Determination of the thermal properties of ceramic sponges

International Journal of Heat and Mass Transfer 53 (2010) 198–205

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Determination of the thermal properties of ceramic sponges B. Dietrich a,*, G. Schell b, E.C. Bucharsky b, R. Oberacker b, M.J. Hoffmann b, W. Schabel a, M. Kind a, H. Martin a a b

Institute of Thermal Process Engineering, Karlsruhe Institute of Technology (KIT), Kaiserstrasse 12, 76128 Karlsruhe, Germany Institute for Ceramics in Mechanical Engineering, Karlsruhe Institute of Technology (KIT), Haid-und-Neu-Strasse 7, 76131 Karlsruhe, Germany

a r t i c l e

i n f o

Article history: Received 30 April 2009 Received in revised form 13 August 2009 Accepted 25 August 2009 Available online 23 October 2009 Keywords: Ceramic sponge Two-phase thermal conductivity Open-celled foam Krischer model Thermal properties

a b s t r a c t The knowledge of thermal properties of technical components or internals in chemical reactors is often a key characteristic for planning and designing chemical engineering processes. As an alternative to packed beds or packings, sponges turned out to be used in new application fields in chemical and process engineering. Therefore an experimental study was performed to investigate the two-phase thermal conductivity of solid ceramic sponges made of alumina, mullite and oxidic-bonded silicon carbide (OBSiC) at moderate temperatures. A two-dimensional model is used for analysing the measured temperature profiles and for calculating the thermal conductivity. It can be observed, that the thermal conductivity increases with decreasing porosity and is nearly constant when the pore size (ppi number) is varied. The thermal conductivity data are modelled by an approach similar to the well known Krischer model. Compared to a packed bed of spherical particles, the values of the thermal conductivity of sponges turn out to be about five times higher. Ó 2009 Elsevier Ltd. All rights reserved.

1. Introduction Solid sponges (i.e. open-celled foams) belong to the cellular materials. The term ‘‘foam” typically stands for cellular materials produced by foaming of liquids with closed cells (gas bubbles). Because of the open-celled solid network structure, the word ‘‘sponge” seems to be more appropriate for the material investigated. The key characteristics of solid sponges are a high and continuously accessible porosity of typically about 75–95%, which leads to a low pressure drop for fluids flowing through them [1], combined with advantageous heat transfer properties. In addition to the fluid phase, sponges have a second, solid, continuous phase. This fact leads to a higher radial heat transfer in comparison to packed beds. In general, the properties of cellular materials depend on their geometric structures and on the material properties of the solid phase. The properties of sponges can be modified over a wide range. This encourages the use of solid ceramic sponges in various applications in chemical and process engineering, including singleand multiphase flow. Some examples are solar receivers, gas burners or alternatives for column packings. Today, the manufacturing process is considered to be advanced enough to open a route to new industrial areas ranging from catalyst supports, hot-gas or molten-metal filters, membranes, gas burners, lightweight construction, sound and heat insulation to energy absorption applica-

* Corresponding author. Tel.: +49 721 608 6830; fax: +49 721 608 3490. E-mail address: [email protected] (B. Dietrich). 0017-9310/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijheatmasstransfer.2009.09.041

tions [2–6]. For all these mentioned applications, the knowledge of thermal properties is of particular interest. 2. Thermal conductivity 2.1. Literature study Heat transfer in porous materials is described by the ‘‘twophase thermal conductivity” depending on solid body properties, like the thermal conductivity ks , porosity w, pore density (ppi number) and cell geometry, as well as the fluid media characteristics, such as thermal conductivity kf , viscosity lf and the fluid velocity u. The two-phase thermal conductivity k2ph of sponges can be understood as the superposition of the conduction of the solid, conduction of the fluid, free and forced convection as well as radiation within the cells. In this contribution, only heat conduction without forced convection and radiation is considered. Experimental data are obtained under steady state heat transfer conditions in closed systems at moderate temperatures (negligible radiation) and at atmospheric pressure. Furthermore, the effect of free convection inside the sponge structure on heat transfer is negligible because of the horizontal placement of the experimental equipment, which is described in Section 3.5. In the future, experiments with a vertical placement of the measuring cell will be performed in order to investigate the effect of free convection. The results will be published in a further paper. Table 1 gives a short overview of existing models in the literature for calculating the two-phase thermal conductivity without flow.

