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High-performance thermal capacitors made by explosion forming
International Journal of Heat and Mass Transfer 83 (2015) 366–371
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
High-performance thermal capacitors made by explosion forming T. Fiedler a,⇑, M. Borovinšek b, K. Hokamoto c, M. Vesenjak b a
School of Engineering, The University of Newcastle, NSW 2287 Callaghan, Australia Faculty of Mechanical Engineering, University of Maribor, Smetanova 17, 2000 Maribor, Slovenia c Institute of Pulsed Power Science, Kumamoto University, 2-39-1 Kurokami, Chuo-ku, Kumamoto 860-8555, Japan b
a r t i c l e
i n f o
Article history: Received 5 June 2014 Received in revised form 8 December 2014 Accepted 8 December 2014
Keywords: Thermal capacitor Cellular metal Phase change material Experimental analysis Finite element method
a b s t r a c t This paper addresses the thermal testing of UniPore–paraffin composites for use as thermal capacitors. UniPore is a relatively new porous material with unidirectional pores formed by the explosive fusion of multiple thin copper pipes filled with paraffin. The current study investigates the suitability of this composite for transient thermal energy storage. The application demands both high thermal diffusivity and a large specific energy storage capacity. These requirements are met by the highly conductive copper and the phase change material paraffin, respectively. Combined experimental and numerical analyses are conducted towards the determination of temperature stabilization performance. Furthermore, key geometric criteria for the design of optimum UniPore structures as thermal capacitors are identified. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction Thermal capacitors take an essential role in temperature control, waste energy usage and power intermittency compensation. Their function is the rapid storage and discharge of thermal energy. For temperature control, thermal capacitors are thermally linked to a fluctuating heat source, e.g. a battery in an electric car. Appropriate design allows absorption of thermal energy at the optimum operation temperature of the component. This can be achieved by using a suitable phase change material (PCM) whose phase transition temperature coincides with the targeted temperature. As a result overheating of components is avoided and temperatures are stabilized within the optimum operational range [1]. Another important example for temperature stabilization is climate control in buildings for the compensation of daily and/or seasonal temperature fluctuation [2]. Furthermore, thermal capacitors allow the storage and subsequent use of thermal energy that would be otherwise lost (waste energy) [3]. Finally, in concentrated solar power generation thermal capacitors can be used to attenuate power intermittencies due to cloud coverage [4]. Thermal capacitors have two main requirements (i) rapid thermal energy transfer and (ii) large specific energy storage capacity. Condition (i) arises from the need of storing and discharging energy. Depending on the application (e.g. concentrated solar power generation) high rates of energy transfer are required. ⇑ Corresponding author. Tel.: +61 (0)2 4921 6188; fax: +61 (0)2 4921 6946. E-mail address: [email protected] (T. Fiedler). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2014.12.025 0017-9310/Ó 2014 Elsevier Ltd. All rights reserved.
Requirement (ii) comes primarily from mobile applications (e.g. temperature control in car batteries) where weight and volume are limited and thus light and compact capacitors are needed. Due to these unique requirements, thermal capacitors are usually composites containing a conductive phase for energy transfer and a phase change material for energy storage. One approach is the use of highly conducting fins that protrude into the PCM in order to increase contact area and energy transfer [5]. The surface area for energy transfer into the PCM can be further increased by using a cellular structure with interconnected porosity. Wang et al. investigated carbonaceous materials as thermally conducting scaffolds that distribute and transfer thermal energy into PCMs [6]. An alternative approach is the use of highly conducting metallic foam for overall conductivity enhancement. Copper foam with interconnected porosity (open-cell foam) has shown great potential for the creation of compact PCM heat sink composites [7]. Mesalhy et al. [8] conducted a numerical heat transfer study of PCM – cellular metal composites. Their results indicated that high porosity foams are advantageous for energy storage and heat conduction since they enable convective heat transfer in the melted PCM. However, this conclusion was challenged in a subsequent study by Tian and Zhao [9]. They argued that due to the large flow resistance of the viscous PCM convective heat transfer is a secondary effect and heat transfer occurs predominantly by conduction. Recently, a new type of cellular structure with uni-directional pores (UniPore structure) has been produced by compressive blast loading. The fabrication and basic microstructural and mechanical properties of UniPore structures are described in [10], while the
T. Fiedler et al. / International Journal of Heat and Mass Transfer 83 (2015) 366–371
effect of the compressive compaction on the mechanical properties of the UniPore base material is in detail addressed in [11]. The manufacturing procedure consists of following steps: (i) the outer copper pipe is tightly packed with thin-walled inner copper pipes of much smaller diameter, (ii) the inner pipes are filled with paraffin preventing their complete compaction during compressive blast loading, (iii) the structure is placed in the center of an explosive chamber and surrounded with the explosive (the explosive charge is detonated with an electric detonator). The high pressure blast loading causes compaction of the structure and the outer and inner pipes walls are bonded by diffusion (the phenomenon is similar to diffusion welding). The final step is the removal of paraffin by heat treatment. This manufacturing procedure results in production of porous material with parallel unidirectional pores. The current study addresses UniPore structure filled with paraffin as thermal capacitors. Their extruded geometry maximizes thermal conductivity in pore direction improving thermal charge and discharge rates. The internal porosity allows the addition of phase change materials such as paraffin for latent heat storage. 2. Methodology 2.1. Experiment Experimental tests have been performed on UniPore–paraffin composite samples. Three cylindrical samples labeled A (1 mm cell wall thickness), B (0.6 mm cell wall thickness) and C (0.4 mm cell wall thickness) with a constant height h = 150.0 mm and average outer diameter d = 27.1 mm have been investigated. The cross sections of these samples are shown in Fig. 1. The selection of the initial pipe diameter and thickness together with the control of the compressive forces during explosive fusion allow the variation of sample porosity. This is reflected in the copper volume fraction UCu of the cross sections ranging from 53.3–77.5%. The internal voids are filled with the phase change material (PCM) paraffin with the corresponding paraffin volume fraction UPa. Since pores are refilled with liquid paraffin and the material contracts upon solidification some residual porosity remains in the PCM. During repeated melting and solidification, these pores tend to accumulate at the upper surface of the samples. The circular sample surfaces (top and bottom) were polished in order to minimize thermal resistance by removing the oxide layer and creating a plane contact surface. Next, the samples were sealed using copper lids that were pressed against these polished surfaces. The sealing of the sample is necessary to prevent the leakage of liquefied paraffin. Sealed samples were positioned upright on a copper heating plate simulating the heat source (see Fig. 2). In an attempt to decrease thermal contact resistance a thin layer of thermal conducting paste (OmegathermÒ 201 silicone paste) was applied between the touching sample lid and heat source.
