Heat Transfer In Metal Foams Research Articles

Heat Transfer and Thermal Energy Storage Enhancement by Foams and Nanoparticles

The use of innovative methods for the design of heating, cooling, and heat storage devices has been mainly oriented in the last decade toward the use of nanofluids, metal foams coupled with working fluids, or phase change materials (PCMs). A network of nine Italian universities achieved significant results and innovative ideas on these topics by developing a collaborative project in the last four years, where different approaches and investigation techniques were synergically employed. They evaluated the quantitative extent of the enhancement in the heat transfer and thermal performance of a heat exchanger or thermal energy storage system with the combined use of nanofluids, metal foams, and PCMs. The different facets of this broad research program are surveyed in this article. Special focus is given to the comparison between the mesoscopic to macroscopic modeling of heat transfer in metal foams and nanofluids, as well as to the experimental data collected and processed in the development of the research.

Experimental investigation of the heat transport and pressure drop in open-cell polyurethane foams

Foam-like materials have a large specific surface area and complex structure that promotes flow turbulence, which makes them useful for heat transfer. In the literature, heat transfer in metal foams (MF) with high thermal conductivity is mainly considered. In the present paper, an experimental study of the hydraulic and heat transfer characteristics of a rectangular channel filled with polyurethane foam (PUF) inserts with a thermal conductivity of 0.2 W⋅m−1⋅K−1 in the air flow was carried out. The open-cell PUF samples had 20 and 80 pores per inch (PPI), 0.97 and 0.98 porosity, 269 µm and 60 µm fiber diameter, respectively. The Reynolds number, based on the fiber diameter ranged from 0.04 to 50. From the results of hydraulic tests, friction coefficients were determined based on the fiber diameter and permeability. The Forchheimer coefficient was 0.198 and 0.318 for 20 and 80 PPI samples, respectively. The permeability was 1.889 10−7 ⋅m2 and 7.535 10−9 ⋅m2 for 20 and 80 PPI samples, respectively. The Nusselt number for both tested PUF samples was correlated with the Reynolds number based on the fiber diameter in a power law with the Reynolds number exponent and constant equal to 0.61 and 0.037 respectively. The intensity of heat transfer in the PUF samples was 7–12 times lower than that in MF. However, a significant heat transfer enhancement is still possible compared to the empty channel up to 7 times. The heat transfer performance of PUF was higher compared to the empty channel, but the thermal performance factor was lower than one. Nevertheless, in practical situations where the mass or cost of the heat exchanger is preferable, PUF can be considered as a heat transfer intensifier.

Forced convection of nanofluids in metal foam: An essential review

The combination of the high conductivity of nanofluids with the huge accessible surface area of open-cell metal foam would indeed be a superb heat exchange technology. While individual ingredients of this technology have been separately investigated, the combination of the two has received only scant attention. Actually, there are only few studies that are focused on nanofluids flow and heat transfer in metal foam. This paper is intended to serve as an orientation for researchers who are interested in both nanofluids heat transfer and metal foam. The paper thus includes discussion of various aspects of nanofluids and their heat-transfer applications, as well as fundamentals of flow and heat transfer of ordinary fluids in metal foam. A section on recent heat transfer studies in metal foam is included, and another section on pore-scale modeling of transport in metal foam is provided. Nanofluids are presented in terms of their definition, brief history, preparation methods, theoretical models, properties, and engineering applications related to heat transfer. The paper then moves to describe metal foam and its morphology, as well as current understanding and theoretical treatment of flow and heat transfer in this class of highly-porous media. Key heat transfer and flow properties of the foam are outlined. The paper also presents the case for nanofluids forced convection heat transfer in open channels to serve as a background for the more complex case that involves heat transfer in porous media in general. The case of forced convection of nanofluids in metal foam in particular is presented next. Studies including complex effects, e.g. magnetism, are briefly described. Based on the above information, some key findings, conclusions and recommendations are made for interested researches.

