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A novel nonintrusive technique based on an air-coupled ultrasonic transducer was used to study the hydrodynamic behavior of falling film over metal foam layered horizontal tube. Copper foam having a porosity of 90.5%, brazed over a copper tube of 25.4 mm diameter was used in this study. Falling film thickness distribution in the circumferential direction and the dynamic characteristics of falling film were studied in the falling film Reynolds number range of 356-715, and at a tube spacing of 5 mm and 15 mm. The falling film characteristics over metal foam layered horizontal tubes were compared with that over a plain horizontal tube surface. Heat transfer studies of falling film over metal foam layered tube were studied in an evaporator of a multi-effect desalination system by experiment. It was observed that the falling film heat transfer coefficient was enhanced 2.7 times by the application of metal foam over the plain horizontal tube. The measurements obtained from hydrodynamic and heat transfer studies were compared with the predictions made by a computational model and were found to be in good agreement. Metal foam properties required for the computational model were obtained using a microcomputed tomography-based study. [ABSTRACT FROM AUTHOR]

Open-cell metal foams are known for their superior heat dissipation capabilities. The morphological, pressure drop, and heat transfer characteristics of stochastic metal foams manufactured through traditional "foaming" processes are well established in the literature. However, employment of stochastic metal foams in next-generation heat exchangers is challenged by the irregularity in the pore- and fiber-geometries, limited control on the pore-volume, and an inherent necessity of a bonding agent between foam and the heat source. On the other hand, additive manufacturing (AM) is capable of printing complex user-defined unit cell topologies with customized fiber shapes directly on the substrates subjected to heat load. Moreover, the user-defined regular lattices are capable of exhibiting better thermal and mechanical properties than stochastic metal foams. In this paper, we present a numerical investigation on fully periodic unit-cells of three different topologies, that is, tetrakaidecahedron (TKD), rhombic-dodecahedron (DDC), and Octet with air as the working fluid. Pressure gradient, interfacial heat transfer coefficient, friction factor, and Nusselt number are reported for each topology. Rhombic-dodecahedron yielded the highest averaged interfacial heat transfer coefficient whereas Octet incurred the highest flow losses. Pore diameter, defined as the maximum diameter of a sphere passing through the polygonal openings of the structures, when used as the characteristic length scale for the presentation of Nusselt number and Reynolds number, resulted in a single trendline for all the three topologies. [ABSTRACT FROM AUTHOR]

A one-dimensional analytical validated model for predicting temperature distribution, heat transfer, pressure drop, and fluid pumping power in an open-cell metal foam (OCMF) fin is developed. A foam length optimization technique based on its performance factor (PF) is proposed. Every optimized foam's efficiency is shown to be 33.2%, regardless of its pores per inch (PPI) or porosity. Although it can be applied to other porous materials, the model has been illustrated for aluminum foams with 5-40 PPI and 0.88-0.96 porosity (ε). The highest PPI, lowest porosity foam gives the best unit area goodness factor φu=jH/f, heat transfer, and heat transfer per unit volume QV, while the greatest goodness factor φ (heat transfer rate to fluid pumping power) is achieved by the lowest PPI, lowest porosity foam. The highest PPI, highest porosity foam yields the best heat transfer per unit mass QM. Thus, optimum foam selections strongly depend on the application. An often-used fin optimization criterion recommends that the fin effectiveness should equal or exceed 2. This study shows that the effectiveness of any optimized foam always exceeds 2. However, the converse, i.e., requiring the foam effectiveness to at least equal 2, does not guarantee an optimal foam, which implies that the PF-based optimization criterion is an inclusive one. It is also proved that a previously suggested optimization criterion of maximizing a foam's geometric mean efficiency will result in a suboptimal foam design. [ABSTRACT FROM AUTHOR]

Metal foams have been often used for thermal management due to their favorable characteristics including high specific surface area (SSA), high thermal conductivity, and low relative density. However, they are accompanied by shortcomings including the significant contact resistances due to attachment method, as well as the need for characterization of foam parameters such as pore diameter and SSA. Additive manufactured (AM) metal foams would eliminate the substrate/foam thermal resistance, decrease the need for pre-usage characterization, and allow for tailoring structures, while also taking advantage of the characteristics of traditionally manufactured foams. A commercial, aluminum foam (nominally 5 pores per inch (PPI), 86.5% porosity) was analyzed using X-ray microcomputed tomography, and a custom-designed metal foam based on the cell diameter and porosity of the commercial sample was subsequently manufactured. Reduced domain computational fluid dynamics/heat transfer (CFD-HT) models were compared against experimental data. Postvalidation, the flow behavior, effect of varying attachment thermal conductivities, and thermal performance were numerically investigated, demonstrating the usefulness of validated pore-scale models, as well as the potential for improved performance using AM metal foams over traditionally manufactured foams. [ABSTRACT FROM AUTHOR]