367
Measurements were conducted inside a vacuum chamber in order to avoid energy loss due to convective heat transfer. Furthermore, reflective radiation shields were used to minimize energy loss by thermal radiation and ceramic stands reduce energy loss due thermal conduction. As a result, the entire system can be considered adiabatic in good approximation. Prior to each experiment, heat source and sample were cooled to ambient temperature to ensure a uniform initial temperature distribution. Next, the pressure inside the vacuum chamber was decreased below 20 mPa before the electric power input P into the heating element was activated. A heating wire is embedded in the copper heating plate and converts the electric power into a thermal energy flux triggering a temperature increase. Temperature change was monitored using a RTD100 temperature sensor positioned on the heating element. Due to the design of the heating element it exhibits a uniform surface temperature with variations below 1 K. Accordingly, the sensor temperature closely represents the interface temperature between heat source and sample. The temperature was recorded in 1 s time intervals using an OM-DAQÒ PRO-5300 (Omega ) data logger. Tests were terminated after the measured temperature exceeded 395 K. For the energy input P = 50 W all tests have been conducted twice in order to test measurement precision. No significant deviation between measurements was observed. Furthermore, the sample orientation was inverted (i.e. the sample was rotated by 180°) and again no visible changes in the measured time–temperature curves were found. 2.2. Simulation Numerical Finite Element simulations were conducted in order to gain additional insight in the temperature distribution within the composite samples. To this end, cross sections shown in Fig. 1 were segmented, i.e. pixel color information was used to identify the metallic phase (see black color, Fig. 3). The internal voids of the segmented images were filled with paraffin (grey color) and the resulting cross sections were extruded to create the three dimensional models. It should be mentioned here that the cross sections of the tested samples are not completely constant but slightly change with the height of the samples. However, the deviation between real samples and extruded model is small. This can be demonstrated by calculating the masses of the model structures and comparing them with the measured masses of the samples. The resulting deviations are less than 3.1%. In the next step, the finite element mesh of the UniPore models was prepared. Due to the extruded geometry of the models it was possible to use exclusively hexagonal finite elements. Special care was taken to ensure that the average aspect ratio of all elements was smaller than two and that the worst aspect ratio was not larger than five. In order to reduce the computational cost of the sim-
Fig. 1. UniPore–paraffin composite cross sections.
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T. Fiedler et al. / International Journal of Heat and Mass Transfer 83 (2015) 366–371
Fig. 2. Experimental setup (not to scale).
Fig. 3. Segmented cross section.
ulation the copper part and the paraffin part of the model were meshed with coincident meshes on the mating surfaces (interface areas). Hexagonal elements with eight nodes and linear shape functions were used for all meshes. For each UniPore model three meshes of copper and paraffin with varied number of finite elements were prepared for the mesh convergence study. Furthermore, the sample lids and heating element were included in all numerical models. The thermal mass of the virtual heating element is defined as the product of heat capacity of copper and the mass of the actual heating element. The same approach is chosen for the lower copper lid. Residual heat loss through the ceramic stands of the heater plate (see Fig. 2) was estimated to be less than 1% of the input power using a thermal resistance model and thus disregarded in the numerical simulation. However, the simulation requires the knowledge of the combined thermal contact resistance between heat source and copper lid as well as copper lid and UniPore composite. First, experimental measurements were conducted on Sample B with fitted lids but without paraffin. Next, the thermal contact resistance was iteratively adjusted in the numerical model until the calculated time–temperature curve closely matched the experimental data. A thermal contact resistance of 0.8 K/W yielded good agreement and was used in all subsequent simulations unless otherwise indicated. The material properties of the composite constituents are summarized in
Table 1 Material model properties. Material
Density Conductivity Specific heat TD [kg/m3] [W/m K] [J/kg K] [K]
Copper [12] 8960 Paraffin (solid) [13] 916 Paraffin (liquid) [13] 790
398 0.34 0.167
385 2510 2950
Latent heat [kJ/kg]
– – 310 173.6
Table 1. It should be mentioned here that the thermal contact resistance between copper and paraffin was disregarded. A constant energy volume flux boundary condition is prescribed on the virtual heating element to simulate the heat generation. Depending on the simulation the total energy input is either P = 50 W or P = 100 W. All remaining surfaces have zero flux boundary conditions to mimic the near-adiabatic conditions encountered in the experimental measurements. Preliminary analysis addressed the mesh independence of the solution. To this end, three meshes of model C were generated containing 547, 1029, and 1554 k elements, respectively. No significant deviation between the calculated time–temperature profiles was observed. As a result, the lowest mesh density was used in all subsequent analysis. In addition to the extruded geometries derived from segmented photographs of sample cross-sections (see Fig. 3) simplified model structures shown in Fig. 4 were used to study optimum design parameters for UniPore structures as thermal capacitors. It was anticipated that the internal surface area between phase change material and metallic matrix is critical for their performance. Thus, three model structures with the copper volume fraction UCu = 58.8% (identical to the model B) were generated. It should be mentioned here that all hexagon models also include the virtual heating element to accurately simulate the heat flux boundary condition. This hexagon (Hex) models are labeled according to their number of pores. Model Hex1 contains a single large hexagonal pore and has therefore the smallest interface area. Model Hex63 has the same number of uni-sized pores (63) as the crosssections of the UniPore cylinder B whereas in Model Hex252 the mean pore size has been halved resulting in four times the number of pores to achieve the same copper volume fraction. Finally, two additional versions of the Hex63 models have been generated to predict the thermal performance of composites with high paraffin volume fractions. To this end, two models with the copper volume fractions UCu = 30.0%, 45.0% (corresponding to
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Fig. 4. Models with hexagonal pores (UCu = 58.8%): (A) Hex1, (B) Hex63, (C) Hex252.
