Approximate Analysis for Darcy-Flow Convection in Porous Media With Zero Fluid Conduction

2009 ◽  
Author(s):  
Nihad Dukhan
Keyword(s):  
Porous Media ◽  
Solid Phase ◽  
Convection Heat Transfer ◽  
Fluid Phase ◽  
Constant Heat Flux ◽  
Local Thermal Equilibrium ◽  
Electronic Systems ◽  
Air Cooling ◽  
Equilibrium Equations ◽  
Heat Rejection

The heat rejection device is a key component in virtually all electronic systems. New core materials for compact and efficient heat exchangers or heat rejection devices are contemporary porous media including metal and graphite foam. In such materials the solid phase has a relatively high conductivity, especially when the fluid phase has a low conductivity. This condition is realized in air-cooling thermal management systems. Simple models are needed for scientists and engineers who work with these materials. Approximate engineering analysis for the convection heat transfer inside a two-dimensional rectangular porous media subjected to constant heat flux on one side is presented. The analysis sets the conduction in the fluid’s governing equation to zero, and for simplicity assumes Darcian flow. The Darcian flow assumption is valid far enough from the solid boundaries, ant it prevails for most of the cross section. The non-local-thermal equilibrium equations are significantly simplified and solved. The solid and fluid temperatures decay in what looks like an exponential fashion as the distance from the heated base increases. The results are in good qualitative agreement with more complex analytical and numerical results in the literature. The proposed model may prove to be time-savings for design purposes.

An Engineering Estimate for Plug-Flow Convection in Porous Media Discarding Fluid Conduction

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
Nihad Dukhan
Keyword(s):  
Porous Media ◽  
Solid Phase ◽  
Plug Flow ◽  
Convection Heat Transfer ◽  
Constant Heat Flux ◽  
Heated Wall ◽  
Local Thermal Equilibrium ◽  
Equilibrium Equations ◽  
Non Local ◽  
Flow Through

Metal and graphite foam are relatively new types of porous materials characterized by having high-solid phase conductivities. In many cooling applications of these materials, including high-power electronics, low-conductivity fluids flow through them, e.g., air. A simple approximate engineering solution for the convection heat transfer inside a two-dimensional rectangular porous media subjected to constant heat flux on one side is presented. The conduction in the fluid is set to zero, and for simplicity, a plug flow is considered. As a result, the non-local-thermal equilibrium equations are significantly simplified and solved. The solid and fluid temperatures decay in what looks like an exponential fashion as the distance from the heated wall increases. The results are in good agreement with one more complex analytical solution in the literature, in the region far from the heated wall only.

Approximate Analysis for Darcy-Flow Convection in Cylindrical Porous Media With Zero Fluid Conduction

2011 ◽  
Author(s):  
Nihad Dukhan
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Solid Phase ◽  
Convection Heat Transfer ◽  
Darcy Number ◽  
Darcy Flow ◽  
Heated Wall ◽  
Local Thermal Equilibrium ◽  
Convection Heat ◽  
Equilibrium Equations

Contemporary porous media that are used in cooling designs include metal and graphite foam. These materials are excellent heat transfer cores due to their large surface area density and the relatively high conductivity of the solid phase. Engineering models for convection heat transfer in such media are needed for thermal system design. When the cooling fluid has a low conductivity, e.g., air, its conduction can be set to zero. Engineering analysis for the fully-developed convection heat transfer inside a confined cylindrical isotropic porous media subjected to constant heat flux is presented. The analysis considers the Darcy flow model and high Pe´clet number. The non-local-thermal equilibrium equations are significantly simplified and solved. The solid and fluid temperatures decay in what looks like an exponential fashion as the distance from the heated wall increases. The effects of the Biot number and the Darcy number are investigated. The results are in qualitative agreement with more complex analytical and numerical results in the literature. The solution is of utility for initial heat transfer designs, and for more complex numerical modeling of the heat transfer phenomenon in porous media.

Developing Nonthermal-Equilibrium Convection in Porous Media With Negligible Fluid Conduction

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
Nihad Dukhan
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Porous Media ◽  
Solid Phase ◽  
Separation Of Variables ◽  
Plug Flow ◽  
Constant Heat Flux ◽  
Axial Distance ◽  
Equilibrium Equations ◽  
Solid Phase Conductivity

In certain contemporary technologies, porous media with high solid-phase conductivity are impregnated with low-conductivity fluids, e.g., metal and graphite foam cooled by air. For such cases, an approximate analytical model for the developing heat transfer inside a two-dimensional rectangular porous medium subjected to constant heat flux is presented. The model neglects conduction in the fluid and assumes plug flow. The resulting nonthermal-equilibrium equations are solved for the solid and fluid temperatures by separation of variables. The temperatures decay exponentially as the distance from the heated base increases. The effects of the Biot and Peclet numbers are presented. Fully developed heat-transfer conditions are achieved at an axial distance equal to five times the height of the porous medium, with a constant Nusselt number equal to 3.