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Nomenclature

w

Latin symbols a Krischer parameter b structure parameter C constant specific heat capacity (kJ/(kg K)) cp T temperature (°C) Q_ heat flux (W) q_ specific heat flux (W/m2)

Subscripts air air calc calculated exp experimental f fluid lit literature parallel parallel serial serial s solid th theoretical 2ph two-phase

Greek symbols j thermal diffusivity (m2/s) k thermal conductivity (W/(mK)) q density (kg/m3)

These can be divided into two parts: Either the correlations are based on the combination of resistances or they are based on ideal unit cells. The majority of the models tabulated in Table 1 are verified for samples made of metal or reticulated vitreous carbon with porosities larger than 0.89. Only the model of Abramenko et al. [7] correlates to experimental results from sponge samples with porosities in the range of 0.69–0.79. So, none of these models consider the whole porosity range (0.75–0.85) as well as the material (ceramics) of the samples investigated in this work. In a first step, the applicability of the models was tested for the investigated ceramic sponges. The model validation was done by the following error equation:

Error ¼

porosity

jkexp  klit j kexp

ð1Þ

where kexp is the experimentally determined two-phase thermal conductivity of the sponges investigated in this work and klit the two-phase thermal conductivity calculated by the models described in Table 1. This error was calculated for each sample type and model. For clearness, Table 2 gives an overview of the maximum error as well as the mean error of each sponge material type. The mean error was calculated by the arithmetic mean of all errors from one material (six values per material). The value of the maximum error ranges from 22% to 178%, the value of the mean error from 12% to 82%. So the models described above turned out to be not very practicable for modelling the experimental results of the investigated sponges in this work. Hence, a model similar to the Krischer model [11], which is based on the combination of resistances is developed and presented in Section 4.4.

However, heat transfer with forced convection and radiation in highly porous, cellular mainly metal sponges has been studied in recent years by several authors. Some examples are Lu and Chen [12], Zhao et al. [13], Giani et al. [14], Younis and Viskanta [15] as well as Calmidi and Mahajan [16]. 2.2. Thermal conductivity of the solid network structure ks In order to generate a model for explaining the two-phase thermal conductivity of sponges at moderate temperatures, the thermal properties of the two continuous phases have to be known Table 2 Literature model evaluation by means of maximum error and mean error with reference to experimentally determined two-phase thermal conductivities (measurements described in Section 3.5). Model

Material Maximum error (%) Mean error (%)

Abramenko et al. [7]

Alumina 62 OBSiC 60 Mullit 178

23 38 82

Singh and Kasana [8]

Alumina OBSiC Mullit

44 63 22

41 57 12

Paek et al. [9]

Alumina 133 OBSiC 46 Mullit 152

56 27 61

Boomsma and Poulikakos [10] Alumina OBSiC Mullit

39 66 38

36 63 28

Table 1 Correlations for the calculation of the thermal conductivity (without flow) of solid sponges. Character

Modelling equation

Correlation

k2ph ¼ C 1 

ks

 þ C2  kf

1w 1ks

k2ph ¼ kFk  k1F ?

kf

1þw



ks kf 1

h  i F ¼ const  C 3 þ C 4  ln w  kksf

kk ¼ weighted arithmetic mean k? ¼ weighted harmonic mean Physical models (unit cells)

Unit cell: cube

Tested system

Reference

Al–air 0.69 < w < 0.79

[7]

Al/RVCa–air, Al/RVCa–water w > 0:9

[8]

Al alloy–air 0:89 < w < 0:96

[9]

Al–air Al–water 0:9 < w < 0:98

[10]

f ks k2ph ¼ ks  t2 þ kf  ð1  tÞ2 þ 2tð1tÞk ks ð1tÞþkf t 1  1 1 4p t ¼ 2 þ cos 3  cos ð2  w  1Þ þ 3 Assumption: one-dimensional heat conduction

Unit cell: tetrakaidecahedron pffiffi 2 k2ph ¼ 2ðRA þRB þR C þRD Þ RAD ¼ f ðks ; kf ; geometrical dimensions of the unit cellÞ a

Reticulated vitreous carbon.