Pore-scale simulation of forced convection heat transfer in metal foams with uniform and gradient structures

Because of their large specific surface areas, metal foams are commonly used in studies of enhanced heat transfer. Modified metal foams with gradient structures are often chosen to reduce high pressure drop. Using computational fluid dynamics (CFD), forced convective heat transfer of metal foam samples for uniform and gradient structures with the same porosity and pore per inch (PPI) were investigated. To study the effect of gradient porosity under the premise of constant control porosity. First, heat transfer was examined in relation to gradient orientation. Gradient metal foam showed a 27.25% improvement in overall heat transfer performance when using the arrangement from small to large porosity than in the opposite direction. In addition, their performance was compared with that of uniform metal foam with 10 PPI and 0.88 porosity. The results showed that for 0.88 porosity, the gradient structure reduced the pressure drop by 23.66% and improved the overall heat transfer performance by 12.07% relative to the uniform structure. The gradient structure was better than the uniform structure at a given porosity value. The sudden change in geometry at the gradient interface of a gradient structure caused changes in flow and heat transfer compared to a uniform structure.

Heat transfer of pulsating water flow through aluminum-foam channel under asymmetric constant heat flux boundary condition

In the present study, the effect of pulsating inlet velocity condition on heat transfer in metal foam was investigated experimentally. Square wave shaped water velocity profiles with different amplitudes and frequencies were applied to the inlet of a rectangular channel filled with aluminum foam having 20 pores per inch and a porosity of 91.8%. A constant heat flux (12787 W/m2) was applied to one side of the porous channel. The non-heated surfaces were insulated. The surface temperatures, water inlet and outlet temperatures and volumetric flow rates were measured and recorded. The dimensionless flow frequency parameter (M) and dimensionless flow amplitude (Rem) parameter were changed in the ranges 4.8–7.3 and 492–1388, respectively. The results showed that there was a strong relationship between average Nusselt number and flow velocity amplitude. Generally, average Nusselt number was seen to increase with increasing frequency parameter and/or amplitude parameter. Correlations for the local time-averaged and surface-averaged Nusselt numbers are proposed. A meaningful comparison between steady-state and pulsating heat transfer is provided. It showed that heat transfer advantages of pulsating flow were only present for a certain low range of Reynolds number, beyond which pulsating flow heat transfer approached that of steady state.

Experimental study of the effect of metal foams on subcooled flow boiling heat transfer of water and developing a correlation for predicting heat transfer

This paper has investigated the effect of different porosities (0.80–0.90) of the metal foam pipes on heat transfer coefficient and pressure drop of subcooled flow boiling of water experimentally. The metal foam pipe with 0.80 porosity has increased the Nusselt number and pressure drop by 41 % and 21 % compared to the 0.90 metal foam pipe, respectively. The heat transfer of water phase change in a porous medium has received less attention due to the complexities of the problem. One of the challenges in this field is the absence of a correlation for predicting heat transfer in metal foams. In this paper, a systematic method based on dimensionless numbers considering the essential parameters, like mass flux, subcooling, and heat flux, was used to provide a correlation for calculating the Nu-number based on 106 experimental points. The mean absolute deviation (MAD) of the results predicted by the new correlation is 8.9 %, and it predicts 95 % of the database with ±20 %.

Study on enhanced heat transfer performance of open-cell metal foams based on a hexahedron model

Due to its high heat transfer performance, the open-cell metal foam has a great potential of applications in heat exchanger industries. Based on the cell structure of the perforated metal foam, a simplified hexahedral structure model was proposed herein. The fluid flow in metal foams was simulated by computational fluid dynamics software. The accuracy of the model was verified by experiments. Based on the numerical simulation, heat transfer performance and the mechanism of enhanced heat transfer were investigated and discussed. The results show that the hexahedron model proposed in this article is feasible and accurate. The heat transfer and pressure drop properties of metal foams were numerically calculated and analyzed at the inlet air velocity of 1–5 m/s. At a certain PPI (pores per inch) and porosity, with the increase of Reynolds number Re, both the heat transfer coefficient h and pressure drop ΔP/L increase gradually. The comprehensive performance of convective heat transfer of metal foams with a lower PPI is relatively better. Increasing PPI or decreasing porosity is conducive to the destruction of the fluid boundary layer, enhancing the fluid disturbance, thus forming a vortex at the back of the skeleton and strengthening the heat transfer.