An analytical and numerical study was conducted for estimation of the effective thermal conductivities of curved metal frame core structures, which can replace metal foams, in views of their advantages over the metal foams for both load bearing and heat dissipation. The trajectory of the frame ligament and its cross-sectional area were allowed to vary arbitrarily in the three-dimensional (3D) space. The analytical formula obtained by extending the formula previously proposed by Bai et al. (2017, "A General Expression for the Stagnant Thermal Conductivity of Stochastic and Periodic Structures," ASME J. Heat Transfer, 140(5), p. 052001) was examined by comparing it with the numerical results directly obtained from full 3D numerical computations. An air layer partially filled with a collection of coiled circular rods was treated both analytically and numerically. Furthermore, the effect of lattice nodes on the effective thermal conductivity was investigated by introducing an analytical model with the lattice ligaments merging together at one nodal point. The analytical expressions thus derived for the lattice structures with nodes were applied to tetrahedral structure and octet-truss structure to find their effective thermal conductivities, which are found to agree closely with the 3D numerical results. Thus, the present analytical expressions can be used to customize the structure to meet its desired thermal performance. [ABSTRACT FROM AUTHOR]

This paper discusses about the numerical prediction of forced convection heat transfer through high-porosity metal foams with discrete heat sources in a vertical channel. The physical geometry consists of a discrete heat source assembly placed at the center of the channel along with high thermal conductivity porous metal foams in order to enhance the heat transfer. The novelty of the present work is the use of combination of local thermal equilibrium (LTE) model and local thermal nonequilibrium (LTNE) model for the metal foam region to investigate the temperature distribution of the heat sources and to obtain an optimal heat distribution so as to achieve isothermal condition. Aluminum and copper metal foams of 10 PPI having a thickness of 20 mm are considered for the numerical simulations. The metal foam region is considered as homogeneous porous media and numerically modeled using Darcy Extended Forchheimer model. The proposed methodology is validated using the experimental results available in literature. The results of the present numerical solution indicate that the excess temperature of the bottom heat source reduces by 100 °C with the use of aluminum metal foam. The overall temperature of the vertical channel reduces based on the combination of LTE and LTNE models compared to only LTNE model. The results of excess temperature for both the empty and the metal foam filled vertical channels are presented in this work. [ABSTRACT FROM AUTHOR]

Laminar forced convection heat transfer from a constant temperature tube wrapped fully or partially by a metal porous layer and subjected to a uniform air cross-flow is studied numerically. The main aim of this study is to consider the thermal performance of some innovative arrangements in which only certain parts of the tube are covered by metal foam. The combination of Navier–Stokes and Darcy–Brinkman–Forchheimer equations is applied to evaluate the flow field. Governing equations are solved using the finite volume SIMPLEC algorithm and the effects of key parameters such as Reynolds number, metal foam thermophysical properties, and porous layer thickness on the Nusselt number are investigated. The results show that using a tube which is fully wrapped by an external porous layer with high thermal conductivity, high Darcy number, and low drag coefficient, can provide a high heat transfer rate in the high Reynolds number laminar flow, increasing the Nusselt number almost as high as 16 times compared to a bare tube. The most important result of thisstudy is that by using some novel arrangements in which the tube is partially covered by the foam layer, the heat transfer rate can be increased at least 20% in comparison to the fully wrapped tube, while the weight and material usage can be considerably reduced. [ABSTRACT FROM AUTHOR]

A general expression has been obtained to estimate thermal conductivities of both stochastic and periodic structures with high-solid thermal conductivity. An air layer partially occupied by slanted circular rods of high-thermal conductivity was considered to derive the general expression. The thermal conductivity based on this general expression was compared against that obtained from detailed three-dimensional numerical calculations. A good agreement between two sets of results substantiates the validity of the general expression for evaluating the stagnant thermal conductivity of the periodic structures. Subsequently, this expression was averaged over a hemispherical solid angle to estimate the stagnant thermal conductivity for stochastic structures such as a metal foam. The resulting expression was found identical to the one obtained by Hsu et al., Krishnan et al., and Yang and Nakayama. Thus, the general expression can be used for both stochastic and periodic structures. [ABSTRACT FROM AUTHOR]

he interstitial heat transfer coefficient (IHTC) is a key parameter in the two-energy equation model usually employed to investigate the thermal performance of high porosity open-cell metal foam/paraffin composite phase change material. Due to the existence of weak convection of liquid paraffin through metal foam during phase change process, the IHTC should be carefully determined for a low Reynolds number range (Re=0-1), which however has been rarely addressed in the literature. In this paper, a direct simulation at foam pore scale is carried out to determine the IHTC between paraffin and metal foam at Re=0-1. For this purpose, the cell structures reflecting realistic metal foams are first constructed based on the three-dimensional (3D) Weaire-Phelan foam cell to serve as the representative elementary volume (REV) of metal foam for direct simulation. Then, by solving the Navier-Stokes equations and energy equation for the REV, the influences of Reynolds number (Re), Prandtl number (Pr), foam porosity (ε), and pore density (PPI) on the dimensionless IHTC, i.e., the Nusselt number Nuv, are investigated. According to the numerical results, a correlation of Nuv at Re=0-1 is proposed for metal foam/paraffin composite material, which covers both diffusion-dominated interstitial heat transfer region (Re ≤ 0.1) and convection-dominated interstitial heat transfer region (0.1

An experimental study of heat transfer in metal foam heat exchangers fabricated from 10 and 40 pores per inch (PPI) was conducted. Heat exchangers were made by either brazing Inconel sheets to foam or plasma spraying Inconel skins on the foam. A burner test rig was built to produce high temperature combustion gases at either 550°C or 750°C that were passed over the exposed surface of heat exchangers that were cooled by passing air through them at rates of up to 200 SLPM. Both pressure drop and temperature rise of the air were measured. Friction factors and volumetric heat transfer coefficients were calculated for air velocities varying from 0.1 to 5 m/s and dimensionless correlations to predict these derived. The heat exchangers with 40 PPI foam were measured to have higher heat transfer rates and larger pressure drop than those with 10 PPI foam. Thermal sprayed heat exchangers were found to perform better than those that were brazed since they had lower thermal contact resistance between the external shell and foam struts. An analytical model was developed assuming local thermal nonequilibrium (LTNE) and predictions from model were found to be in good agreement with experimental results. [ABSTRACT FROM AUTHOR]