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and therefore investigated. The thermal conductivity of most pure materials is well known and tabulated in the literature (see for example for air [17]). But in the case of the investigated commercial sponges, these properties of the solid network structure could be modified due to impurities. So, in a first step the thermal conductivity of the strut material has to be determined. It can be obtained by the following equation:

ks ¼ js  qs  cp;s ;

ð2Þ

if thermal diffusivity, density and specific heat capacity of the solid phase are known. Because the struts are too small for common measurement methods, solid plate samples (in the following identified as discs) were prepared from each sponge material. Characteristics such as density and grain size distribution must be considered for preparing these discs in order to have properties comparable to the original sponge. 3. Experimental

employing an Accupyc 1330, Micromeritics. The samples were previously dried at constant weight before the measurements were performed. 3.3. Preparation of discs from sponge materials The sponges were crushed in a mortar, passed through a sieve with an average mesh width of 180 lm. To homogenize the size distribution, the powder was ball milled for 2 h in isopropyl alcohol (balls made of zirconium oxide with a diameter of 10 mm, rational speed 300 U/min). The powder was uniaxially pressed (50 MPa) in a die with 20 mm in diameter followed by an isostatic pressing (400 MPa). The idea was to produce specimens with the same degree of density and approximately the same average grain size as the original struts of the sponges. For this purpose the specimens were sintered in air with the parameters shown in Table 3. Grain size and density were tested after each experiment until they matched with the porosities of the original material. The discs had a diameter of 10 mm and a height of 2 mm. The values for the density and the grain size of the discs finally used are given in Table 4.

3.1. Description of the sponge samples The investigated sponges (see Fig. 1) were supplied by Vesuvius Becker & Piscantor, Grossalmeroder Schmelztiegelwerke GmbH, Germany, using a replica process called the Schwarzwalder process [2]. They are made of alumina (Al2O3), mullite (3Al2O32SiO2) and oxidic-bonded silicon carbide (OBSiC). The samples are cylinders of 50 mm in height and 100 mm in diameter and have a nominal porosity of 75%, 80% and 85%. The nominal ppi number (pores per inch) of the samples was 10, 20, 30 and 45 ppi. The nominal values were provided by the supplier. Control measurements of the nominal porosity showed a deviation of ±1% with respect to the nominal values (see [1]). 3.2. Microstructural analysis The microstructure was characterized by scanning electron microscopy (SEM) using a Stereoscan 440 (Leica, Germany). The samples were previously etched by thermal treatment for both oxides, alumina and mullite, 10 min at 1350 °C and 1400 °C, respectively. In the case of OBSiC samples, etching was performed in a commercial plasma-etching apparatus with a CF4/O2 ratio of 2:1 and a forward power of 100 W, three times for 3 min. The phase composition was investigated by X-ray diffraction analysis (XRD) using a Siemens D500 diffractometer equipped with a graphite crystal monochromator. The radiation employed was Cu Ka with 2h between 12 and 70 °C. To obtain information of the true density of the investigated materials, helium pycnometry measurements were carried out

3.4. Determination of the material properties for calculating the thermal conductivity ks First the thermal diffusivity js was determined by means of laser flash technique using an LFA427, Netzsch equipment. This method is described extensively in the literature [18]. Therefore, the theory is not mentioned here. All laser flash experiments in the present work were performed under vacuum conditions and were carried out at room temperature and at 100 °C. Usually, 10 measurements were made at every temperature and averaged for further evaluation. The density qs was determined as described in Section 3.2. For each sponge material, 12 different samples were measured and afterwards arithmetically averaged. The specific heat capacity cp,s was determined by means of differential scanning calorimetry (DSC). The data were obtained in a temperature range from 20 to 600 °C by a Netzsch DSC 204 Phoenix with a heating rate of 10 K/min. 3.5. Determination of the two-phase thermal conductivity k2ph – experimental setup For the determination of the two-phase thermal conductivity (without flow) the experimental setup shown in Fig. 2 has been used. The sponge (4) is clamped between a heating (1) and a cooling plate (2). For the determination of the temperature profile a reference material (3) (here: Teflon) with known thermal conductivity is placed between the sponge and the heating plate as well as

Fig. 1. Alumina, mullite and OBSiC sponges investigated in this work with w = 80% and 30 ppi.