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.

Convection Heat Transfer Analysis for Darcy Flow in Porous Media: A New Two-Dimensional Solution

2010 ◽  
Author(s):  
Nihad Dukhan ◽  
Jeff Ratowski
Keyword(s):  
Porous Media ◽  
Solid Phase ◽  
Convection Heat Transfer ◽  
Constant Heat Flux ◽  
Darcy Flow ◽  
Flow In Porous Media ◽  
Heat Transfer Analysis ◽  
Two Dimensional ◽  
Dimensional Solution ◽  
Energy Equations

The two-equation energy equations are solved analytically for the temperature of the solid phase inside a two-dimensional rectangular porous media subjected to constant heat flux on one side. The fluid conduction is neglected in the governing equations and the Darcy flow model is used. Several simplifying assumptions are made regarding the boundary layers. The solid temperature decays in what looks like an exponential fashion as the distance from the heated base increases. Applications of such solution may be found in porous media with high solid phase conductivity cooled by low-conductivity fluids, e.g., open-cell metallic and graphite foams cooled by air.

Thermal Analysis of Multijet Impingement Through Porous Media to Design a Confined Heat Management System

2019 ◽  
Vol 141 (8) ◽  
Author(s):  
Carlos Zing ◽  
Shadi Mahjoob
Keyword(s):  
Porous Media ◽  
High Efficiency ◽  
Solid Phase ◽  
Electronics Cooling ◽  
Jet Impingement ◽  
Fluid Phase ◽  
Volume Averaging ◽  
High Heat Flux ◽  
Base Temperature ◽  
Heat Management

Thermal management has a key role in the development of advanced electronic devices to keep the device temperature below a maximum operating temperature. Jet impingement and high conductive porous inserts can provide a high efficiency cooling and temperature control for a variety of applications including electronics cooling. In this work, advanced heat management devices are designed and numerically studied employing single and multijet impingement through porous-filled channels with inclined walls. The base of these porous-filled nonuniform heat exchanging channels will be in contact with the devices to be cooled; as such the base is subject to a high heat flux leaving the devices. The coolant enters the heat exchanging device through single or multijet impingement normal to the base, moves through the porous field and leaves through horizontal exit channels. For numerical modeling, local thermal nonequilibrium model in porous media is employed in which volume averaging over each of the solid and fluid phase results in two energy equations, one for solid phase and one for fluid phase. The cooling performance of more than 30 single and multijet impingement designs are analyzed and compared to achieve advantageous designs with low or uniform base temperature profiles and high thermal effectiveness. The effects of porosity value and employment of 5% titanium dioxide (TiO2) in water in multijet impingement cases are also investigated.

Convective Instability of the Darcy Flow in a Horizontal Layer With Symmetric Wall Heat Fluxes and Local Thermal Nonequilibrium

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
A. Barletta ◽  
M. Celli ◽  
A. V. Kuznetsov
Keyword(s):  
Rayleigh Number ◽  
Linear Stability ◽  
Solid Phase ◽  
Fluid Phase ◽  
Heat Fluxes ◽  
Local Thermal Equilibrium ◽  
Neutral Stability ◽  
Thermal Nonequilibrium ◽  
Local Thermal Nonequilibrium ◽  
Darcy Rayleigh Number

The linear stability of the parallel Darcy throughflow in a horizontal plane porous layer with impermeable boundaries subject to a symmetric net heating or cooling is investigated. The onset conditions for the secondary thermoconvective flow are expressed through a neutral stability bound for the Darcy–Rayleigh number associated with the uniform heat flux supplied or removed from the walls. The study is performed by taking into account a condition of local thermal nonequilibrium between the solid phase and the fluid phase. The linear stability analysis is carried out according to the normal modes' decomposition of the perturbations to the basic state. The governing equations for the disturbances are solved numerically as an eigenvalue problem leading to the neutral stability condition. If compared with the asymptotic condition of local thermal equilibrium, the regime of local nonequilibrium manifests an enhanced instability. This behavior is displayed by lower critical values of the Darcy–Rayleigh number, eventually tending to zero when the thermal conductivity of the solid phase is much larger than the conductivity of the fluid phase. In this special limit, which can be invoked as an approximate model of a gas-saturated metallic foam, the basic throughflow is always unstable to external disturbances of arbitrarily small amplitude.

