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Thermal conductivity and permeability of consolidated expanded natural graphite treated with sulphuric acid
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Thermal conductivity and permeability of consolidated expanded natural graphite treated with sulphuric acid L.W. Wang a b
a,b
, S.J. Metcalf b, R.E. Critoph
b,* ,
R. Thorpe b, Z. Tamainot-Telto
b
Institute of Refrigeration and Cryogenics, Shanghai Jiao Tong University, Shanghai 200240, China School of Engineering, University of Warwick, Coventry CV4 7AL, UK
A R T I C L E I N F O
A B S T R A C T
Article history:
The thermal conductivity and permeability of consolidated expanded natural graphite trea-
Received 29 October 2010
ted with sulphuric acid (ENG-TSA) were measured both parallel and perpendicular to the
Accepted 29 June 2011
direction of compression used to produce the samples. Results showed that the thermal
Available online 3 July 2011
conductivity and permeability were highly anisotropic. The thermal conductivity perpendicular to the direction of compression was 50 times higher than that parallel to the direction of compression and the permeability was 200 times higher. The maximum thermal conductivity measured was 337 W m1K1 at a bulk density of 831 kg m3. The permeability perpendicular to the direction of compression varied in the range of 1011 to 1016 m2 as the density increased from 111 to 539 kg m3. The specific heat was measured, and the average value is 0.89 kJ kg1K1 in the temperature range 30–150 C. As a type of heat transfer matrix the thermal diffusivity was about five times higher than that of, for example, pure aluminium due to the combination of improved thermal conductivity with comparatively low density and reasonable specific heat. 2011 Elsevier Ltd. All rights reserved.
1.
Introduction
Adsorbents such as active carbons, zeolites etc. are used in adsorption cycles for refrigeration, heat pumping or energy storage. The cycles are all discontinuous batch process involving periodic adsorption and desorption. A major technical challenge is to achieve high thermal conductivity within the bed without a correspondingly large increase in the thermal capacity. For example, activated carbon (AC) is mainly utilised for adsorbates such as ammonia or methanol for refrigeration [1,2] and methane for energy storage [3], and poor heat transfer performance will lead to longer cycle time and smaller refrigeration power or low energy storage and discharge rate. The greatest heat transfer resistance is a result of the poor thermal conductivity of granular adsorbent, which is typically 0.2 W m1K1. In order to improve the thermal conductivity of adsorbents, compressed mixtures of expanded natural graphite (ENG) and
adsorbent in which the graphite forms a highly conductive matrix around the particles of adsorbent have been studied. For example, ENG impregnated with CaCl2, termed IMPEX [4] was evaluated as an adsorbent for ammonia. Later, Han and Lee studied the permeability of composites of ENG-metallic salt for heat pumps, and found that the permeability of gas was in the range of 1016 to 1012 m2, depending on the reacting pair, bulk density and mass fraction of the ENG [5]. Fujioka et al. developed a composite adsorbent composed of CaCl2, ENG, and AC fibre, which improves the thermal conductivity of the adsorbent from less than 0.15 to over 0.6 W m1K1 [6]. Consolidated composites of LaNi5 and compressed ENG improved the thermal conductivity of the metal hydride from 0.1 to 3–6 W m1K1 showing a good potential for the development of devices for the storage of hydrogen with high power density [7]. However, the thermal conductivity of ENG is limited – a pure pellet of ENG with a porosity of 79.1% only
* Corresponding author: Fax: +44 2476 418922. E-mail address: [email protected] (R.E. Critoph). 0008-6223/$ - see front matter 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.carbon.2011.06.093
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has a conductivity of 8 W m1K1 when the density of ENG is 1250 kg m3 [8]. Thus in applications of ENG to enhanced conductivity of adsorbent beds the thermal conductivity is always lower than 6–7 W m1K1 [7,9,10]. Py et al. proposed a new method to improve thermal conductivity [11], which is a little complex, requiring that the precursor and the activation agent for composite preparation for AC and ENG were pre-mixed, followed by compression and activation (physical or chemical). Such methods achieved a thermal conductivity as high as 32 W m1K1 [11], but the composites were only evaluated for CO2 adsorption for gas purification [9]. Chemical and electrochemical oxidation of graphite in acid leads to the formation of salt-like intercalated compounds [12–14]. Such materials are mainly utilised for the improvement of performance in PEM fuel cells [15] or batteries [16]. One type of expanded graphite previously evaluated as an enhancer of thermal conductivity for phase change materials was produced by consolidating graphite flakes that had been impregnated with sulphuric and nitric acid and then heattreated at 900 C. The results showed that the thermal conductivity of the consolidated material was as high as 16.6 W m1K1 [17] when the density of the graphite was 220 kg m3. However, there is no research on the permeability and thermal conductivity of consolidated pure ENG treated with acid. In order to have an overview of the suitability of consolidated expanded natural graphite treated with acid for enhancing heat transfer performance, the thermal conductivity, permeability and specific heat of consolidated expanded natural graphite treated by sulphuric acid (ENG-TSA) with different density (obtained by using different compaction pressures) have been measured. Since thermal conductivity and permeability are anisotropic in consolidated ENG [18] they are measured both parallel and perpendicular to the direction of compression.
