Numerical Study on the Performance of a Tube With Inserted Porous Media of Various Thermal Conductivities

2016 ◽  
Author(s):  
Tariq Amin Khan ◽  
Wei Li
Keyword(s):  
Thermal Conductivity ◽  
Porous Medium ◽  
Porous Media ◽  
Velocity Profile ◽  
Fluid Transport ◽  
Energy Transport ◽  
Numerical Study ◽  
Darcy Number ◽  
Local Thermal Equilibrium ◽  
Working Fluid

Numerical study is performed on the effect of thermal conductivity of porous media (k) on the Nusselt number (Nu) and performance evaluation criteria (PEC) of a tube. Two-dimensional axisymmetric forced laminar and fully developed flow is assumed. Porous medium partially inserted in the core of a tube is investigated under varied Darcy number (Da), i.e., 10−6 ≤ Da ≤ 10−2. The range of Re number used is 100 to 2000 and the conductivity of porous medium is 1.4 to 202.4 W/(m.K) with air as the working fluid. The momentum equations are used to describe the fluid flow in the clear region. The Darcy-Forchheimer-Brinkman model is adopted for the fluid transport in the porous region. The mathematical model for energy transport is based on the one equation model which assumes a local thermal equilibrium between the fluid and the solid phases. Results are different from the conventional thoughts that porous media of higher thermal conductivity can enhance the performance (PEC) of a tube. Due to partial porous media insertion, the upstream parabolic velocity profile is destroyed and the flow is redistributed to create a new fully develop velocity profile downstream. The length of this flow redistribution to a new developed laminar flow depends on the Da number and the hydrodynamic developing length increases with increasing Da number. Moreover, the temperature profile is also readjusted within the tube. The Nu and PEC numbers have a nonlinear trend with varying k. At very low Da number and at a lower k, the Nu number decreases with increasing Re number while at higher k, the Nu number first increases to reach its peak value and then decreases. At higher Re number, the results are independent of k. However, at a higher Da number, the Nu and PEC numbers significantly increases at low Re number while slightly increases at higher Re number. Hence, the change in Nu and PEC numbers neither increases monotonically with k, nor with Re number. Investigation of PEC number shows that at very low Da number (Da = 10−6), inserting porous media of a low k is effective at low Re number (Re ≤ 500) while at high Re number, using porous material is not effective for the overall performance of a tube. However, at a relatively higher Da number (Da = 10−2), high k can be effective at higher Re number. Moreover, it is found that the results are not very sensitive to the inertia term at lower Da number.

Porous Medium Interconnector Effects on the Thermohydraulics of Near-Compact Heat Exchangers Treated as Porous Media

2006 ◽  
Vol 129 (3) ◽  
pp. 273-281 ◽  
Author(s):  
K. Sumithra Raju ◽  
Arunn Narasimhan
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Heat Exchangers ◽  
Fluid Transport ◽  
Energy Transport ◽  
Metal Foam ◽  
Volume Ratio ◽  
Numerical Data ◽  
Darcy Number ◽  
Compact Heat Exchangers

A novel approach of treating near-compact heat exchangers (NCHX) (surface to volume ratio, α=100-300m2∕m3 with hydraulic diameter DM∼6mm) as a “global” porous media, whose thermohydraulic performance is being influenced by the presence of “local” tube-to-tube porous medium interconnectors, connecting the in-line arrangement of tubes (D=2mm) having square pitch of XT=XL=2.25, is investigated in this study using numerical methods. The thermohydraulics of the global porous media (NCHX) are characterized by studying the effect of transverse thickness (δ) and permeability (represented by Dai) of the local metal foam type porous medium interconnectors on the global heat transfer coefficient (Nu) and nondimensional pressure drop (ξ). The fluid transport in the porous medium interconnectors is governed by the Brinkman–Darcy flow model while the volume averaged energy equation is used to model energy transport, with the tube walls kept at constant temperature and exchanging heat with the cooling fluid having Pr=0.7 under laminar flow (10<Re<100). For the chosen NCHX configuration, ξ and Nu increases for an increase in Re and also with an increase in the thickness (δ) of the interconnecting porous medium. However, as the local Darcy number (Dai) of the interconnecting porous medium increases, the ξ decreases but the Nu increases. Treating the heat exchanger as a global porous media this result translates to an increase in the ξ and Nu as the global permeability (represented by Dag) decreases, where the decrease in Dag is because of either an increase in δ or a decrease in Dai. Separate correlations predicting ξ and Nu as a function of Re and Dag (which in turn is correlated to δ and Dai) have been developed for the chosen NCHX configuration, both of which predict the numerical data with ±20% accuracy.

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.