70.0 and 55.0 vol.% paraffin) were created by increasing the size of the hexagons shown in Fig. 4B. 3. Results 3.1. Effective thermal properties The geometry of UniPore–paraffin composites can be approximated as an extruded two-phase profile. As a result, their effective properties can be estimated using the following analytic relations. The effective thermal conductivity keff of an extruded composite is the arithmetic mean [14] of the constituent conductivity ki weighted with the volume fractions Ui of each phase
keff ¼
X
Ui ki :
ð1Þ
i
It must be highlighted here that keff is a directional conductivity parallel to the pore directions. The effective conductivity in other directions is lower and the minimum values are found inside the plane that is perpendicular to the longitudinal cylinder axis (this conductivity could be estimated using the Maxwell relation). The average density qavg can be calculated using
qavg ¼
X
Ui qi ;
ð2Þ
i
and the effective heat capacity Ceff is obtained using the arithmetic mean of constituent capacities Ci weighted with the mass fractions /i of the constituents:
C eff ¼
X /i C i :
ð3Þ
i
For the three sample cross sections (see Fig. 3) the corresponding values are summarized in Table 2. It can be seen that the increase of the copper content increases the effective conductivity and average density. Conversely, the effective heat capacity and latent heat storage capacity EL increase with paraffin content. It should be mentioned here that for the calculation of the average density and mass fractions the liquid paraffin density is used. This is due to the fact that the UniPore samples have been refilled with liquid paraffin and thus exhibit a small residual porosity after the solidification and concurrent contraction of the paraffin.
Table 2 Calculated effective thermal properties. /Cu [mass%]
keff [W/m K]
qavg
[vol.%] A
77.5
97.5
7120
B
58.8
94.2
C
53.3
92.8
308.5 308.5 234.2 234.1 212.3 212.3
Sample
UCu
(s) (l) (s) (l) (s) (l)
[kg/m3]
5590 5150
Ceff [J/kg K]
EL [kJ]
438.0 440.0 508.6 513.3 537.4 543.1
2.33
(s) (l) (s) (l) (s) (l)
4.26 4.83
3.2. Transient thermal response Fig. 5 shows the transient heat source temperature for four different configurations (i.e. heat source only and heat source in contact with samples A–C) and the energy inputs P = 50, 100 W. The full line corresponds to the case when no sample is positioned on the heat source. In this configuration, the temperature rapidly increases and reaches 380 K after 173 s (50 W) and 87 s (100 W), respectively. The remaining lines correspond to the heat source in contact with a thermal capacitor. Results are shown for experimental measurements (thick lines) and numerical simulations (thin lines). The high thermal mass of the samples significantly decelerates temperature increase. This can be quantified using the corresponding times required to reach 380 K that are in average 409 s (50 W) and 186 s (100 W). The comparison between samples A–C shows only minor variation and the best performance in delaying temperature increase is found for sample C. This can be explained by its maximum paraffin content (i.e. highest UniPore structure porosity) and thus superior latent heat storage capacity (see Table 2). Next, the energy input rate P strongly affects the transient response. As expected, higher energy input causes a faster temperature increase. In addition, the approximately linear temperature increase for P = 100 W becomes slightly non-linear for P = 50 W above heat source temperatures of 340 K. This is an indication for increased latent heat energy storage. In the case of P = 100 W the low thermal conductivity of the paraffin apparently does not allow for sufficiently fast latent heat storage to match the accelerated heat generation P = 100 W. As a result, a slightly larger fraction of thermal energy is stored as sensible heat within the copper matrix. This is reflected in a more linear temperature increase of heat source and capacitor [15,16]. The good agreement between experimental and numerical data allows some conclusions on the dominant heat transfer mechanism: since the numerical model only simulates energy transfer by conduction, convective and radiant heat transfer are of minor importance for the considered pore diameters (<0.5 mm) and boundary conditions. Numerical analysis allows further evaluation of the temperature distribution inside the samples. Fig. 6 exemplarily shows cross-sectional temperature maps of sample B at t = 250 s. The longitudinal view shows a temperature decrease with increasing distance from the heat source. Perturbations in the temperature map are caused by the different thermal diffusivities of the matrix (copper) and the PCM (paraffin). Each paraffin channel is visible as a notch where the temperature is lower compared to the surrounding matrix. This can also be seen in the axial view where the phase change material is in average 1 K cooler than the metallic matrix. The figures show that temperature variations within the samples are relatively small. The highest temperature gradient (not shown) is found between heat source and sample due to thermal contact resistance. In the case of P = 100 W (not shown) this temperature difference increases to approximately 2 K; however the shape of temperature maps remains similar. The increased temperature
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T. Fiedler et al. / International Journal of Heat and Mass Transfer 83 (2015) 366–371
Fig. 5. Heat source temperatures for energy inputs (A) P = 50 W, (B) P = 100 W.
Fig. 6. Temperature maps of sample B at t = 250 s, P = 50 W.
deviation between metallic matrix and PCM indicates that a slightly larger fraction of thermal energy is stored in the form of sensible heat compared to the lower power input P = 50 W.
3.3. Hexagonal model structures Hexagonal model structures have been numerically analyzed in order to gain further insight in the optimum design of UniPore structure as thermal capacitors. To this end, the irregular pores (see Figs. 1 and 3) are replaced by the uniform hexagons shown in Fig. 4. In the first group of models, the volume fractions of copper and paraffin are identical to sample B; however, the number and size of hexagons is modified. As a result, their total Cu/paraffin interface areas are 0.074 m2 (sample B), 0.009 m2 (Hex1), 0.117 m2 (Hex63), and 0.136 m2 (Hex252). Their transient thermal response is shown in Fig. 7. For P = 50 W (contact resistance) no significant deviation between Hex63, Hex252 and sample B if found. This indicates that the heat capacitors’ performance is not limited by heat transfer to the paraffin. However, the heat source temperature increase for Hex1 is accelerated which can be explained by an insufficient interface area between copper matrix and PCM. A similar behavior is found for P = 100 W. Additional curves have been computed for the case where thermal contact resistance between heat source and thermal capacitor has been eliminated. This can be achieved by joining technologies such as brazing or diffusion bonding (this of course is impractical for the experimental measurements since it would damage the experimental setup). The results of this simulation show a drastic performance improvement. The temperature increase of the heat source is distinctly decelerated since heat is more efficiently
Fig. 7. Transient thermal response of hexagon models.