Wave propagation in heterogeneous porous media formulated in the frequency-space domain using a discontinuous Galerkin method

Geophysics ◽  
2011 ◽  
Vol 76 (4) ◽  
pp. N13-N28 ◽  
Author(s):  
Bastien Dupuy ◽  
Louis De Barros ◽  
Stephane Garambois ◽  
Jean Virieux
Keyword(s):  
Porous Media ◽  
Wave Propagation ◽  
Galerkin Method ◽  
Frequency Domain ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Solid Phase ◽  
Numerical Models ◽  
Fluid Phase ◽  
Heterogeneous Porous Media

Biphasic media with a dynamic interaction between fluid and solid phases must be taken into account to accurately describe seismic wave amplitudes in subsurface and reservoir geophysical applications. Consequently, the modeling of the wave propagation in heteregeneous porous media, which includes the frequency-dependent phenomena of the fluid-solid interaction, is considered for 2D geometries. From the Biot-Gassmann theory, we have deduced the discrete linear system in the frequency domain for a discontinuous finite-element method, known as the nodal discontinuous Galerkin method. Solving this system in the frequency domain allows accurate modeling of the Biot wave in the diffusive/propagative regimes, enhancing the importance of frequency effects. Because we had to consider finite numerical models, we implemented perfectly matched layer techniques. We found that waves are efficiently absorbed at the model boundaries, and that the discretization of the medium should follow the same rules as in the elastodynamic case, that is, 10 grids per minimum wavelength for a P0 interpolation order. The grid spreading of the sources, which could be stresses or forces applied on either the solid phase or the fluid phase, did not show any additional difficulties compared to the elastic problem. For a flat interface separating two media, we compared the numerical solution and a semianalytic solution obtained by a reflectivity method in the three regimes where the Biot wave is propagative, diffusive/propagative, and diffusive. In all cases, fluid-solid interactions were reconstructed accurately, proving that attenuation and dispersion of the waves were correctly accounted for. In addition to this validation in layered media, we have explored the capacities of modeling complex wave propagation in a laterally heterogeneous porous medium related to steam injection in a sand reservoir and the seismic response associated to a fluid substitution.

Numerical Study of Radiative Heat Flux Emitted by Stainless Wire-Net Porous Media

2020 ◽  
Vol 861 ◽  
pp. 509-513
Author(s):  
Niwat Ketchat ◽  
Bundit Krittacom
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Porous Media ◽  
Radiative Heat ◽  
Solid Phase ◽  
Numerical Study ◽  
Convection Heat Transfer ◽  
Radiative Heat Flux ◽  
Air Velocity ◽  
Lower Volume

Numerical model of the convective-radiative heat transfer of porous media was proposed. A stainless wire-net was used as porous media. The physical properties, consisting of porosity (φ) and optical thickness (τ0), of porous media were independent variables. The air velocity was reported in the form of Reynolds number (Re). Two equations of the conservative energy with local thermal non-equilibrium were analyzed. The gas (θf) and solid (θs) phases of conservative energy equation inside porous media were investigated. The radiative heat flux (ψ) at down-stream of solid phase emitted into outside was dealt by the P1 approximation. From the study, it was found that the level of θf and θs decreased as Re increased because the effect of convection heat transfer. Inversely, the level of ψ increased as increasing Re. The level of θf, θs and ψ were decreased as φ increased owing to a lower volume of material depended on the increasing level of φ resulting to the heat transfer rate became lower. The level of θf, θs and ψ gave increased with τ0 becaues a wider distance in absorping energy leading to a higher emission energy from the porous media was achieved.

Numerical Simulation of Convection Heat Transfer in a Plate Channel with Sintered Copper Porous Ribs

2012 ◽  
Vol 605-607 ◽  
pp. 1350-1355
Author(s):  
Xin Wei Lu ◽  
De Zhi Yang ◽  
Wen Jiong Cao ◽  
Zhao Yao Zhou
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Reynolds Number ◽  
Porous Media ◽  
Convection Heat Transfer ◽  
Copper Plate ◽  
Local Thermal Equilibrium ◽  
Convection Heat ◽  
Sintered Copper ◽  
Plate Channel

Convection heat transfer in a plate channel periodically fitted with sintered copper porous ribs attached to a copper plate was numerically studied. The local thermal equilibrium model was adopted in the energy equation to evaluate the temperature of fluid and solid. The effect of porosity, Reynolds number and heat flux applied to the copper plate on the heat transfer characteristic of the porous media was investigated respectively. The numerical results show that the heat transfer can be enhanced by increasing Reynolds number, decreasing the porosity and the heat transfer enhancement of the porous media took effect significantly when subjected to high heat flux. Detailed development of the porous media temperature field and the Nusselt number of the wall as a function of Reynolds number for different porosity and heat flux were also presented.

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