Open-cell metal foams exhibit distinctive advantages in fluid control and heat transfer enhancement in thermal and chemical engineering. The thermofluidic transport characteristics at pore scale such as topological microstructure and morphological appearance significantly affect fluid flow and conjugated heat transfer in open-cell metal foams, important for practically designed applications. The present study employed an idealized tetrakaidecahedron unit cell (UC) model to numerically investigate the transport properties and conjugated heat transfer in highly porous open-cell metal foams (porosity--0.95). The effects of foam ligaments and nodes (size and cross-sectional shape) on thermal conduction, fluid flow, and conjugated heat transfer were particularly studied. Good agreement was found between the present predictions and the results in open literature. The effective thermal conductivity was found to decrease with increasing node-size-to-ligament ratio, while the permeability and volume-averaged Nusselt number were increased. This indicated that the effects of node size and shape upon thermofluidic transport need to be considered for open-cell metal foams having high porosities. [ABSTRACT FROM AUTHOR]

High porosity open-cell metal foams have captured the interest of thermal industry due to their high surface area density, low weight, and ability to create tortuous mixing of fluid. In this work, application of metal foams as heat sinks has been explored. The foam has been represented as a simple cubic structure and heat transfer from a heated base has been treated analogous to that of solid fins. Based on this model, three performance parameters namely, foam efficiency, overall foam efficiency, and foam effectiveness have been evaluated for metal foam heat sinks. Parametric studies with varying foam length, porosity, pore density, material, and fluid velocity have been conducted. It has been observed that geometric mean of foam efficiency and foam effectiveness can be a useful parameter to exactly determine the optimum foam length. Additionally, the variation in temperature profile of different foams heated from one end has been determined experimentally by cooling these with atmospheric air. The experimental results have been presented for open-cell metal foams (10 and 30 PPI) made of copper/aluminium/Fe–Ni–Cr alloy with porosity in the range of 0.908–0.964. [ABSTRACT FROM AUTHOR]

We present a study on the apparent thermal resistance of metal foams as a thermal interface in electronics cooling applications. Metal foams are considered beneficial for several applications due to its significantly large surface area for a given volume. Porous heat sinks made of aluminum foam have been well studied in the past. It is not only cost effective due to the unique production process but also appealing for the theoretical modeling study to determine the performance. Instead of allowing the refrigerant flow through the open cell porous medium, we instead consider the foam as a thermal conductive network for thermal interfaces. The porous structure of metal foams is moderately compliant providing a good contact and a lower thermal resistance. We consider foam filled with stagnant air. The major heat transport is through the metal struts connecting the two interfaces with high thermally conductive paths. We study the effect of both porosity and pore density on the observed thermal resistance. Lower porosity and lower pore density yield smaller bulk thermal resistance but also make the metal foam stiffen. To understand this tradeoff and find the optimum, we developed analytic models to predict intrinsic thermal resistance as well as the contact thermal resistance based on microdeformation at the contact surfaces. The variants of these geometries are also analyzed to achieve an optimum design corresponding to maximum compliance. Experiments are carried out in accordance with ASTM D5470 standard. A thermal resistance between the range 17 and 5 K cm2IW is observed for a 0.125 in, thick foam sample tested over a pressure range of 1-3 MPa. The results verify the calculation based on the model consisting the intrinsic thermal conductivity and the correlation of constriction resistance to the actual area of contact. The area of contact is evaluated analytically as a function of pore size (5-40 PPI), porosity (0.88-0.95), orientation of struts, and the cut plane location of idealized tetrakaidecahedron (TKDH) structure. The model is developed based on assumptions of elastic deformations and TKDH structures which are applicable in the high porosity range of 0.85-0.95. An optimum value of porosity for minimizing the overall interface thermal resistance was determined with the model and experimentally validated. [ABSTRACT FROM AUTHOR]

The knowledge of thermal transport characteristics is of primary importance in the application of foams. The thermal characteristics of a foam heavily depend on its microstructure and, therefore, have to be investigated at a pore level. However, this analysis is a challenging task, because of the complex geometry of a foam. The use of foam models is a promising tool in their study. The Kelvin and the Weaire-Phelan foam models, among the most representative practical foam models, are used in this paper to numerically investigate heat transfer and pressure drop in metallic foams. They are developed in the "surface evolver" open source software. Mass, momentum, and energy equations, for air forced convection in open cell foams, are solved with a finite-element method, for different values of cell size and porosity. Heat transfer and pressure drop results are reported in terms of volumetric Nusselt number and Darcy-Weisbach friction factor, respectively. Finally, a comparison between the numerical predictions obtained with the two foam models is carried out, in order to evaluate the feasibility to substitute the more complex and computationally heavier Weaire-Phelan foam structure with the simpler Kelvin foam representation. Negligible differences between the two models are exhibited at high porosities. [ABSTRACT FROM AUTHOR]