transferred into the thermal capacitor. Furthermore, a strong deviation is found between Hex1 and Hex63/Hex252. As already observed, the interface area of Hex1 is insufficient to support optimum heat transfer to the PCM. The heat source temperatures for Hex63 and Hex252 are almost identical. It can be concluded that Hex63 already exhibits a sufficiently large interface area (0.117 m2) and no further improvement can be gained by creating smaller pores (i.e. using smaller copper pipes in UniPore sample manufacturing) for the considered thermal loading. Fig. 8 numerically investigates the effect of high PCM content. Results are shown for three different Hex63 models with varying copper (hence paraffin) volume fraction. The solid line corresponds to the Hex63 model with a copper content of UCu = 58.8% already discussed in Fig. 7. The two additional Hex63 models have lower copper contents UCu = 30.0%, 45.0% and thus higher volume
T. Fiedler et al. / International Journal of Heat and Mass Transfer 83 (2015) 366–371
371
Conflict of interest None declared. Acknowledgments
Fig. 8. Numerical study of composites with high PCM content.
fractions of the PCM paraffin equal to 100% UCu. Considering simulations with thermal contact resistance (P = 50, 100 W) the 45.0% and 58.8% models yield similar results. In the case of the 30.0% model a faster temperature increase is observed that can be explained by the significantly decreased thermal conductivity of the material (119.7 W/m K, see Eq. (1)). Analogous to Fig. 7, three additional simulations without thermal contact resistance have been conducted. Initially the 58.8% capacitor achieves the lowest heat source temperature indicating that the high thermal conductivity of the copper is the critical requirement. However, at t 600 s the heat source temperature increases rapidly. This indicates that most of the PCM is liquefied and additional energy is stored predominantly as sensitive heat. As a result, the 58.8% model exhibits the highest heat source temperatures at times t > 800 s. Fig. 8 confirms the importance of low thermal contact resistance between heat source and thermal capacitor for effective temperature stabilization. 4. Conclusions The presented study addressed the performance of UniPore structure filled with paraffin (UniPore–paraffin composites) as thermal capacitors. Transient thermal experiments were conducted to test their ability to stabilize the temperature of a heat source. Additional numerical calculations showed good agreement with the experimentally measured data. Thermal conduction was identified as the dominant heat transfer mechanism. The composites were found to successfully decrease the temperature of the heat source and thus are effective thermal capacitors. For the considered thermal load cases, changes in the copper and paraffin volume fractions only slightly affected the transient response of the capacitors. Furthermore, hexagonal model structures were generated to identify key design parameters of UniPore structures as capacitors. The increase of the copper–paraffin interface area has shown to improve thermal performance. However, after exceeding a critical size no further improvement could be found. In addition, thermal contact resistance was found to strongly affect heat source temperature and should be minimized using appropriate joining techniques.
The authors would like to acknowledge the support of Mr A. Sato and Mr R. Tsunoda (Kumamoto University, Japan). The research work was also produced within the framework of the operation entitled ‘‘Centre of Open innovation and ResEarchUM (CORE@UM)’’. The operation is co-funded by the European Regional Development Fund and conducted within the framework of the Operational Programme for Strengthening Regional Development Potentials for the period 2007–2013, development priority 1: ‘‘Competitiveness of companies and research excellence’’, priority axis 1.1: ‘‘Encouraging competitive potential of enterprises and research excellence’’, contact No. 3330-13-500032. One of the authors (T. Fiedler) further acknowledges financial support by the Australian Research Council (ARC) in framework of the Discovery Project DP1094698. References [1] N.R. Jankowski, F.P. McCluskey, A review of phase change materials for vehicle component thermal buffering, Appl. Energy 113 (2014) 1525–1561. [2] M. Pomianowski, P. Heiselberg, Y. Zhang, Review of thermal energy storage technologies based on PCM application in buildings, Energy Build. 67 (2013) 56–69. [3] C.W. Chan, J. Ling-Chin, A.P. Roskilly, A review of chemical heat pumps, thermodynamic cycles and thermal energy storage technologies for low grade heat utilisation, Appl. Therm. Eng. 50 (2013) 1257–1273. [4] K.M. Powell, T.F. Edgar, Modeling and control of a solar thermal power plant with thermal energy storage, Chem. Eng. Sci. 71 (2012) 138–145. [5] S.F. Hosseinizadeh, F.L. Tan, S.M. Moosania, Experimental and numerical studies on performance of PCM-based heat sink with different configurations of internal fins, Appl. Therm. Eng. 31 (17–18) (2011) 3827–3838. [6] Q. Wang, X.H. Han, A. Sommers, Y. Park, C.T. Joen, A. Jacobi, A review on application of carbonaceous materials and carbon matrix composites for heat exchangers and heat sinks, Int. J. Refrig 35 (2012) 7–26. [7] T. Fiedler, J. Loosemore, I.V. Belova, G.E. Murch, A comparative study of heat sink composites for temperature stabilisation, Appl. Therm. Eng. 58 (1–2) (2013) 314–320. [8] O. Mesalhy, K. Lafdi, A. Elgafy, K. Bowman, Numerical study for enhancing the thermal conductivity of phase change material (PCM) storage using high thermal conductivity porous matrix, Energy Convers. Manage. 46 (2005) 847– 867. [9] Y. Tian, C.Y. Zhao, A numerical investigation of heat transfer in phase change materials (PCMs) embedded in porous metals, Energy 36 (2011) 5539–5546. [10] K. Hokamoto, M. Vesenjak, Z. Ren, Fabrication of cylindrical uni-directional porous metal with explosive compaction, Mater. Lett. 137 (2014) 323–327. [11] M. Vesenjak, K. Hokamoto, I. Anzˇel, A. Sato, R. Tsunoda, L. Krstulovic´-Opara, Z. Ren, Influence of the explosive treatment on the mechanical properties and microstructure of copper, Mater. Design, (submitted for publication). [12] R.C. Weast, CRC Handbook of Chemistry and Physics, Sixty second ed., CRC Press, Boca Raton, FL, 1981. [13] N. Ukrainczyk, S. Kurajica, J. Šipušiæ, Thermophysical Comparison of FiveCommercial ParaffinWaxes as Latent Heat StorageMaterials, Chem. Biochem. Eng. Q. 24 (2010) 129–137. [14] E. Solorzano, J.A. Reglero, M.A. Rodrı´guez-Perez, D. Lehmhus, M. Wichmann, J.A.d. Saja, An experimental study on the thermal conductivity of aluminium foams by using the transient plane source method, Int. J. Heat Mass Transfer 51 (25–26) (2008) 6259–6267. [15] L.J. Gibson, M.F. Ashby, Cellular Solids: Structure and Properties, Cambridge University Press, Cambridge, 1997. [16] M. Vesenjak, Z. Zˇunicˇ, Z. Ren, A. Öchsner, Computational study of heat transfer in honeycomb structures accounting for gaseous pore filler, Defect Diffus. Forum 273–276 (2008) 669–706.
