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 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.

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.

scholarly journals Active wall through a porous media foam type: flow and transfer characterization

2020 ◽  
Vol 330 ◽  
pp. 01052
Author(s):  
Rafael Deptulski ◽  
Gisele Vieira ◽  
Rachid Bennacer
Keyword(s):  
Thermal Conductivity ◽  
Porous Media ◽  
Solid Phase ◽  
Cross Flow ◽  
Structured Media ◽  
Medium Porosity ◽  
Flow Through ◽  
Thermodynamic Coupling ◽  
Volume Method ◽  
Solid Phase Composition

Despite the efforts to develop new solutions to achieve the objectives of positive buildings in energy, a few studies in this area has been performed using a porous media foam type. The aim of this paper is to present the behaviour transfers of flow through a multi-structured porous media and to achieve the influence of the porosity and the thermal conductivity properties of the skeletal phase, and the interaction with a cross flow in order to get the equivalent of a perfect insulator. Therefore, in a specially made device, a finite volume method was applied to study a flow through a porous media foam-type, which was simulated to characterize the properties of the equivalent medium in terms of permeability and thermal conductivity. The analysis demonstrates that the solid phase composition and the medium porosity, as well as the distribution of pore size, are preponderant characteristics to constitute a foam structured media. Furthermore, the thermal boundary layer given by a forced convection through the porous medium has demonstrated the important influence of the flow phenomenon in a thermodynamic coupling. Lastly, three optimum configurations for the construction envisaging a balance of depleted thermal and dynamic powers for a relative conductivity *=10 were found between the velocity 2 10-3 (m/s) and 4 10-3 (m/s).

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.

Formulation and Numerical Solution of Non-Local Thermal Equilibrium Equations for Multiple Gas/Solid Porous Metal Hydride Reactors

2000 ◽  
Vol 123 (3) ◽  
pp. 520-526 ◽  
Author(s):  
George M. Lloyd ◽  
A. Razani ◽  
Kwang J. Kim
Keyword(s):  
Boundary Conditions ◽  
Metal Hydride ◽  
Thermal Equilibrium ◽  
Porous Metal ◽  
High Energy ◽  
Local Thermal Equilibrium ◽  
Equilibrium Equations ◽  
Interphase Heat Transfer ◽  
Non Local ◽  
Coupled Reactors

The assumption of local thermal equilibrium (LTE) is very common in the study of reacting flows in porous media. The assumption simplifies the structure of the solutions and places fewer constraints on computational methods for the domain and boundary conditions. However, in certain systems, such as gas/solid metal hydride reactors, the boundary conditions may impose high energy transfer rates which produce slowly evolving phase change fronts coupled with rapid kinetics. Overall performance of the systems is proportional to the release or absorption of hydrogen, and this is sensitively related to temperature. Thus, capturing local departures from LTE is required. This paper directly evaluates the influence of these effects by solving an NLTE (non-local thermal equilibrium) formulation for coupled reactors as a function of the interphase heat transfer coefficient, hsf. The reactor dynamics and overall energy balances are compared to solutions previously obtained from LTE calculations. The results appear to be the first NLTE results for coupled reactors. They confirm the existence of NLTE effects and suggest the magnitude of hsf for which they can be minimized.

Sign in / Sign up

Export Citation Format

Share Document