Because of their light weight, open porosity, high surface area per unit volume, and ther-mal characteristics, metal foams are a promising material for many industrial applica-tions involving fluid flow and heat transfer. The pressure drop and heat transfer in porous media have inspired a number of experimental and numerical studies, and many models have been proposed in the literature that correlate the pressure gradient and the heat transfer coefficient with the mean cell size and porosity. However, large differences exist among results predicted by different models, and most studies are based on idealized per-iodic cell structures. In this study, the true three-dimensional microstructure of the metal foam is obtained by employing x-ray computed microtomography (XCT). This is the "real" structure. For comparison, ideal Kelvin foam structures are developed in thefree-to-use software "surface evolver" surface energy minimization program. These are "ideal" structures. Pressure drop and heat transfer are then investigated in each struc-ture using the CFD module of COMSOL' Multiphysics code. A comparison between the numerical predictions from the real and ideal geometries is carried out. The predictions showed that heat transfer characteristics are very close for low values of Reynolds num-ber, but larger Reynolds numbers create larger differences between the results of the idea! and real structures. Conversely, the differences in pressure drop at any Reynolds number are nearly 100%. Results from the models are then validated by comparing them with experimental results taken from the literature. The validation suggests that the ideal structure poorly predicts the heat transfer and pressure drops. [ABSTRACT FROM AUTHOR]

Thermal energy storage is a distinguishing component of a concentrating solar power (CSP) system, which enables uninterrupted operation of plant during periods of cloudy or intermittent solar availability. Latent thermal energy storage (LTES) which utilizes phase change material (PCM) as a heat storage medium is attractive due to its high energy storage density and low capital cost. However, the low thermal conductivity of the PCM restricts its solidification rate, leading to inefficient heat transfer between the PCM and the heat transfer fluid which carries thermal energy to the power block. To address this limitation, LTES embedded with heat pipes and PCM's stored within the framework of porous metal foam that have one to two orders of magnitude higher thermal conductivity than the PCM are considered in the present study. A transient, computational analysis of the metal foam enhanced LTES system with embedded heat pipes is performed to investigate the enhancement in the thermal performance of the system for different arrangements of heat pipes and design parameters of metal foam, during both charging and discharging operation. [ABSTRACT FROM AUTHOR]

This paper presents a methodology for obtaining the convective heat transfer coefficient from the wall of a heated aluminium plate, placed in a vertical channel filled with open cell metal foams. For accomplishing this, a thermal resistance model from literature for metal foams is suitably modified to account for contact resistance. The contact resistance is then evaluated using the experimental results. A correlation for the estimation of the contact resistance as a function of the pertinent parameters, based on the above approach is developed. The model is first validated with experimental results in literature for the asymptotic case of negligible contact resistance. A parametric study of the effect of different foam parameters on the heat transfer is reported with and without the presence of contact resistance. The significance of the effect of contact resistance in the mixed convection and forced convection regimes is discussed. The procedure to employ the present methodology in an actual case is demonstrated and verified with additional, independent experimental data. [ABSTRACT FROM AUTHOR]

Assuming uniform particulate deposit layer, with deposition layer thickness in the range of 10-400 µm, on the ligaments of a metal foam heat sink, the effects of airborne particle deposition on the steady-state thermohydraulic performance of a metal foam heat sink are examined theoretically. Using a cubic cell model, changes in the foam internal structure, due to deposition, have been theoretically related to the increased pressure drop due to partial blockage of the pores. Our results suggest that the fouled to clean pressure drop ratio is only a function of the ligament to pore diameter ratio. Another interesting observation is that, compared to clean foams, the pressure drop can increase by orders of magnitude depending on the extent to which the pores are blocked. To examine the fouling effects on heat transfer from the foams, a thermal resistance network has been used. Moreover, the heat transfer from metal foams is more affected by fouling at higher fluid velocities. For example, when air is pushed through foams which their ligaments are uniformly covered by particles at 3 mis, up to 15% decrease in the total heat transfer from the heated surface is predicted. [ABSTRACT FROM AUTHOR]

A thermal spray coating process was used to deposit dense 2 mm thick metal skins on the surfaces of square cross-section channels (300 mm χ 20 mm χ 20 mm) of nickel and copper foams with 10 and 40 PPI (pores per inch) pore densities. A heater was wrapped around the channels to apply surface heat-fluxes varying from 427 to 6846 W/m2. Compressed air was blown through the channels at flow rates of 5-80 llmin. Foam and fluid temperature distributions along the length of the channel and the pressure drop across it were measured. The foam was modeled as a porous medium and properties such as permeability Κ and inertial coefficient CF were determined from the experimental data. Local and average convective heat transfer coefficients were calculated from air and foam temperature measurements. Nusselt numbers were calculated and correlated in terms of the Reynolds, Prandtl, and Dairy numbers. Heat transfer to air flowing through a 10 PPI foam channel was shown to have increased nearly seven times compared to that of hollow tube with the same dimensions. [ABSTRACT FROM AUTHOR]

Transient solid-liquid phase change occurring in a phase-change material (PCM) embedded in a metal foam is investigated. Natural convection in the melt is considered. Volume-averaged mass and momentum equations are employed, with the Brinkman-Forchheimer extension to the Darcy law to model the porous resistance. Owing to the difference in the thermal diffusivities between the metal foam and the PCM, local thermal equilibrium between the two is not assured. Assuming equilibrium melting at the pore scale, separate volume-averaged energy equations are written for the solid metal foam and the PCM and are closed using an interstitial heat transfer coefficient. The enthalpy method is employed to account for phase change. The governing equations are solved implicitly using the finite volume method on a fixed grid. The influence of Rayleigh, Stefan, and interstitial Nusselt numbers on the temporal evolution of the melt front location, wall Nusselt number, temperature differentials between the solid and fluid, and the melting rate is documented and discussed. The merits of incorporating metal foam for improving the effective thermal conductivity of thermal storage systems are discussed. [ABSTRACT FROM AUTHOR]

Presents a study which examined the convective heat transfer and friction drag in a duct inserted with aluminum foams. Assumptions and simplifications employed in establishing a mathematical model; Heat transfer characteristics; Development of the empirical correlations of pore Nusselt number for three aluminum foams under a specific length.