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
High-performance thermal capacitors made by explosion forming T. Fiedler a,⇑, M. Borovinšek b, K. Hokamoto c, M. Vesenjak b a
School of Engineering, The University of Newcastle, NSW 2287 Callaghan, Australia Faculty of Mechanical Engineering, University of Maribor, Smetanova 17, 2000 Maribor, Slovenia c Institute of Pulsed Power Science, Kumamoto University, 2-39-1 Kurokami, Chuo-ku, Kumamoto 860-8555, Japan b
a r t i c l e
i n f o
Article history: Received 5 June 2014 Received in revised form 8 December 2014 Accepted 8 December 2014
Keywords: Thermal capacitor Cellular metal Phase change material Experimental analysis Finite element method
a b s t r a c t This paper addresses the thermal testing of UniPore–paraffin composites for use as thermal capacitors. UniPore is a relatively new porous material with unidirectional pores formed by the explosive fusion of multiple thin copper pipes filled with paraffin. The current study investigates the suitability of this composite for transient thermal energy storage. The application demands both high thermal diffusivity and a large specific energy storage capacity. These requirements are met by the highly conductive copper and the phase change material paraffin, respectively. Combined experimental and numerical analyses are conducted towards the determination of temperature stabilization performance. Furthermore, key geometric criteria for the design of optimum UniPore structures as thermal capacitors are identified. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction Thermal capacitors take an essential role in temperature control, waste energy usage and power intermittency compensation. Their function is the rapid storage and discharge of thermal energy. For temperature control, thermal capacitors are thermally linked to a fluctuating heat source, e.g. a battery in an electric car. Appropriate design allows absorption of thermal energy at the optimum operation temperature of the component. This can be achieved by using a suitable phase change material (PCM) whose phase transition temperature coincides with the targeted temperature. As a result overheating of components is avoided and temperatures are stabilized within the optimum operational range [1]. Another important example for temperature stabilization is climate control in buildings for the compensation of daily and/or seasonal temperature fluctuation [2]. Furthermore, thermal capacitors allow the storage and subsequent use of thermal energy that would be otherwise lost (waste energy) [3]. Finally, in concentrated solar power generation thermal capacitors can be used to attenuate power intermittencies due to cloud coverage [4]. Thermal capacitors have two main requirements (i) rapid thermal energy transfer and (ii) large specific energy storage capacity. Condition (i) arises from the need of storing and discharging energy. Depending on the application (e.g. concentrated solar power generation) high rates of energy transfer are required. ⇑ Corresponding author. Tel.: +61 (0)2 4921 6188; fax: +61 (0)2 4921 6946. E-mail address: [email protected] (T. Fiedler). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2014.12.025 0017-9310/Ó 2014 Elsevier Ltd. All rights reserved.
Requirement (ii) comes primarily from mobile applications (e.g. temperature control in car batteries) where weight and volume are limited and thus light and compact capacitors are needed. Due to these unique requirements, thermal capacitors are usually composites containing a conductive phase for energy transfer and a phase change material for energy storage. One approach is the use of highly conducting fins that protrude into the PCM in order to increase contact area and energy transfer [5]. The surface area for energy transfer into the PCM can be further increased by using a cellular structure with interconnected porosity. Wang et al. investigated carbonaceous materials as thermally conducting scaffolds that distribute and transfer thermal energy into PCMs [6]. An alternative approach is the use of highly conducting metallic foam for overall conductivity enhancement. Copper foam with interconnected porosity (open-cell foam) has shown great potential for the creation of compact PCM heat sink composites [7]. Mesalhy et al. [8] conducted a numerical heat transfer study of PCM – cellular metal composites. Their results indicated that high porosity foams are advantageous for energy storage and heat conduction since they enable convective heat transfer in the melted PCM. However, this conclusion was challenged in a subsequent study by Tian and Zhao [9]. They argued that due to the large flow resistance of the viscous PCM convective heat transfer is a secondary effect and heat transfer occurs predominantly by conduction. Recently, a new type of cellular structure with uni-directional pores (UniPore structure) has been produced by compressive blast loading. The fabrication and basic microstructural and mechanical properties of UniPore structures are described in [10], while the
T. Fiedler et al. / International Journal of Heat and Mass Transfer 83 (2015) 366–371
effect of the compressive compaction on the mechanical properties of the UniPore base material is in detail addressed in [11]. The manufacturing procedure consists of following steps: (i) the outer copper pipe is tightly packed with thin-walled inner copper pipes of much smaller diameter, (ii) the inner pipes are filled with paraffin preventing their complete compaction during compressive blast loading, (iii) the structure is placed in the center of an explosive chamber and surrounded with the explosive (the explosive charge is detonated with an electric detonator). The high pressure blast loading causes compaction of the structure and the outer and inner pipes walls are bonded by diffusion (the phenomenon is similar to diffusion welding). The final step is the removal of paraffin by heat treatment. This manufacturing procedure results in production of porous material with parallel unidirectional pores. The current study addresses UniPore structure filled with paraffin as thermal capacitors. Their extruded geometry maximizes thermal conductivity in pore direction improving thermal charge and discharge rates. The internal porosity allows the addition of phase change materials such as paraffin for latent heat storage. 2. Methodology 2.1. Experiment Experimental tests have been performed on UniPore–paraffin composite samples. Three cylindrical samples labeled A (1 mm cell wall thickness), B (0.6 mm cell wall thickness) and C (0.4 mm cell wall thickness) with a constant height h = 150.0 mm and average outer diameter d = 27.1 mm have been investigated. The cross sections of these samples are shown in Fig. 1. The selection of the initial pipe diameter and thickness together with the control of the compressive forces during explosive fusion allow the variation of sample porosity. This is reflected in the copper volume fraction UCu of the cross sections ranging from 53.3–77.5%. The internal voids are filled with the phase change material (PCM) paraffin with the corresponding paraffin volume fraction UPa. Since pores are refilled with liquid paraffin and the material contracts upon solidification some residual porosity remains in the PCM. During repeated melting and solidification, these pores tend to accumulate at the upper surface of the samples. The circular sample surfaces (top and bottom) were polished in order to minimize thermal resistance by removing the oxide layer and creating a plane contact surface. Next, the samples were sealed using copper lids that were pressed against these polished surfaces. The sealing of the sample is necessary to prevent the leakage of liquefied paraffin. Sealed samples were positioned upright on a copper heating plate simulating the heat source (see Fig. 2). In an attempt to decrease thermal contact resistance a thin layer of thermal conducting paste (OmegathermÒ 201 silicone paste) was applied between the touching sample lid and heat source.