B. Dietrich et al. / International Journal of Heat and Mass Transfer 53 (2010) 198–205 Table 3 Sinter parameters employed to obtain a solid strut disc of the different ceramic materials. Material

Heating

Holding

Cooling

Alumina

20–1700 °C 3 K/min

1700 °C 5h

1700–20 °C 5 K/min

Mullite

20–1700 °C 3 K/min

1700 °C 2.8 h

1700–20 °C 5 K/min

OBSiC

20–1600 °C 3 K/min

1600 °C 2h

1600–20 °C 5 K/min

Table 4 Grain size and density of the discs used for the determination of the thermal conductivity.

a

Material

Relative densitya (%)

Porosity (%)

Grain size (lm)

Alumina Mullite OBSiC

91.7 95.1 82.3

8.4 4.9 17.7

5–10 1–10 10–100

Relative density values were calculated employing density pycnometry results.

the sponge and the cooling plate. For this purpose each Teflon cylinder is equipped with three thermocouples (Type T). The whole equipment has been insulated with 7 mm polystyrene (6) and 8 mm Teflon layer (7). Furthermore, the measurement section was put into a vacuum chamber (8). Experiments were realized with a temperature difference of 20 K between the two plates, which results a temperature difference of maximal 7 K over the sponge. The placement of the whole equipment is horizontal in order to avoid the effect of free convection inside the sponge structure. 4. Results and discussion 4.1. Sponge material characterization In order to reshape the struts into more voluminous discs with similar properties, the microstructure of the sponges had to be

201

analyzed. Table 5 contains, among others, the results of the strut solid density qs obtained from helium pycnometry measurements. The densities of the three materials were compared with the theoretical density qs,th of the corresponding pure substances [19]. For alumina the theoretical and experimental values are comparable, otherwise for mullite and OBSiC the experimental values differ significantly from the theoretical ones. Explanations of this discrepancy can be made considering the results obtained from the microstructure (SEM), elemental (EDX) and phase (XRD) analysis. In the case of OBSiC, SEM micrographs (see Fig. 3) show a matrix, in which the SiC grains are randomly distributed. XRD measurements indicated that the matrix is based on aluminosilicates with montmorillonites as the main component. In the case of alumina and mullite a matrix can also be suspected, but their fraction is low and recognized as glass-phase. Quantitative grain size analysis for mullite and alumina samples showed grain sizes between 2 and 10 lm, for OBSiC samples the values lied in the range of 30– 100 lm. 4.2. Results for the solid thermal conductivity ks obtained from the discs In Fig. 4 SEM micrographs of the strut as well as of the final disc for Alumina is shown. It can be seen that the grain sizes match very well. So, the discs are suitable for determining the solid thermal conductivity according to Eq. (2). In Table 5 the results of the determination of ks for the three materials alumina, mullite and OBSiC are presented. The obtained values differ from the pure material values in the literature [19], because of the facts described above. As expected, experimental determination of ks was thus essential. The value for the solid thermal conductivity of OBSiC lies between those of mullite and alumina. This was not expected, because the thermal conductivity of pure SiC is, with about 90 W/ (mK) [19], significantly higher. The effect of the lower conductivity is caused by the matrix, in which SiC splitters are ingrained (see Fig. 3). The matrix has a comparably low thermal conductivity and insulates the splitters, which causes the low thermal conductivity of the OBSiC strut material.

Fig. 2. Experimental setup for the determination of the two-phase thermal conductivity: (1) heating plate, (2) cooling plate, (3) Teflon cylinder, (4) sponge, (5) thermocouples, (6) polystyrene insulation, (7) Teflon insulation, (8) vacuum chamber, and (9) o-rings.

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Table 5 Thermal diffusivity, density, specific heat capacity and obtained solid thermal conductivity (at room temperature) of alumina, mullite and OBSiC, measured on the discs (= replica strut). T/°C

Alumina

Mullite

OBSiC

ks =ðW m1 K1 Þ

25 25 25 25–600 25

8.94  106 3891 3997 [19] 0.110  ln T/°C + 0.438 25.9

1.82  106 2951 3170 [19] 0.116  ln T/°C + 0.428 4.4

4.06  106 3033 3210 [19] 0.125  ln T/°C + 0.348 8.1

ks;th =ðW m1 K1 Þ

100

35.0 [19]

6.1 [19]

SiC: 90 [19]

js =ðm2 s1 Þ qs/(kg m3) qs,th/(kg m 3) cp,s/(kJ kg1 K1)

Fig. 3. SEM micrographs of the original sponge material in two different scales: (a) alumina, (b) mullite, and (c) OBSiC.