Numerical Analysis of Wooden Porous Media Effects on Heat Transfer From a Staggered Tube Bundle

2008 ◽  
Vol 130 (1) ◽  
Author(s):  
Mohammad Layeghi
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Porous Medium ◽  
Porous Media ◽  
Numerical Analysis ◽  
Pressure Drop ◽  
Tube Bundle ◽  
Numerical Data ◽  
Darcy Number ◽  
Finite Volume Approach

A numerical analysis of forced convective heat transfer from a staggered tube bundle with various low conductivity wooden porous media inserts at maximum Reynolds numbers 100 and 300, Prandtl number 0.7, and Darcy number 0.25 is presented. The tubes are at constant temperature. The extended Darcy–Brinkman–Forchheimer equations and corresponding energy equation are solved numerically using finite volume approach. Parametric studies are done for the analysis of porous medium thermal conductivity and Reynolds number on the local Nusselt number distribution. Three different porous media with various solid to fluid thermal conductivity ratios 2.5, 5, and 7.5 are used in the numerical analysis. The results are compared with the numerical data for tube bundles without porous media insert and show that the presence of wooden porous media can increase the heat transfer from a tube bundle significantly (more than 50% in some cases). It is shown that high conductivity porous media are more effective than the others for the heat transfer enhancement from a staggered tube bundle. However, the presence of a porous medium increases the pressure drop. Therefore, careful attention is needed for the selection of a porous material with good heat transfer characteristics and acceptable pressure drop.

Local Thermal Equilibrium in Forced Convection Through Porous Media

2010 ◽  
Author(s):  
A. Nouri-Borujerdi
Keyword(s):  
Porous Medium ◽  
Pressure Gradient ◽  
Forced Convection ◽  
Thermal Equilibrium ◽  
Fluid Transport ◽  
Convection Heat Transfer ◽  
Darcy Number ◽  
Equation Model ◽  
Temperature Fields ◽  
Local Thermal Equilibrium

Forced convection heat transfer through a channel filled with a porous medium is investigated using perturbation method. Two-energy equation model is utilized to represent the assumption of local thermal non-equilibrium which exists between the solid and fluid phases. The Brinkman-Forchheimer extension of the Darcy model is used to represent the fluid transport within the porous medium. Analytical solution is obtained for both fluid and solid temperature fields incorporating the effects of various pertinent parameters such as the Darcy number, the Biot number, the thermal conductivity and the pressure gradient. It is found that the Darcy number and the pressure gradient have significant effects on the local thermal equilibrium assumption.

scholarly journals Numerical Study of Suspension Filtration Model in Porous Medium with Modified Deposition Kinetics

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 696
Author(s):  
Bekzodjon Fayziev ◽  
Gafurjan Ibragimov ◽  
Bakhtiyor Khuzhayorov ◽  
Idham Arif Alias
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Chemical Engineering ◽  
Numerical Study ◽  
Kinetic Equations ◽  
Sufficient Conditions ◽  
Computational Mathematics ◽  
Deposition Kinetics ◽  
Dynamic Factors ◽  
Suspension Filtration

Filtration is one of the most used technologies in chemical engineering. Development of computer technology and computational mathematics made it possible to explore such processes by mathematical modeling and computational methods. The article deals with the study of suspension filtration in a porous medium with modified deposition kinetics. It is suggested that deposition is formed in two types, reversible and irreversible. The model of suspension filtration in porous media consists of the mass balance equation and kinetic equations for each type of deposition. The model includes dynamic factors and multi-stage deposition kinetics. By using the symmetricity of porous media, the higher dimensional cases are reduced to the one-dimensional case. To solve the problem, a stable, effective and simple numerical algorithm is proposed based on the finite difference method. Sufficient conditions for stability of schemes are found. Based on numerical results, influences of dynamic factors on solid particle transport and deposition characteristics are analyzed. It is shown that the dynamic factors mainly affect the profiles of changes in the concentration of deposition of the active zone.

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.

Lattice Boltzmann Simulations for Thermal Conductivity Estimation in Heterogeneous Materials

2009 ◽  
Vol 283-286 ◽  
pp. 364-369 ◽  
Author(s):  
M.R. Arab ◽  
Bernard Pateyron ◽  
Mohammed El Ganaoui ◽  
Nicolas Calvé
Keyword(s):  
Thermal Conductivity ◽  
Porous Medium ◽  
Lattice Boltzmann ◽  
Numerical Study ◽  
Theoretical Models ◽  
Short Description ◽  
Physical Parameters ◽  
Two Dimensional ◽  
Lattice Boltzmann Simulations ◽  
Boltzmann Method

For simulating flows in a porous medium, a numerical tool based on the Lattice Boltzmann Method (LBM) is developed with regards to the classical D2Q9 model. A short description of this model is presented. This technique, applied to two-dimensional configurations, indicates its ability to simulate phenomena of heat and mass transfer. The numerical study is extended to estimate physical parameters that characterize porous materials, like the so-called Effective Thermal Conductivity (ETC) which is of our interest in this paper. Obtained results are compared with those which could be found analytically and by theoretical models. Finally, a porous medium is considered to find its ETC.