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Measurements were conducted inside a vacuum chamber in order to avoid energy loss due to convective heat transfer. Furthermore, reflective radiation shields were used to minimize energy loss by thermal radiation and ceramic stands reduce energy loss due thermal conduction. As a result, the entire system can be considered adiabatic in good approximation. Prior to each experiment, heat source and sample were cooled to ambient temperature to ensure a uniform initial temperature distribution. Next, the pressure inside the vacuum chamber was decreased below 20 mPa before the electric power input P into the heating element was activated. A heating wire is embedded in the copper heating plate and converts the electric power into a thermal energy flux triggering a temperature increase. Temperature change was monitored using a RTD100 temperature sensor positioned on the heating element. Due to the design of the heating element it exhibits a uniform surface temperature with variations below 1 K. Accordingly, the sensor temperature closely represents the interface temperature between heat source and sample. The temperature was recorded in 1 s time intervals using an OM-DAQÒ PRO-5300 (Omega ) data logger. Tests were terminated after the measured temperature exceeded 395 K. For the energy input P = 50 W all tests have been conducted twice in order to test measurement precision. No significant deviation between measurements was observed. Furthermore, the sample orientation was inverted (i.e. the sample was rotated by 180°) and again no visible changes in the measured time–temperature curves were found. 2.2. Simulation Numerical Finite Element simulations were conducted in order to gain additional insight in the temperature distribution within the composite samples. To this end, cross sections shown in Fig. 1 were segmented, i.e. pixel color information was used to identify the metallic phase (see black color, Fig. 3). The internal voids of the segmented images were filled with paraffin (grey color) and the resulting cross sections were extruded to create the three dimensional models. It should be mentioned here that the cross sections of the tested samples are not completely constant but slightly change with the height of the samples. However, the deviation between real samples and extruded model is small. This can be demonstrated by calculating the masses of the model structures and comparing them with the measured masses of the samples. The resulting deviations are less than 3.1%. In the next step, the finite element mesh of the UniPore models was prepared. Due to the extruded geometry of the models it was possible to use exclusively hexagonal finite elements. Special care was taken to ensure that the average aspect ratio of all elements was smaller than two and that the worst aspect ratio was not larger than five. In order to reduce the computational cost of the sim-
Fig. 1. UniPore–paraffin composite cross sections.
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Fig. 2. Experimental setup (not to scale).
Fig. 3. Segmented cross section.
ulation the copper part and the paraffin part of the model were meshed with coincident meshes on the mating surfaces (interface areas). Hexagonal elements with eight nodes and linear shape functions were used for all meshes. For each UniPore model three meshes of copper and paraffin with varied number of finite elements were prepared for the mesh convergence study. Furthermore, the sample lids and heating element were included in all numerical models. The thermal mass of the virtual heating element is defined as the product of heat capacity of copper and the mass of the actual heating element. The same approach is chosen for the lower copper lid. Residual heat loss through the ceramic stands of the heater plate (see Fig. 2) was estimated to be less than 1% of the input power using a thermal resistance model and thus disregarded in the numerical simulation. However, the simulation requires the knowledge of the combined thermal contact resistance between heat source and copper lid as well as copper lid and UniPore composite. First, experimental measurements were conducted on Sample B with fitted lids but without paraffin. Next, the thermal contact resistance was iteratively adjusted in the numerical model until the calculated time–temperature curve closely matched the experimental data. A thermal contact resistance of 0.8 K/W yielded good agreement and was used in all subsequent simulations unless otherwise indicated. The material properties of the composite constituents are summarized in
Table 1 Material model properties. Material
Density Conductivity Specific heat TD [kg/m3] [W/m K] [J/kg K] [K]
Copper [12] 8960 Paraffin (solid) [13] 916 Paraffin (liquid) [13] 790
398 0.34 0.167
385 2510 2950
Latent heat [kJ/kg]
– – 310 173.6
Table 1. It should be mentioned here that the thermal contact resistance between copper and paraffin was disregarded. A constant energy volume flux boundary condition is prescribed on the virtual heating element to simulate the heat generation. Depending on the simulation the total energy input is either P = 50 W or P = 100 W. All remaining surfaces have zero flux boundary conditions to mimic the near-adiabatic conditions encountered in the experimental measurements. Preliminary analysis addressed the mesh independence of the solution. To this end, three meshes of model C were generated containing 547, 1029, and 1554 k elements, respectively. No significant deviation between the calculated time–temperature profiles was observed. As a result, the lowest mesh density was used in all subsequent analysis. In addition to the extruded geometries derived from segmented photographs of sample cross-sections (see Fig. 3) simplified model structures shown in Fig. 4 were used to study optimum design parameters for UniPore structures as thermal capacitors. It was anticipated that the internal surface area between phase change material and metallic matrix is critical for their performance. Thus, three model structures with the copper volume fraction UCu = 58.8% (identical to the model B) were generated. It should be mentioned here that all hexagon models also include the virtual heating element to accurately simulate the heat flux boundary condition. This hexagon (Hex) models are labeled according to their number of pores. Model Hex1 contains a single large hexagonal pore and has therefore the smallest interface area. Model Hex63 has the same number of uni-sized pores (63) as the crosssections of the UniPore cylinder B whereas in Model Hex252 the mean pore size has been halved resulting in four times the number of pores to achieve the same copper volume fraction. Finally, two additional versions of the Hex63 models have been generated to predict the thermal performance of composites with high paraffin volume fractions. To this end, two models with the copper volume fractions UCu = 30.0%, 45.0% (corresponding to
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Fig. 4. Models with hexagonal pores (UCu = 58.8%): (A) Hex1, (B) Hex63, (C) Hex252.