3D numerical results are presented to compare the heat transfer augmentation from a plate by using pin fins and metal foams. It is observed that maximizing the inlet velocity and pores per inch maximizes the overall heat transfer rate. The thickness of the foam layer has minimal effect on overall rates of heat transfer, but great effect on the maximum plate temperature. It has been shown that an optimum thickness exists which minimizes the hot spot temperature. Hot spots are generally located in the corners where velocities are the lowest. While the pressure drop remains almost unaltered, the heat transfer increases by 146% and 12% compared with a smooth channel and the optimal pinfin data available in the literature, respectively. Interestingly, the additional mass of the foams, to achieve this performance, is approximately one-quarter of the best pinfin sink quoted above. [ABSTRACT FROM AUTHOR]

High-porosity metal foam (MF) is a popular option for high-performance heat exchangers as it offers significantly higher heat transfer participation area per unit volume compared to other convection enhancement cooling methods. Further, metal foams provide highly tortuous flow paths resulting in thermal dispersion assisted by enhanced mixing. This paper presents experimental and numerical studies and the detailed underlying physics of jet array impingement onto high-porosity (ε ~ 0.95?) thin aluminum foams. The jet and foam configurations were designed for the maximum utilization of the foam area for heat transfer and reduced penalty on the pumping power requirement. Three different pore density foams were tested with three different array-jet impingement configurations. The minimum possible thickness for each pore density was tested, viz., 5 pores-per-inch (PPI): 19?mm, 10 PPI: 12.7?mm, and 20 PPI: 6.35?mm. The baseline case for these foam-based jet impingement configurations was the corresponding configuration of orthogonal jet impingement onto a smooth heated surface, where the distance between the jet-issuing plane and the heated surface was maintained at the foam thickness level. In general, thinner foams facilitated greater jet penetration and increased foam volume usage, resulting in higher heat transfer rates for a given pore density, especially when combined with jet configurations with larger open areas. Finally, we evaluated the thermal hydraulic performance for different foam configurations and the optimum value of a given PPI was found to be at an intermediate rather than the lowest foam thickness. [ABSTRACT FROM AUTHOR]

Metal foams have been widely used in many fields requiring excellent heat and mass transfer performance such as heat exchangers and catalytic reactors. However, the movements of gas--solid interfacial heat transfer characteristic curve with the structural parameters of foams for uncoated metal foams and the washcoat thickness for coated metal foams are not explained in depth. In this work, gas--solid interfacial heat transfer characteristics of metal foams without and with a washcoat were studied in detail in both laminar and turbulent flows using the body-centered-cubic (BCC) unit cell model by the method of computational fluid dynamics, considering that the structural parameters of uncoated/coated foams could be accurately controlled in the numerical method. The movements of gas--solid interfacial heat transfer characteristic curve with the structural parameters of foams and the washcoat thickness were successfully verified and explained using the numerical data in both laminar and turbulent flows. The results show that the porosity not the pore/cell diameter is the reason of the moving of gas--solid interfacial heat transfer characteristic curve for uncoated/coated foams. In laminar flow, the porosity influences interfacial heat transfer characteristic curve through the effective thermal conduction of fluid phase; and in turbulent flow, interfacial heat transfer characteristic curve is affected by porosity through the inertial effect of flow. A new correlation of gas--solid interfacial heat transfer coefficient for uncoated/coated metal foams suitable for both laminar and turbulent flows was proposed by taking into consideration this phenomenon. [ABSTRACT FROM AUTHOR]

Two-dimensional computational fluid dynamics simulations of mixed convection heat transfer through aluminum metal foams partially filled in a vertical channel are carried out numerically. The objective of the present study is to quantify the effect of metal foam thickness on the fluid flow characteristics and the thermal performance in a partially filled vertical channel with metal foams for a fluid velocity range of 0.05-3 m/s. The numerical computations are performed for metal foam filled with 40%, 70%, and 100% by volume in the vertical channel for four different pores per inch (PPIs) of 10, 20, 30, and 45 with porosity values varying from 0.90 to 0.95. To envisage the characteristics of fluid flow and heat transfer, two different models, namely, Darcy Extended Forchheirmer (DEF) and Local thermal non-equilibrium, have been incorporated for the metal foam region. The numerical results are compared with experimental and analytical results available in the literature for the purpose of validation. The results of the parametric studies on vertical channel show that the Nusselt number increases with the increase of partial filling of metal foams. The thermal performance of the metal foams is reported in terms of Colburn j and performance factors. [ABSTRACT FROM AUTHOR]