In Fig. 5(a) the DSC results for determining the specific heat capacity for the alumina, mullite and OBSiC samples are shown. The fit function of each set of these data has a logarithmic trend, the equation is given in Table 5. The comparison with the literature data [20] shows a good agreement (exemplary shown for Alumina in Fig. 5(b)). 4.3. Determination of the two-phase thermal conductivity k2ph From measurements of the temperature at selected locations (see Fig. 2), the two-phase thermal conductivity can be deduced

with the help of a two-dimensional model, which considers the axial as well the radial heat flux. The latter is caused by a non-ideal insulation, but the heat fluxes are very small due to the vacuum chamber. The temperature profile calculated with the two-dimensional model, which considers the sponge as one continuous phase, can be fitted to the measured temperatures by variation of the thermal conductivity of the solid sponge. The two-dimensional model is based on the energy balances in differential volume elements. Each element exchanges heat with its four neighbouring elements via the surrounding surfaces. The boundary conditions are defined by the temperature of the heating

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Fig. 4. SEM micrographs comparing the original strut material with the sintered solid discs: (a) original alumina strut material and (b) disc of alumina.

Fig. 5. (a) Temperature dependence of the specific heat capacity of alumina, mullite and OBSiC strut material, and (b) comparison of the experimental determined specific heat capacity of alumina strut material with the literature data [20].

and the cooling plate as well as the temperature of the surrounding. The properties of the polystyrene and Teflon insulations as well as the metal of the housing of the vacuum chamber are well known and integrated in the calculation model. The heat transfer coefficient between the Teflon cylinders and the sponge has been estimated. These heat transfer coefficients are quite high because of the small air gap due to the high contact pressure in the experimental setup. Furthermore, radiation between the Teflon layer and the metal of the housing has been integrated in the calculation model.

In Fig. 6 the two-phase thermal conductivity of alumina, mullite and OBSiC sponges in dependence of the temperature is shown. The temperature of each experimental value corresponds to the arithmetic mean of the two surface temperatures of the reference material (Teflon). The varied parameter is the ppi number; the porosity of the investigated samples was nearly constant (±1.5%). From the results presented in Fig. 6 no clear dependence of the two-phase thermal conductivity from the ppi number can be noticed. The small differences are caused by the porosity variation and by the

Fig. 6. Two-phase thermal conductivity of alumina, mullite and OBSiC sponges at constant porosity and varying ppi number in dependence of the temperature.

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measurement error (ffi15%). This observation corresponds with results of Paek et al. [9], who described that the thermal conductivity of aluminum-based metal sponges is scarcely affected by variations in the cell size at constant porosity in comparison to the influence of the porosity at constant cell size. Paek et al. investigated porosities from 89% to 96% and cell diameters from 650 lm to 2500 lm, which are similar to the investigated sponges in this work. The temperature dependence of the two-phase thermal conductivity at the investigated temperature range can also be neglected. Fig. 7 shows exemplary the results for alumina sponges due to variation of the porosity at constant ppi number. With increasing solid mass in the sample (decreasing porosity) the two-phase thermal conductivity increases considerable, which results from the higher thermal conductivity of the solid in comparison to the fluid (here: air). This agrees also with Paek et al. [9], who described, that the two-phase thermal conductivity of aluminum-based metal sponges increases as porosity decreases. An interesting point is the significant difference between the thermal conductivity of the sponges and of air (kf ¼ 0:03 W=ðmKÞ, [17]) due to the second continuous phase of the solid material. 4.4. Modelling of data employing a modified Krischer model For theoretical description of the obtained experimental data, a model similar to the well known Krischer model is used. The original Krischer model can be expressed by the following equation [11]:

k2ph ¼

1 ðused for packed beds of spheresÞ a=kserial þ ð1  aÞ=kparallel ð3Þ

Fig. 7. Two-phase thermal conductivity of alumina sponges at constant ppi number and varying porosity in dependence of the temperature.

with kserial ¼

1 w=kf þ ð1  wÞ=ks

and

kparallel ¼ w  kf þ ð1  wÞ  ks It is based on the combination of resistances (compare also Table 1). The two marginal cases are the serial connection of the thermal conductivities of the solid and the fluid as maximum and the parallel connection of these as minimum resistance (see Fig. 8(a) and (b)). Unlike Krischer, we combine these two marginal cases by a parallel combination (see Fig. 8(d)) instead of a serial combination (see Fig. 8(c)):