Numerical Study of Free Convection in a Doubly Stratified Non-Darcy Porous Medium Using Spectral Quasilinearization Method

2015 ◽  
Vol 16 (3-4) ◽  
pp. 173-183 ◽  
Author(s):  
D. Srinivasacharya ◽  
Sandile S. Motsa ◽  
O. Surender
Keyword(s):  
Porous Medium ◽  
Free Convection ◽  
Numerical Study ◽  
Saturated Porous Medium ◽  
Nonlinear Partial Differential Equations ◽  
Darcy Number ◽  
Skin Friction Coefficient ◽  
Linearization Method ◽  
Convection Boundary Layer ◽  
Local Skin

AbstractFree convection boundary layer flow past a semi-infinite vertical plate in a doubly stratified fluid-saturated porous medium in the presence of constant suction/injection is analyzed. The flow in the porous medium is described by the Brinkman–Forchheimer-based model. A suitable coordinate transformation is introduced, and the obtained system of non-similar, coupled and nonlinear partial differential equations is solved numerically using the spectral quasi-linearization method. The effects of buoyancy parameter, Darcy number, Forchheimer parameter, suction/injection parameter, thermal and solutal stratification parameters on the dimensionless velocity, temperature and concentration are presented graphically. Further, the local skin friction coefficient, heat and mass transfer rates are presented graphically.

Simulation of water/FMWCNT nanofluid forced convection in a microchannel filled with porous material under slip velocity and temperature jump boundary conditions

2019 ◽  
Vol 30 (5) ◽  
pp. 2329-2349 ◽  
Author(s):  
Ehsan Gholamalizadeh ◽  
Farzad Pahlevanzadeh ◽  
Kamal Ghani ◽  
Arash Karimipour ◽  
Truong Khang Nguyen ◽  
...  
Keyword(s):  
Velocity Profile ◽  
Porous Material ◽  
Forced Convection ◽  
Slip Velocity ◽  
Stokes Equations ◽  
Computer Code ◽  
Darcy Number ◽  
Navier Stokes ◽  
Working Fluid ◽  
Content Type

Purpose This study aims to numerically study the forced convection effects on a two-dimensional microchannel filled with a porous material containing the water/FMWCNT nanofluid. The upper and lower microchannel walls were fully insulated thermally along 15 per cent of their lengths at each end of the microchannel, with the in-between length being exposed to a constant temperature. The slip velocity boundary condition was applied along the microchannel walls. Design/methodology/approach The Navier–Stokes equations were discretized before being solved numerically via a FORTRAN computer code. The following ranges were considered for the studied parameters: slip factor (B) equal to 0.001, 0.01 and 0.1; Reynolds number (Re) between 10 and 100; solid nanoparticle mass fraction (ϕ) between 0.0012 and 0.0025; Darcy number (Da) between 0.001 and 0.1; and porosity factor (ε) between 0.4 and 0.9. Findings Increasing the Da caused a greater increase in the velocity profile than increasing Re, whereas increasing porosity did not affect the velocity profile growth at all. Originality/value This paper is the continuation of the authors’ previous studies. Using the water/FMWCNT nanofluid as the working fluid in microchannels is among the achievements of this study.

Numerical Study of Heat Transfer in Turbulent Cross-Flow Over Porous-Coated Cylinder

2017 ◽  
Author(s):  
N. Rahmati ◽  
Z. Mansoori ◽  
M. Saffar-Avval ◽  
G. Ahmadi
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Nusselt Number ◽  
Turbulent Flows ◽  
Metal Foam ◽  
Numerical Study ◽  
Flow Analysis ◽  
Cross Flow ◽  
Local Thermal Equilibrium ◽  
Turbulent Regime

In the present paper, a numerical study has been conducted to investigate the heat transfer from a constant temperature cylinder covered with metal foam. The cylinder is placed horizontally and is subjected to a constant mean cross-flow in turbulent regime. The Reynolds Averaged Navier-Stokes (RANS) and Darcy-Brinkman-Forchheimer equations are combined and used for flow analysis. The energy equation used assumes local thermal equilibrium between fluid and solid phases in porous media. The k-ω SST turbulence model is used to evaluate the eddy viscosity that is implemented in the momentum and energy equations. The flow in the metal foam (porous media) is in laminar regime. Governing equations are solved using the finite volume SIMPLEC algorithm. The effect of thermophysical properties of metal foam such as porosity and permeability on the Nusselt number is investigated. The results showed that using a metal porous layer with low porosity and high Darcy number in high Reynolds number turbulent flows markedly increases heat transfer rates. The corresponding increase in the Nusselt number is as high as 10 times that of a bare tube without the metal foam.

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