Fully developed forced convective heat transfer within a channel filled with a functionally graded metal foam matrix was investigated analytically for the case of constant wall heat flux. A series of functionally graded metal foam matrices of the same mass (i.e., the same solidity) were examined in views of their heat transfer performances. The porosity either increases or decreases toward the heated wall following a parabolic function. Among the metal foam matrices of the same mass, the maximum heat transfer coefficient exists for the case in which the porosity decreases toward the heated wall (i.e., more metal near the wall). The heat transfer coefficients in such channels filled with a functionally graded metal foam matrix are found 20-50% higher than that expected from the increase in the effective thermal conductivity. Hence, functionally graded metal foam matrices are quite effective to achieve substantially high heat transfer coefficient with an acceptable increase in pressure drop. [ABSTRACT FROM AUTHOR]

Open-cell metal foams exhibit distinctive advantages in fluid control and heat transfer enhancement in thermal and chemical engineering. The thermofluidic transport characteristics at pore scale such as topological microstructure and morphological appearance significantly affect fluid flow and conjugated heat transfer in open-cell metal foams, important for practically designed applications. The present study employed an idealized tetrakaidecahedron unit cell (UC) model to numerically investigate the transport properties and conjugated heat transfer in highly porous open-cell metal foams (porosity--0.95). The effects of foam ligaments and nodes (size and cross-sectional shape) on thermal conduction, fluid flow, and conjugated heat transfer were particularly studied. Good agreement was found between the present predictions and the results in open literature. The effective thermal conductivity was found to decrease with increasing node-size-to-ligament ratio, while the permeability and volume-averaged Nusselt number were increased. This indicated that the effects of node size and shape upon thermofluidic transport need to be considered for open-cell metal foams having high porosities. [ABSTRACT FROM AUTHOR]

In this paper, a numerical model employing an approximately realistic three-dimensional (3D) foam structure represented by Weaire-Phelan foam cell is developed to study the steady-state heat conduction of high porosity open-cell metal foam/paraffin composite at the pore-scale level. The conduction problem is considered in a cubic representative computation unit of the composite material with a constant temperature difference between one opposite sides of the cubic unit (the other outer surfaces of the cubic unit are thermally insulated). The effective thermal conductivities (ETCs) of metal foam/paraffin composites are calculated with the developed pore-scale model considering small-scale details of heat conduction, which avoids using adjustable free parameters that are usually adopted in the previous analytical models. Then, the reason why the foam pore size has no evident effect on ETC as reported in the previous macroscopic experimental studies is explored at pore scale. Finally, the effect of air cavities existing within solid paraffin in foam pore region on conduction capacity of metal foam/paraffin composite is investigated. It is found that our ETC data agree well with the reported experimental results, and thus by direct numerical simulation (DNS), the ETC data of different metal foam/paraffin composites are provided for engineering applications. The essential reason why pore size has no evident effect on ETC is due to the negligible interstitial heat transfer between metal foam and paraffin under the present thermal boundary conditions usually used to determine the ETC. It also shows that overlarge volume fraction of air cavity significantly weakens the conduction capacity of paraffin, which however can be overcome by the adoption of high conductive metal foam due to enhancement of conduction. [ABSTRACT FROM AUTHOR]

The present study presents a concept of biporous metal foam heat sink applicable to electronic cooling. This heat sink has two metal foam layers arranged in parallel along the primary flow direction, with different metal foam thickness, porosity, and pore density for each layer. The forced convective heat transfer in biporous metal foam heat sink is numerically investigated by employing the Forchheimer-Brinkman extended Darcy momentum equation and local thermal nonequilibrium energy equation. The effects of geometrical and morphological parameters on thermal and hydraulic performance are discussed in detail, and the heat transfer enhancement mechanism of biporous metal foam is analyzed. The thermal performance of biporous metal foam heat sink is compared with that of uniform metal foam heat sink. The results show that the thermal resistance of the biporous metal foam heat sink decreases with decrease of top layer metal foam porosity at a fixed bottom metal foam porosity of 0.9. It is seen that the biporous metal foam heat sink can outperform the uniform metal foam heat sink with a proper selection of foam geometrical and morphological parameters, which is attributed to the presence of high velocity gradient at the boundary layer that can enhance the convective heat transfer. The best observed thermal performance of biporous metal foam heat sink is achieved by employing 30 pores per inch (PPI) metal foam at the bottom layer, with a fixed 50 PPI metal foam at the top layer for the porosities of both layers equal to 0.9, and the optimal thickness of the bottom foam layer is about 1mm. [ABSTRACT FROM AUTHOR]

The article focuses on the use of X-ray Micro-Computed Tomography to obtain accurate geometric information about open-cell metal foams.

An abstract of the article "Exact Solutions for a Thermal Nonequilibrium Model of Fluid Saturated Porous Media Based on an Effective Porosity," by F. Kuwahara and colleagues is presented.

An abstract of the article "Thermal Assessment of Forced Convection Through Metal Foam Heat Exchangers," by A. Tamayol and K. Hooman is presented.

