porous media, a pore-scale model is developed to obtain the macroscopic properties, especially the convective heat transfer coefficient between two phases. A single cell is simulated to represent a small region in a much larger porous medium. The complex porous structure is reconstructed based on the review of the previous studies and the computational fluid dynamic technique is used to predict flow and heat transfer process. The present work can be extended to study the phase change phenomena in complex structured media, which is normally applied in the latent heat thermal energy storage.

Sign in / Sign up

Export Citation Format

Share Document