2.
Experiments
2.1.
Production of the consolidated blocks
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The ENG-TSA was manufactured by Mersen (previously Carbone Lorraine) in France. The sample was made from natural graphite that was soaked in sulphuric acid, which became intercalated in the layered structure of the graphite. Finally the sample was exfoliated by heating in a flame, forming expanded graphite with much lower density than normal ENG whilst the intercalated acid was removed. The composition of this material, as supplied by Mersen, is shown in Table 1. The carbon content in the material is greater than 99.8%,
and the ash content is less than 0.2%. The density of the material is only 5–6 kg m3, which is about three times less than that of ENG. In order to measure the anisotropic properties, two moulds were used to produce samples with the compression direction either in the plane of a disk or along its axis, as shown in Fig. 1. Fig. 1a shows a disk for which the direction of compression was parallel to the axis. Fig. 1b shows a sample of plate, which was compressed in a rectangular section tube, and a circular disk was then cut from the plate as shown. For the disk sample in Fig. 1a the diameter is 50.8 mm. The plate is 72 mm in width and 95 mm in length. The diameter of the disk cut from it is also 50.8 mm. The two types of sample were both heated in an oven at 150 C for 4 h to make sure there was no retained water before they were compressed.
2.2.
Measurement of thermal conductivity
Thermal conductivity was measured by an Anter Quickline-10 using the ASTM E1530 guarded thermal flow meter method. The principle is shown in Fig. 2. The instrument includes a heater, upper plate, lower plate, reference calorimeter, and heat sink. The sample was placed between the upper plate and lower plate, and the temperatures of the upper plate, lower plate and heat sink were measured by thermistors.The thermal conductivity is calculated as follows: k¼
d Rs
ð1Þ
where k is the thermal conductivity (W m1 K1), d is the thickness of the sample (m), and Rs is the thermal resistance of the sample (m2 K W1). d ðTu Tl Þ F ðTu Tl Þ Rint ¼ ¼ Rint Q k ðTl Th Þ DTs ¼F Rint DTr
Rs ¼
ð2Þ
where Tu, Tl and Th are values of temperature for upper plate, lower plate and heat sink (K), respectively, as shown in Fig. 2; Q is the thermal flux through the sample (W m2); Rint is the interfacial thermal resistance (m2 K W1) between the surface of sample and plates; F is the reference thermal resistance (m2 K W1); DTs is the temperature difference across the sample (K), and DTr is the temperature difference across the referenced sample (K). Before the thermal conductivity of samples was measured the apparatus must be calibrated with three samples with known thermal conductivity to determine reliable values for Rint and F in Eq. (2).
Table 1 – The composition of ENG-TSA. Carbon content (%) >99.8
Ash content (%) <0.2 Average ash content (ppm) Fe 150
Si 230
Mg 60
Al 20
Ca 10
Cr 10
Mn 10
Cu 10
Resistance to temperature in oxidising atmosphere
Density kg m3
500 C
5–6
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Since the samples to be tested were porous media with very low gas velocity, the Ergun model is applicable. Assuming the gas to be ideal and no accumulation of gas inside the sample, for axial flow of gas, the intrinsic characteristic of the material is given by the following expression [19]: W¼
1 þ BX K
ð3Þ
In which W¼ Fig. 1 – Consolidated ENG-TSA, (a) sample of disk, (b) sample of plate.