Thermal analysis in the evaporation of flowing thin liquid film confined by gradient or double-layered porous layer subjected to air jet impingement

The porous metal foam subjected to air jet impinging is set above thin liquid fluid passing through the heating surface to maintain its thickness, in which the heat from heating surface is released in the convection with the thin liquid film to the surroundings, as well as across the thin liquid film and metal foam to the outside surface where the evaporation and convection occur. Local thermal non-equilibrium (LTNE) occurs, so the double energy equations together with Brinkman-Darcy model are employed to describe the heat transfer in metal foam, as well as N–S equations account for the flow of thin liquid film. The effects of the different porosity and particle diameter distributions (e.g. constant, linearly increasing/decreasing and stepwise increasing/decreasing), as well as thickness ratio between the bottom and upper layers with different porosities and particle diameters in stepwise variation on the cooling performances are numerically analyzed. The simulations are validated with the published experiment data. The lower heating surface and larger heat transfer coefficient (HTC) occur in the presented mode with the relatively lower porosity and particle diameter. The 67.47% rise ratio of the peak HTC in the mode with porosity of 0.3 happens than that with porosity of 0.9. The optimized thickness ratio together with the porosity and particle diameter in the bottom and upper layers influence the heat to be transported in the convection with liquid fluid to the downstream side or across the metal foam to its outside surface. All results can be considered into the promotion and application of coupling the air jet impingement and porous metal foam above thin liquid film to enhance heat transfer.

Simulating Solid-Liquid Phase-Change Heat Transfer in Metal Foams via a Cascaded Lattice Boltzmann Model.

A cascaded lattice Boltzmann (CLB) model is constructed for simulating heat transfer in metal-foam-based solid-liquid phase change materials (PCMs). The present model captures the phase interface implicitly via the enthalpy methodology, and to avoid iterations in simulations, the CLB equation of the PCM employs the enthalpy as the basic evolution variable through modifying the cascaded collision process. Numerical results demonstrate the effectiveness and practicability of the CLB model for investigating heat transfer in solid-liquid PCMs with metal foams. The effects of the inertial coefficient, permeability and porosity on the melting process are investigated. The results indicate that the empirical correlations of inertial coefficient and permeability based on packed beds overestimate the melting rate at high porosities. Moreover, the porosity has significant impact on phase-change processes. The melting rate increases as the porosity of the metal foam decreases since heat conduction through high thermal conductive metal foam dominates the total heat transfer.

Comparison of forced convective heat transfer between pillar and real foam structure under high Reynolds number

Owing to the complex structure of open-cell foam, Kelvin cell have been widely used to represent foam structures in recent years. In this study, Kelvin cells (pillar model) with different porosities (90%, 95%) and cells per inch (CPI) values (11, 21, 32), as well as foam structures with different porosities (87%, 90%) and 20 pores per inch, were fabricated to investigate forced convective heat transfer in metal foams using computational fluid dynamics (CFD). A comparison between the pillar model and foam structures showed that they had similar changing rule in pressure drops, although the pillar model exhibited 49.2% better comprehensive heat-transfer properties at 90 m/s. The transverse area of the throat and the microstructure of the skeleton had a significant effect on the pressure drop. The heat-transfer behavior can be improved by increasing the CPI and optimizing the joints of the pillar model. Furthermore, the area goodness factors of pillar model with the 95% porosity and 32 CPI is 78.7% better than model with 90% porosity and 11 CPI. Optimization of the transverse area of the throat and the shapes of the skeleton and joints is a potential method for improving the comprehensive heat-transfer performance of Kelvin cells.