Because of their interesting heat transfer and mechanical properties, metal foams have been proposed for several different applications, thermal and structural. This paper aims at pointing out the effective thermal fluid dynamic behavior of these new enhanced surfaces, which present high heat transfer area per unit of volume at the expense of high pressure drop. The paper presents the experimental heat transfer and pressure drop measurements relative to air flowing in forced convection through four different aluminum foams, when electrically heated. The tested aluminum foams present 5, 10, 20 and 40 PPI (pores per inch), porosity around 0.92-0.93, and 0.02 m of foam core height. The experimental heat transfer coefficients and pressure drops have been obtained by varying the air mass flow rate and the electrical power, which has been set at 25.0 kW m-2, 32.5 kW m-2, and 40.0 kW m-2. The results have been compared against those measured for 40 mm high samples, in order to study the effects of the foam core height on the heat transfer. Moreover, predictions from two recent models are compared with heat transfer coefficient and pressure drop experimental data. The predictions are in good agreement with experimental data. [ABSTRACT FROM AUTHOR]

Melting of phase change materials (PCMs) embedded in metal foams is investigated. The two-temperature model developed accounts for volume change in the PCM upon melting. Volume-averaged mass and momentum equations are solved, with the Brinkman-Forchheimer extension to Darcy's law employed to model the porous-medium resistance. Local thermal equilibrium does not hold due to the large difference in thermal diffusivity between the metal foam and the PCM. Therefore, a two-temperature approach is adopted, with the heat transfer between the metal foam and the PCM being coupled by means of an interstitial Nusselt number. The enthalpy method is applied to account for phase change. The governing equations are solved using a finite-volume approach. Effects of volume shrinkage/expansion are considered for different interstitial heat transfer rates between the foam and PCM. The detailed behavior of the melting region as a function of buoyancy-driven convection and interstitial Nusselt number is analyzed. For strong interstitial heat transfer, the melting region is significantly reduced in extent and the melting process is greatly enhanced as is heat transfer from the wall; the converse applies for weak interstitial heat transfer. The melting process at a low interstitial Nusselt number is significantly influenced by melt convection, while the behavior is dominated by conduction at high interstitial Nusselt numbers. Volume shrinkage/expansion due to phase change induces an added flow, which affects the PCM melting rate. [ABSTRACT FROM AUTHOR]

Heat transfer measurements for natural convection in superposed metal foam and water layers are reported. Two systems heated at the lower boundary are considered: a water-filled cavity with a foam layer on the heated surface and a water-filled cavity with foam layers on the upper and lower surfaces. The present experiments use open cell copper foams with a nominal porosity of 92%, and the relative thicknesses of the water and foam layers are varied. Steady state Nusselt numbers show that the presence of foam on the boundaries enhances overall heat transfer coefficients over that for the water-only layer. Enhancement of overall Nusselt numbers varies from 12% to 60% depending on Rayleigh number. Sublayer configurations with foam on both heat transfer surfaces are more effective for enhancement than a configuration with foam only on the heated surface. [ABSTRACT FROM AUTHOR]

The two-phase flow and boiling heat transfer in horizontal metal-foam filled tubes are experimentally investigated. The results show that the heat transfer is almost doubled by reducing the cell size from 20 ppi to 40 ppi for a given porosity, thanks to more surface area and strong flow mixing for the smaller cell size. The boiling heat transfer coefficient keeps steady rising, albeit slowly, by increasing the vapor quality for high mass flow rates, while the same story does not hold for the cases of low mass flow rates. The flow pattern can be indirectly judged through monitoring the cross-sectional wall surface temperature fluctuations and wall-refrigerant temperature difference. As the operating pressure increases, the boiling heat transfer at low vapor quality (x<0.1) exhibits similar behavior with pool boiling heat transfer, namely, the heat transfer is enhanced by improving the pressure. However the flow boiling heat transfer is suppressed to some extent as the pressure increases. The heat transfer coefficient of copper foam tubes is approximately three times higher than that of plain tubes. [ABSTRACT FROM AUTHOR]

High porosity open-cell metal foam is considered to be an attractive choice for compact heat exchanger applications because of its high area density and superior thermal performance. A systematic study has been made in the present article to verify the suitability of the porous material as an extended heat transfer surface. The area goodness (j/f) factor has been chosen as performance evaluation criterion. This governing parameter has been computed using the existing correlations for the heat transfer and pressure drop coefficients. Conservative estimate shows that the thermohydraulic characteristics of high porosity open-cell metal foam are almost alike, if not better than those of the conventional heat transfer surfaces. Importantly, the analysis has been found to be consistent with the Reynolds analogy. This study helps the designer in making the initial selection of foam surfaces for the heat exchanger application. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Direct simulation of thermal transport in open-cell metal foams is conducted using different periodic unit-cell geometries. The periodic unit-cell structures are constructed by assuming the pore space to be spherical and subtracting the pore space from a unit cube of the metal. Different types of packing arrangement for spheres are considered--body centered cubic, face centered cubic, and the A15 lattice (similar to a Weaire-Phelan unit cell)--which give rise to different foam structures. Effective thermal conductivity, pressure drop, and Nusselt number are computed by imposing periodic boundary conditions for aluminum foams saturated with air or water. The computed values compare well with existing experimental measurements and semiempirical models for porosities greater than 80%. The effect of different foam packing arrangements on the computed thermal and fluid flow characteristics is discussed. The capabilities and limitations of the present approach are identified. [ABSTRACT FROM AUTHOR]

Convective heat transfer in aluminum metal foam sandwich panels is investigated with potential applications to actively cooled thermal protection systems in hypersonic and re-entry vehicles. The size effects of the metal foam core are experimentally investigated and the effects of foam thickness on convective transfer are established. Four metal foam specimens are utilized with a relative density of 0.08 and pore density of 20 pores per inch (ppi) in a range of thickness from 6.4 mm to 25.4 mm, in increments of approximately 6 mm. An exact-shape-function finite element model is developed that envisions the foam as randomly oriented cylinders in cross flow with an axially varying coolant temperature field. A fully developed velocity profile is obtained through a semi-empirical, volume-averaged form of the momentum equation for flow through porous media, and used in the numerical analysis. The experimental results show that larger foam thicknesses produce increased heat transfer levels, but that this effect diminishes for thicker foams. The finite element simulations capture the thickness dependence of the heat transfer process and good agreement between experimental and numerical results is obtained for larger foam thicknesses. [ABSTRACT FROM AUTHOR]