Heater Upper plate
•
Tu
Sample Lower plate
•
Tl
Reference
Heat flux
calorimeter
transducer
•
X¼
ma ; lS
ma ¼ qSva
ð4Þ
where K is permeability (m2), B is the shape factor of the sample, p1 and p2 are the pressure of inlet and outlet air (Pa), obtained from the measured outlet pressure and the pressure drop. S is the cross sectional area of sample (m2), R is the gas constant (J kg1 K1), T is the temperature of sample (K), which does not change significantly through the sample, l and q are the viscosity (Pa s) and density (kg m3), respectively, of gas; ma is the mass flowrate of gas (kg s1), and va is the mean free stream axial velocity of the gas (m s1). To measure the permeability, W and X were calculated using the experimental data of flowrate, pressure drop, ambient temperature, and pressure of outlet gas, etc., and then K was obtained from the relationship between W and X, which was linear with 1/K being the intercept.
Th
Heat sink
Fig. 2 – Thermal conductivity test principle.
2.3.
ðp21 p22 ÞS ; 2RTlma Dz
Measurement of permeability
The permeability of the samples was measured using a specially designed unit shown in Fig. 3. The main components are a sample holder, a differential pressure transducer to measure the pressure drop in the flow of gas through the sample and a flow meter. The sample is placed between the steel ring and steel step inside the sample holder with PTFE tape to prevent leakage of gas around the outside. The permeability experiments comprised measurement of the pressure drop Dp across the block when compressed air was flowing through it with flowrate qv. Two methods were used to measure the flowrate; higher flowrates were measured using a Rotameter, and low flowrates was measured by air collection in an inverted measuring cylinder initially full of water.
Fig. 3 – The permeability test unit.
3.
Results and discussion
3.1. Thermal conductivity of disks (parallel to the compacting direction) of consolidated ENG-TSA The thermal conductivity of the disks of consolidated ENGTSA was measured as described above. The three calibration samples were: a steel cylinder with diameter 50.8 · 12.7 mm thickness and two Vespel disks with diameter 50.8 · 3.175 mm thickness and diameter 50.8 · 6.35 mm thickness. The calibration results are shown in Fig. 4, in which point A is the steel sample, point B is the Vespel sample with thickness of 3.175 mm, and point C is the Vespel sample with thickness of 6.35 mm. From Fig. 4 the values of F and Rint in Eq. (2) were calculated as 2.26 · 103 m2 K W1 and 5.99 · 104 m2 K W1 respectively. Then the thermal conductivity of the samples was obtained by measurement of Tu, Tl, and Th. For the test results to be accurate, the thermal resistance obtained must fall
Fig. 4 – Characteristic line for calibration samples.
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within the range of samples used for calibration, which were from 8.74 · 104 to 1.6759 · 102 m2 K W1. 31 Consolidated samples of disk were tested, and the density, thickness, and thermal resistance of samples are shown in Fig. 5. Their density ranged from 42 to 1263 kg m3. As Eq. (2) shows, the thermal resistance is larger when the thickness of the sample is larger. Because the thermal resistance must lie within the range of the calibrated experiments, i.e. 8.74 · 104 to 1.68 · 102 m2 K W1, in the experiments the thickness of the samples was controlled to give a thermal resistance within the desired range. The highest and lowest values of resistance obtained from different samples were 4.84 · 103 and 8.80 · 104 m2 K W1, respectively. The thermal conductivity of the consolidated samples of disk is shown in Fig. 6. The thermal conductivity increases rapidly as density increases, then stabilises, and finally decreases. The thermal conductivity stabilises at a value of about 5–6 W m1K1 when the density is between 1000 and 1200 kg m3. The thermal conductivity of the consolidated disks of ENG-TSA is much higher than that of consolidated disks of ENG [18], and the highest value for ENG-TSA is 8.9 W m1K1, which is about five times more than the highest value for ENG [18]. The corresponding compacting pressure needed for producing consolidated disks of ENGTSA is shown in Fig. 6. We can see there is a relationship between thermal conductivity and compacting pressure or density. The thermal conductivity of the material decreases when the density is higher than 600 kg m3. The relationship between compacting pressure and density is roughly linear when the density is lower than 600 kg m3, and increases rapidly and non-linearly when the density is higher than 600 kg m3. It means that the consolidated ENG-TSA is much more difficult to compress when the density is higher than 600 kg m3. Fig. 6 also shows that the density beyond which compaction pressure increases rapidly is the same density beyond which conductivity decreases.