Pore-scale simulation of forced convection heat transfer under turbulent conditions in open-cell metal foam

Previously, extensive efforts have been made in investigating heat transfer in open-cell metal foams in order to better understand and apply them in engineering applications. As a step in this direction, this study prepared five three-dimensional models of copper foam with various porosities (0.82, 0.87, and 0.90) and pores per inch (PPI) (10, 20, and 40) using X-ray computed tomography and several software applications to simulate forced convection heat transfer in a metal foam at a high velocity. The effects of porosity, PPI, and closed pores on the pressure drop and heat transfer properties were investigated. The results indicated that the pressure drop and heat transfer coefficient were more sensitive to porosity than PPI. However, the specific surface area of the metal foam significantly affected the volumetric heat transfer performance. Additionally, the area goodness factors (j/f) were used to evaluate the comprehensive heat transfer performance (CHTP) of each sample. The value of j/f decreased rapidly in the velocity range of 0–20 m/s but slowly in the range of 20–70 m/s, and sample 40–0.87 exhibited a better CHTP. Moreover, the closed pores in the metal foam had a significant effect on the pressure drop, heat transfer properties, and CHTP due to the obstructions posed by the closed pores. Our work helps provide a better understanding for the application of metal foam in heat transfer enhancement at high velocities.

Effect of Pore Distribution on Melting Behavior of Paraffin in Fractal Metal Foam**Supported by the National Natural Science Foundation of China under Grant No. 51706101, Key Laboratory of Solar Energy Science and Technology Foundation of Jiangsu Province under Grant No. KLSST201704, and the Fundamental Research Funds for the Central Universities under Grant No. 30917011328

An unsteady model of melting heat transfer in metal foam filled with paraffin is developed and numerically analyzed. In the model, the pore distribution of metal foam is described by Sierpinski fractal. By this fractal description, six types of metal foams with the identical porosity, different pore distributions are reconstructed. The effect of pores distribution on the heat transfer performance of the paraffin/copper foam composite is emphatically investigated. The solid-liquid distribution, the evolution of the melting front, the dynamic temperature response and the total melting time in these six fractal structures are all examined and analyzed. The results indicate that, the pores distribution has a significant impact on the melting heat transfer of the paraffin in the metal foam. When the first-level fractal pore is located near the heat source boundary, the thermal hysteresis effect of the paraffin on the solid matrix heat transfer is more significant. If the cross-sectional length of the pores along the normal direction of heat transfer is larger, the heat transfer barrier of the solid matrix is greater. It is favorable for the paraffin heat transfer when the pores specific surface area is larger.

Pore-scale investigation of gravity effects on phase change heat transfer characteristics using lattice Boltzmann method

Latent heat thermal energy storage (LTES) has been recommended to complicated aerospace systems due to the excellent ability of storing thermal energy in recent years. Metal foam, as an effective additive to enhance the effective thermal conductive coefficient of phase change materials, has been wildly used in the LTES system. In support of the future space exploration, solid–liquid phase change within metal foam under different gravitational accelerations and corresponding heat transfer characteristics are investigated in this work to enhance understanding of heat transfer capability in reduced gravity conditions. A pore-scale lattice Boltzmann method with the double distribution functions is developed to study the solid–liquid phase change problems with the natural convection heat transfer in metal foam. Here, microstructure of metal foam is experimentally obtained by the use of X-ray computed tomography. Two numerical validation cases are performed, one for fluid–solid conjugate heat transfer problem, and the other for melting process in a square cavity without the porous media. The presented lattice Boltzmann results are in good agreement with previous analytical and numerical results. Based on the analysis of temperature and velocity fields during melting within metal foam, it is found that the clockwise circulation, caused by the temperature gradient, leads to the inhomogeneous distribution of liquid–solid interface along vertical direction. What’s more, gravity effects on the temperature and velocity fields together with the average Nusselt number and liquid fraction coefficient are investigated. Results show that with the decrease of gravitational accelerations from 1g to 0g, the maximum vertical velocity reduces and the thickness of velocity boundary layer thickens accordingly, and results in the pronounced reduction of average Nusselt number and melting rate. The natural convection appears to be even more tenuous as gravitational acceleration decreases, leading to the dominant heat transfer mechanism transited from convection to conduction, and finally alleviating the phase change process. The liquid fraction under 0g, 0.01g and 0.1g conditions are 54.6%, 58.9% and 67.9% respectively of that under 1g conditions at Fo = 0.06. In addition, porosity effects on phase change heat transfer characteristics are discussed by comparing the liquid fraction with porosity of 0.9, 0.94 and 1. It is found that metal foam with lower porosity shows higher effective thermal conductivity and outstanding heat transfer performance, while the restriction on natural convection should not be neglected, especially for melting region which is dominated by natural convection.