k2ph ¼ b  kserial þ ð1  bÞ  kparallel

ðused for spongesÞ

ð4Þ

This makes more sense for a material with a continuous solid phase, because heat transfer can occur in the parallel part without restriction from a serial part. For weighting the two marginal cases the parameter b is used, where b = 0 stands for a parallel connection and b = 1 for a serial connection. Typically, the marginal cases as well as the modelling results are shown in a diagram ‘‘two-phase thermal conductivity of the sponge divided by the thermal conductivity of the fluid” versus ‘‘porosity”. For the calculation of kserial and kparallel , the thermal conductivity of air at 50 °C (kf ¼ 0:03 W=ðmKÞ, [17]) and the thermal conductivities of the ceramics for ks shown in Table 5 were used. In Fig. 9 the comparison of the modelling results to the experimental data for sponges made of alumina (20 ppi) is presented. The weighting parameter b has been fitted to the experimental data of all investigated sponge samples, where the material, the porosity and the pore density (ppi number) were varied. The fitting procedure has been done by minimizing the root mean square deviation (RMSD). So, the parameter b can be taken as a universal constant for the investigated sponge samples and results in b = 0.51. In Table 6 the calculated two-phase thermal conductivities based on the modelled parameter b ðkcalc Þ in comparison to the experimental values ðkexp Þ for all three types of sponges are given. For the alumina samples a maximum error of 4% and a mean error of 2% have been determined, for mullite 23% and 12%, respectively. In the case of OBSiC the errors turned out to be 48% and 44% (errors calculated from Eq. (1)). The higher error for these samples is assumedly caused by the thermal conductivity of the solid, which could be to low due to the procedure of producing the replica discs. By milling the sponge powder, the SiC splitters have been crushed, too, resulting in a higher quantity of much smaller SiC splitters. Since the thermal resistance mainly lies in the contact between the SiC phase and the matrix, the thermal conductivity of the OBSiC sponges might be higher than the values measured for the replica discs. When fitting the parameter b, the maximum error and the mean error could be reduced to 16% and 7%, respectively, by

Fig. 8. (a) Serial connection, (b) parallel connection, (c) serial combination of (a) and (b) (Krischer model), and (d) parallel combination of (a) and (b) as used for modelling the sponges.

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on the results. It could be shown that, compared with packed beds of spheres, the sponges are more advantageous because of their higher two-phase thermal conductivity in combination with higher porosity, which means less pressure drop. For the determination of the thermal conductivity of the solid network structure, the authors propose a procedure to replicate the characteristics of the strut material. Acknowledgments The authors thank the German Research Foundation (DFG) for funding the Research Group FOR 583 ‘‘Solid Sponges – Application of monolithic network structures in process engineering”. They also thank Michael Rohmer and Markus Schlegel for supporting the authors in the experiments. References Fig. 9. Results of the modelling of alumina sponges and the original Krisher model [11] for packed beds of spheres (w = 0.4 and a = 0.2) compared with the experimental results (20 ppi sample, black triangles).

Table 6 Comparison of calculated and experimentally determined values for the two-phase thermal conductivity of alumina, mullite and OBSiC sponges. Porosity

75% 80%

85%

ppi

20 10 20 30 45 20

Alumina

Mullite

OBSiC

kexp =kair

kcalc =kair

kexp =kair

kcalc =kair

kexp =kair

kcalc =kair

112.39 89.49 92.79 90.01 93.42 67.67

115.90 92.91 92.91 92.91 92.91 69.93

22.01 13.47 15.48 18.28 15.40 11.94

20.56 16.64 16.64 16.64 16.64 12.72

70.43 52.16 56.53 57.09 48.52 36.20

36.96 29.76 29.76 29.76 29.76 22.57

assuming a value for the solid thermal conductivity of ks;OBSiC ¼ 15 W=ðmKÞ. In comparison to this, the calculation for packed beds of spherical particles is also presented in Fig. 9. For this calculation the original Krischer model was used (see Eq. (3)). These packed beds have typical porosities of 40%, the parameter a is chosen to a = 0.2 (see [11]). It is evident, that the two-phase thermal conductivity of the sponge is about five times higher than that of packed beds with the same material, although the porosity of the sponges is higher by about a factor of two. Due to a high contact resistance, the low thermal conductivity of packed beds of spheres compared to sponges is caused by the point contact between the solid spheres. So sponges have a better heat conduction combined with less pressure drop in comparison to packed beds of spheres. This might be very favourable for industrial applications. 5. Conclusion In this contribution the experimental results of measurements for the thermal conductivity of sponges made of alumina, mullite and oxidic-bonded silicon carbide (OBSiC) (without flow, free convection and radiation) are presented. In all cases, the two-phase thermal conductivities of the sponges increase with decreasing porosity and are nearly constant by varying the ppi number. It was possible to apply a model similar to the Krischer model [11]

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