Solid/liquid phase change occurring in a rectangular container with and without metal foams subjected to periodic pulsed heating is investigated. Natural convection in the melt is considered. Volume-averaged mass and momentum equations are employed, with the Brinkman-Forchheimer extension to Darcy's law used to model the porous resistance. A local thermal nonequilibrium model, assuming equilibrium melting at the pore scale, is employed for energy transport through the metal foams and the interstitial phase change material (PCM). Separate volume-averaged energy equations for the foam and the PCM are written and are closed using a heat transfer coefficient. The enthalpy method is employed to account for phase change. The governing equations for the PCM without foam are derived from the porous medium equations. The governing equations are solved implicitly using a finite volume method on a fixed grid. The coupled effect of pulse width and natural convection in the melt is found to have a profound effect on the overall melting behavior. The influence of pulse width, Stefan number, and Rayleigh number on the temporal evolution of the melt front location and the melting rate for both the cases with and without metal foams is investigated. [ABSTRACT FROM AUTHOR]

Many engineering applications require thermal cycling of granular materials. Since these materials generally have poor effective thermal conductivity various techniques have been proposed to improve bed thermal transport. These include insertion of metal foam with the granular material residing in the interstitial space. The use of metal foam introduces a parasitic thermal capacitance, disrupts packing, and reduces the amount of active material. In order to optimize the combined high porosity metal foam-granular material matrix and study local thermal nonequilibrium, multiple energy equations are required. The interfacial conductance coefficients, specific interface area, and the effective thermal conductivities of the individual components, which are required for a multiple energy equation analysis, are functions of the foam geometry. An ideal three-dimensional geometric model of open-celled Duocell® foam is proposed. Computed tomography is used to acquire foam cell and ligament diameter distribution, ligament shape, and specific surface area for a range of foam parameters to address various shortcomings in the literature. These data are used to evaluate the geometric self-consistency of the proposed geometric model with respect to the intensive and extensive geometry parameters. Experimental thermal conductivity data for the same foam samples are acquired and are used to validate finite element analysis results of the proposed geometric model. A simple relation between density and thermal conductivity ratio is derived using the results. The foam samples tested exhibit a higher dependence on relative density and less dependence on interstitial fluid than data in the literature. The proposed metal foam geometric model is shown to be self-consistent with respect to both its geometric and thermal properties. [ABSTRACT FROM AUTHOR]

The use of open-cell metal foam in contemporary technologies is increasing rapidly. Certain simplifying assumptions for the combined conduction/convection heat transfer analysis in metal foam have not been exploited. Solving the complete, and coupled, fluid flow and heat transfer governing equations numerically is time consuming. A simplified analytical model for the heat transfer in open-cell metal foam cooled by a low-conductivity fluid is presented. The model assumes local thermal equilibrium between the solid and fluid phases in the foam, and neglects the conduction in the fluid. The local thermal equilibrium assumption is supported by previous studies performed by other workers. The velocity profile in the foam is taken as non-Darcean slug flow. An approximate solution for the temperature profile in the foam is obtained using a similarity transform. The solution for the temperature profile is represented by the error function, which decays in what looks like an exponential fashion as the distance from the heat base increases. The model along with the simplifying assumptions were verified by direct experiment using air and several aluminum foam samples heated from below, for a range of Reynolds numbers and pore densities. The foam samples were either 5.08- or 20.32-cm-thick in the flow direction. Reasonably good agreement was found between the analytical and the experimental results for a considerable range of Reynolds numbers, with the agreement being generally better for higher Reynolds numbers, and for foam with higher surface area density. [ABSTRACT FROM AUTHOR]

This study investigates and demonstrates the two conflicting effects of the height on the cooling performance of aluminum-foam heat sinks, under the impinging-jet flow condition. In addition, the nonlocal thermal equilibrium phenomena are also investigated. When the H/D (the height to diameter ratio) of the aluminum-foam heat sinks is reduced from 0.92 to 0.15, the Nusselt number of aluminum-foam heat sinks is found to first increase and then decrease. The increase in the Nusselt number is caused by the increased percentage of the cooling air reaching the top surface of the waste-heat generation block, resulting from the reduced flow resistance. The decrease in the Nusselt number is mainly caused by the reduction in the heat-transfer area between the cooling air and the solid phase of the aluminum-foam heat sink. As the porosity and pore density decrease, the Nusselt number increases and the convective heat transfer is enhanced. The correlation between the Nusselt and Reynolds numbers for each of the 15 samples studied in this work is reported. For samples with a H/D>0.31, the temperature difference between the solid and gas phases of aluminum-foam heat sinks decreases with the increase of the distance from the heated surface. The non-local thermal equilibrium regime is observed to exist at low Reynolds number and small dimensionless height. On the other hand, for samples with a H/D⇐0.31, the temperature difference first increases and then decreases with the increase of the distance from the heated surface; the maximum temperature difference is located at z/H 0.25 and is independent of the Reynolds number. [ABSTRACT FROM AUTHOR]