70.0 and 55.0 vol.% paraffin) were created by increasing the size of the hexagons shown in Fig. 4B. 3. Results 3.1. Effective thermal properties The geometry of UniPore–paraffin composites can be approximated as an extruded two-phase profile. As a result, their effective properties can be estimated using the following analytic relations. The effective thermal conductivity keff of an extruded composite is the arithmetic mean [14] of the constituent conductivity ki weighted with the volume fractions Ui of each phase
keff ¼
X
Ui ki :
ð1Þ
i
It must be highlighted here that keff is a directional conductivity parallel to the pore directions. The effective conductivity in other directions is lower and the minimum values are found inside the plane that is perpendicular to the longitudinal cylinder axis (this conductivity could be estimated using the Maxwell relation). The average density qavg can be calculated using
qavg ¼
X
Ui qi ;
ð2Þ
i
and the effective heat capacity Ceff is obtained using the arithmetic mean of constituent capacities Ci weighted with the mass fractions /i of the constituents:
C eff ¼
X /i C i :
ð3Þ
i
For the three sample cross sections (see Fig. 3) the corresponding values are summarized in Table 2. It can be seen that the increase of the copper content increases the effective conductivity and average density. Conversely, the effective heat capacity and latent heat storage capacity EL increase with paraffin content. It should be mentioned here that for the calculation of the average density and mass fractions the liquid paraffin density is used. This is due to the fact that the UniPore samples have been refilled with liquid paraffin and thus exhibit a small residual porosity after the solidification and concurrent contraction of the paraffin.
Table 2 Calculated effective thermal properties. /Cu [mass%]
keff [W/m K]
qavg
[vol.%] A
77.5
97.5
7120
B
58.8
94.2
C
53.3
92.8
308.5 308.5 234.2 234.1 212.3 212.3
Sample
UCu
(s) (l) (s) (l) (s) (l)
[kg/m3]
5590 5150
Ceff [J/kg K]
EL [kJ]
438.0 440.0 508.6 513.3 537.4 543.1
2.33
(s) (l) (s) (l) (s) (l)
4.26 4.83
3.2. Transient thermal response Fig. 5 shows the transient heat source temperature for four different configurations (i.e. heat source only and heat source in contact with samples A–C) and the energy inputs P = 50, 100 W. The full line corresponds to the case when no sample is positioned on the heat source. In this configuration, the temperature rapidly increases and reaches 380 K after 173 s (50 W) and 87 s (100 W), respectively. The remaining lines correspond to the heat source in contact with a thermal capacitor. Results are shown for experimental measurements (thick lines) and numerical simulations (thin lines). The high thermal mass of the samples significantly decelerates temperature increase. This can be quantified using the corresponding times required to reach 380 K that are in average 409 s (50 W) and 186 s (100 W). The comparison between samples A–C shows only minor variation and the best performance in delaying temperature increase is found for sample C. This can be explained by its maximum paraffin content (i.e. highest UniPore structure porosity) and thus superior latent heat storage capacity (see Table 2). Next, the energy input rate P strongly affects the transient response. As expected, higher energy input causes a faster temperature increase. In addition, the approximately linear temperature increase for P = 100 W becomes slightly non-linear for P = 50 W above heat source temperatures of 340 K. This is an indication for increased latent heat energy storage. In the case of P = 100 W the low thermal conductivity of the paraffin apparently does not allow for sufficiently fast latent heat storage to match the accelerated heat generation P = 100 W. As a result, a slightly larger fraction of thermal energy is stored as sensible heat within the copper matrix. This is reflected in a more linear temperature increase of heat source and capacitor [15,16]. The good agreement between experimental and numerical data allows some conclusions on the dominant heat transfer mechanism: since the numerical model only simulates energy transfer by conduction, convective and radiant heat transfer are of minor importance for the considered pore diameters (<0.5 mm) and boundary conditions. Numerical analysis allows further evaluation of the temperature distribution inside the samples. Fig. 6 exemplarily shows cross-sectional temperature maps of sample B at t = 250 s. The longitudinal view shows a temperature decrease with increasing distance from the heat source. Perturbations in the temperature map are caused by the different thermal diffusivities of the matrix (copper) and the PCM (paraffin). Each paraffin channel is visible as a notch where the temperature is lower compared to the surrounding matrix. This can also be seen in the axial view where the phase change material is in average 1 K cooler than the metallic matrix. The figures show that temperature variations within the samples are relatively small. The highest temperature gradient (not shown) is found between heat source and sample due to thermal contact resistance. In the case of P = 100 W (not shown) this temperature difference increases to approximately 2 K; however the shape of temperature maps remains similar. The increased temperature
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Fig. 5. Heat source temperatures for energy inputs (A) P = 50 W, (B) P = 100 W.
Fig. 6. Temperature maps of sample B at t = 250 s, P = 50 W.
deviation between metallic matrix and PCM indicates that a slightly larger fraction of thermal energy is stored in the form of sensible heat compared to the lower power input P = 50 W.
3.3. Hexagonal model structures Hexagonal model structures have been numerically analyzed in order to gain further insight in the optimum design of UniPore structure as thermal capacitors. To this end, the irregular pores (see Figs. 1 and 3) are replaced by the uniform hexagons shown in Fig. 4. In the first group of models, the volume fractions of copper and paraffin are identical to sample B; however, the number and size of hexagons is modified. As a result, their total Cu/paraffin interface areas are 0.074 m2 (sample B), 0.009 m2 (Hex1), 0.117 m2 (Hex63), and 0.136 m2 (Hex252). Their transient thermal response is shown in Fig. 7. For P = 50 W (contact resistance) no significant deviation between Hex63, Hex252 and sample B if found. This indicates that the heat capacitors’ performance is not limited by heat transfer to the paraffin. However, the heat source temperature increase for Hex1 is accelerated which can be explained by an insufficient interface area between copper matrix and PCM. A similar behavior is found for P = 100 W. Additional curves have been computed for the case where thermal contact resistance between heat source and thermal capacitor has been eliminated. This can be achieved by joining technologies such as brazing or diffusion bonding (this of course is impractical for the experimental measurements since it would damage the experimental setup). The results of this simulation show a drastic performance improvement. The temperature increase of the heat source is distinctly decelerated since heat is more efficiently
Fig. 7. Transient thermal response of hexagon models.
transferred into the thermal capacitor. Furthermore, a strong deviation is found between Hex1 and Hex63/Hex252. As already observed, the interface area of Hex1 is insufficient to support optimum heat transfer to the PCM. The heat source temperatures for Hex63 and Hex252 are almost identical. It can be concluded that Hex63 already exhibits a sufficiently large interface area (0.117 m2) and no further improvement can be gained by creating smaller pores (i.e. using smaller copper pipes in UniPore sample manufacturing) for the considered thermal loading. Fig. 8 numerically investigates the effect of high PCM content. Results are shown for three different Hex63 models with varying copper (hence paraffin) volume fraction. The solid line corresponds to the Hex63 model with a copper content of UCu = 58.8% already discussed in Fig. 7. The two additional Hex63 models have lower copper contents UCu = 30.0%, 45.0% and thus higher volume
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Conflict of interest None declared. Acknowledgments
Fig. 8. Numerical study of composites with high PCM content.