Volumetric Convective Heat Transfer Coefficient Model for Metal Foams

ABSTRACTThis study investigates the heat transfer in metal foams assuming that all the foam cells are cubic. An improved model for the volumetric convective heat transfer coefficient of metal foam was obtained by considering the convective heat transfer and the thermal conduction in the connected foam ligaments. Numerical simulations of a metal foam-filled channel were performed using the local thermal non-equilibrium model to evaluate the model. The theoretical and experimental data agree better with the present model than with other models. The velocity gradient near the metal foam-filled channel wall is greater than in an empty channel, with the wall boundary layer becoming thinner. The temperature differences between the fluid and solid phases are predicted by the model with the pore density affecting the volumetric convective heat transfer coefficient more than the porosity. The volumetric convective heat transfer coefficient significantly increases as the pore density increases. However, the relationship between the volumetric convective heat transfer coefficient and the porosity is not linear. As the porosity increases, the volumetric convective heat transfer coefficient first increases and then decreases. The effect of the solid thermal conductivity on the volumetric convective heat transfer coefficient has an upper limit with a critical value of the solid thermal conductivity for the present conditions.

Numerical simulation of heat transfer in metal foams

This paper reports a numerical study of forced convection heat transfer in high porosity aluminum foams. Numerical modeling is done considering both local thermal equilibrium and non local thermal equilibrium conditions in ANSYS-Fluent. The results of the numerical model were validated with experimental results, where air was forced through aluminum foams in a vertical duct at different heat fluxes and velocities. It is observed that while the LTE model highly under predicts the heat transfer in these foams, LTNE model predicts the Nusselt number accurately. The novelty of this study is that once hydrodynamic experiments are conducted the permeability and porosity values obtained experimentally can be used to numerically simulate heat transfer in metal foams. The simulation of heat transfer in foams is further extended to find the effect of foam thickness on heat transfer in metal foams. The numerical results indicate that though larger foam thicknesses resulted in higher heat transfer coefficient, this effect weakens with thickness and is negligible in thick foams.

Enthalpy-based multiple-relaxation-time lattice Boltzmann method for solid-liquid phase-change heat transfer in metal foams.

In this paper, an enthalpy-based multiple-relaxation-time (MRT) lattice Boltzmann (LB) method is developed for solid-liquid phase-change heat transfer in metal foams under the local thermal nonequilibrium (LTNE) condition. The enthalpy-based MRT-LB method consists of three different MRT-LB models: one for flow field based on the generalized non-Darcy model, and the other two for phase-change material (PCM) and metal-foam temperature fields described by the LTNE model. The moving solid-liquid phase interface is implicitly tracked through the liquid fraction, which is simultaneously obtained when the energy equations of PCM and metal foam are solved. The present method has several distinctive features. First, as compared with previous studies, the present method avoids the iteration procedure; thus it retains the inherent merits of the standard LB method and is superior to the iteration method in terms of accuracy and computational efficiency. Second, a volumetric LB scheme instead of the bounce-back scheme is employed to realize the no-slip velocity condition in the interface and solid phase regions, which is consistent with the actual situation. Last but not least, the MRT collision model is employed, and with additional degrees of freedom, it has the ability to reduce the numerical diffusion across the phase interface induced by solid-liquid phase change. Numerical tests demonstrate that the present method can serve as an accurate and efficient numerical tool for studying metal-foam enhanced solid-liquid phase-change heat transfer in latent heat storage. Finally, comparisons and discussions are made to offer useful information for practical applications of the present method.