fractions of the PCM paraffin equal to 100% UCu. Considering simulations with thermal contact resistance (P = 50, 100 W) the 45.0% and 58.8% models yield similar results. In the case of the 30.0% model a faster temperature increase is observed that can be explained by the significantly decreased thermal conductivity of the material (119.7 W/m K, see Eq. (1)). Analogous to Fig. 7, three additional simulations without thermal contact resistance have been conducted. Initially the 58.8% capacitor achieves the lowest heat source temperature indicating that the high thermal conductivity of the copper is the critical requirement. However, at t 600 s the heat source temperature increases rapidly. This indicates that most of the PCM is liquefied and additional energy is stored predominantly as sensitive heat. As a result, the 58.8% model exhibits the highest heat source temperatures at times t > 800 s. Fig. 8 confirms the importance of low thermal contact resistance between heat source and thermal capacitor for effective temperature stabilization. 4. Conclusions The presented study addressed the performance of UniPore structure filled with paraffin (UniPore–paraffin composites) as thermal capacitors. Transient thermal experiments were conducted to test their ability to stabilize the temperature of a heat source. Additional numerical calculations showed good agreement with the experimentally measured data. Thermal conduction was identified as the dominant heat transfer mechanism. The composites were found to successfully decrease the temperature of the heat source and thus are effective thermal capacitors. For the considered thermal load cases, changes in the copper and paraffin volume fractions only slightly affected the transient response of the capacitors. Furthermore, hexagonal model structures were generated to identify key design parameters of UniPore structures as capacitors. The increase of the copper–paraffin interface area has shown to improve thermal performance. However, after exceeding a critical size no further improvement could be found. In addition, thermal contact resistance was found to strongly affect heat source temperature and should be minimized using appropriate joining techniques.
The authors would like to acknowledge the support of Mr A. Sato and Mr R. Tsunoda (Kumamoto University, Japan). The research work was also produced within the framework of the operation entitled ‘‘Centre of Open innovation and ResEarchUM (CORE@UM)’’. The operation is co-funded by the European Regional Development Fund and conducted within the framework of the Operational Programme for Strengthening Regional Development Potentials for the period 2007–2013, development priority 1: ‘‘Competitiveness of companies and research excellence’’, priority axis 1.1: ‘‘Encouraging competitive potential of enterprises and research excellence’’, contact No. 3330-13-500032. One of the authors (T. Fiedler) further acknowledges financial support by the Australian Research Council (ARC) in framework of the Discovery Project DP1094698. References [1] N.R. Jankowski, F.P. McCluskey, A review of phase change materials for vehicle component thermal buffering, Appl. Energy 113 (2014) 1525–1561. [2] M. Pomianowski, P. Heiselberg, Y. Zhang, Review of thermal energy storage technologies based on PCM application in buildings, Energy Build. 67 (2013) 56–69. [3] C.W. Chan, J. Ling-Chin, A.P. Roskilly, A review of chemical heat pumps, thermodynamic cycles and thermal energy storage technologies for low grade heat utilisation, Appl. Therm. Eng. 50 (2013) 1257–1273. [4] K.M. Powell, T.F. Edgar, Modeling and control of a solar thermal power plant with thermal energy storage, Chem. Eng. Sci. 71 (2012) 138–145. [5] S.F. Hosseinizadeh, F.L. Tan, S.M. Moosania, Experimental and numerical studies on performance of PCM-based heat sink with different configurations of internal fins, Appl. Therm. Eng. 31 (17–18) (2011) 3827–3838. [6] Q. Wang, X.H. Han, A. Sommers, Y. Park, C.T. Joen, A. Jacobi, A review on application of carbonaceous materials and carbon matrix composites for heat exchangers and heat sinks, Int. J. Refrig 35 (2012) 7–26. [7] T. Fiedler, J. Loosemore, I.V. Belova, G.E. Murch, A comparative study of heat sink composites for temperature stabilisation, Appl. Therm. Eng. 58 (1–2) (2013) 314–320. [8] O. Mesalhy, K. Lafdi, A. Elgafy, K. Bowman, Numerical study for enhancing the thermal conductivity of phase change material (PCM) storage using high thermal conductivity porous matrix, Energy Convers. Manage. 46 (2005) 847– 867. [9] Y. Tian, C.Y. Zhao, A numerical investigation of heat transfer in phase change materials (PCMs) embedded in porous metals, Energy 36 (2011) 5539–5546. [10] K. Hokamoto, M. Vesenjak, Z. Ren, Fabrication of cylindrical uni-directional porous metal with explosive compaction, Mater. Lett. 137 (2014) 323–327. [11] M. Vesenjak, K. Hokamoto, I. Anzˇel, A. Sato, R. Tsunoda, L. Krstulovic´-Opara, Z. Ren, Influence of the explosive treatment on the mechanical properties and microstructure of copper, Mater. Design, (submitted for publication). [12] R.C. Weast, CRC Handbook of Chemistry and Physics, Sixty second ed., CRC Press, Boca Raton, FL, 1981. [13] N. Ukrainczyk, S. Kurajica, J. Šipušiæ, Thermophysical Comparison of FiveCommercial ParaffinWaxes as Latent Heat StorageMaterials, Chem. Biochem. Eng. Q. 24 (2010) 129–137. [14] E. Solorzano, J.A. Reglero, M.A. Rodrı´guez-Perez, D. Lehmhus, M. Wichmann, J.A.d. Saja, An experimental study on the thermal conductivity of aluminium foams by using the transient plane source method, Int. J. Heat Mass Transfer 51 (25–26) (2008) 6259–6267. [15] L.J. Gibson, M.F. Ashby, Cellular Solids: Structure and Properties, Cambridge University Press, Cambridge, 1997. [16] M. Vesenjak, Z. Zˇunicˇ, Z. Ren, A. Öchsner, Computational study of heat transfer in honeycomb structures accounting for gaseous pore filler, Defect Diffus. Forum 273–276 (2008) 669–706.