Prospective of employing high porosity open-cell metal foams in passive cryogenic radiators for space applications

Passive cryogenic radiators work on the principle of dissipating heat to the outer space purely by radiation. High porosity open-cell metal foams are a relatively new class of extended surfaces. These possess the advantages of high surface area density and low weight, characteristics which the space industry looks for. In case of radiative heat transfer, the porous nature of metal foams permits a deeper penetration of the incident radiation. Consequently, the heat transfer area participating in radiative heat exchange increases thereby enhancing the heat transfer rate. However, effective heat conduction in between the foam struts reduces as a result of the void spaces. These two conflicting phenomenon for radiation heat transfer in metal foams have been studied in this work. Similar to the foam conduction-convection heat transfer analysis, a conduction-radiation heat transfer model has been developed for metal foams in analogy with the conventional solid fin theory. Metal foams have been theoretically represented as simple cubic structures. A comparison of the radiative heat transfer through metal foams and solid fins attached to a surface having constant temperature has been presented. Effect of changes in foam characteristic properties such as porosity and pore density have also been studied.

CFD study on thermal transport in open-cell metal foams with and without a washcoat: Effective thermal conductivity and gas-solid interfacial heat transfer

Metal foams are considered to be attractive catalyst carriers for strongly exothermic/endothermic catalytic processes, but the washcoat may have a significant influence on the thermal transport properties of the metal foams. In this work, the effective thermal conductivity and the gas-solid interfacial heat transfer of coated metal foams were studied using a periodic unit cell model in the CFD method. We emphasizedanalysing the effect of the washcoat on the effective thermal conductivity, pressure drop and interfacial heat transfer of metal foams. The results indicated that the influence of the washcoat on the effective thermal conductivity depends on the conductivity in three phases. A large deviation was found when we used the available empirical correlations for metal foams to predict the effective thermal conductivity of the coated metal foams. A correlation for the effective thermal conductivity of coated metal foams was proposed by considering the washcoat as a separate phase. With increasing washcoat thickness, it was found that the pressure drop increases but the gas-solid interfacial heat transfer decreases. Moreover, we verified the enhancement of viscous flow within the washcoat for coated metal foams. It was revealed that a maximum increase of the Nusselt number by a factor of approximately 13 was obtainable in turbulent flow if the viscous flow within the washcoat was accounted for. The present study may provide a guide for structured catalyst and reactor design for strongly exothermic/endothermic catalytic processes.

Experimental results for oscillatory water flow in 10-ppi metal foam at low-frequencies

This experimental study presents results and interpretation of oscillatory water flow in open-cell metal foam. The tested foam had 10 pores per inch and a porosity of 88%. At relatively low frequencies, three flow displacements were employed in the experiment. The influence of frequency and displacement on pressure loss and friction factor is discussed. A correlation of friction factor as a function of the kinetic Reynolds number was determined. Porous media parameters, permeability and drag coefficient, were also found for the same foam via steady-state flow experiments in the Darcy and Forchheimer regimes. The friction factor of oscillating flow was found to be higher than that of steady state. The findings of this study are considered important for oscillating heat transfer in metal foam.

Experimental investigation on pressure drop and heat transfer in metal foam filled tubes under convective boundary condition

Heat transfer under convective boundary condition is common in heat exchangers. This paper presented the experimental results of air flow and heat transfer through three stainless steel foam filled tubes under convection boundary condition. The air flow velocity inside the tube is relatively high, which varied from 7.0 to 26.0m/s. The stainless steel foam filled tubes, manufactured using high-temperature metallic sintering technique, are of different pore densities (10, 30 and 70 PPI) but have the same porosity of 0.93.The air pressure drop through the stainless steel foam filled tubes was measured. It was found that the inertial drag is the dominant part of the pressure drop at higher velocity. The pressure drop experimental data under high velocity were compared to the predictions by the correlations obtained under relatively low velocity and great discrepancies have been found. A new correlation for the pressure drop through metal foams under high velocity was presented. The effect of the boundary condition on the heat transfer performance was addressed by the comparison of Nusselt number obtained in the present study with that obtained under constant heat flux boundary condition in the published investigation. It was found that the Nusselt number obtained under convective boundary condition is much lower than that obtained under constant heat flux boundary condition. A new correlation for Nusselt number under convective boundary condition was developed.