3.2. Thermal conductivity (perpendicular to direction of compression) of consolidated plates of ENG-TSA The consolidated plates of ENG-TSA had much higher thermal conductivity than disks of consolidated ENG-TSA due to the orientation of the micro layers. Three calibration lines were needed for the samples of plate in order to enable the thermal resistance obtained to fall within the range of calibration. One was the calibration line shown in Fig. 4, and the other two lines are shown in Fig. 7. Four samples are utilised for the calibration experiments in Fig. 7. Point of A is for
Fig. 5 – Thermal resistance and thickness vs. density of the consolidated samples of disk.
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Fig. 6 – Thermal conductivity and compacting pressure vs. density of consolidated disks of ENG-TSA.
a stainless steel sample with 50.8 mm diameter · 12.7 mm thickness. Points of D, E, F are aluminium 6082 samples with 50.8 diameter · 39 mm thickness, 50.8 diameter · 18 mm thickness, and 50.8 mm diameter · 14 mm thickness, respectively. For the calibration line of RsL, values of F and Rint in Eq. (2) are calculated from the slope of 1.621 · 103 and the intercept of 3.31 · 104 m2 K W1 of the line of best fit, and the calibrated range is from 7.8 · 105 to 2.17 · 104 m2 K W 1 . For the calibration line of RsH, values of F and Rint in Eq. (2) are calculated from the slope of 1.769 · 103 and the intercept of 3.74 · 104 m2 K W1 of the line of best fit, respectively, and the calibrated range is from 1.0 · 104 to 8.74 · 10 4 m2 K W1. 10 Samples were tested, and density, thickness, and thermal resistance of the samples are shown in Fig. 8. The thermal resistance decreases very rapidly with increasing density. For the samples with density equal to or lower than 204 kg m3 the thermal resistance is between 9.15 · 104 and 4.87 · 103 m2 K W1, and the calibration line of Fig. 4 is utilised for the calculation of the thermal resistance of the samples. For the samples with density higher than 204 kg m3 and equal to or lower than 679 kg m3, Fig. 8 shows that the thermal resistance is between 2.11 · 104 and 5.20 · 104 m2 K W 1 , and the calibration line of RsH in Fig. 7 is used For the samples with density of 754 and 831 kg m3, the thermal resistance is 1.71 · 104 and 1.28 · 104 m2 K W1, respectively, and the calibration line of RsL in Fig. 7 is used. When the thermal resistance is lower than 5 · 104 m2 K W1, the measuring error due to the interfacial thermal resistance will greatly influence the accuracy if the surface of the samples is much different from that of the calibration samples. In order to obtain accurate data, the surface of the samples with density equal to or higher than 259 kg m3 was machined
Fig. 7 – Calibration results for consolidated plates of ENGTSA.
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which the compacting pressure required increases rapidly is somewhat higher than the density beyond which conductivity increases rapidly. This is in complete contrast to the trends shown for disk samples (conductivity parallel to direction of compression) above.
3.3.
Fig. 8 – Thermal resistance and thickness vs. density of consolidated plates.
with same finishing process as the surface of aluminium 6082 calibrated samples. The measurement error will be smaller when the thermal resistance of sample is larger, thus for the samples with smaller thermal resistance, i.e. for the samples with density larger than 600 kg m3, the largest thickness of 43 mm for experiments is utilised in order to maximise the thermal resistance and reduce the measurement error. The thermal conductivity of the consolidated plates is shown in Fig. 9. Thermal conductivity increases rapidly as the density increases. The highest thermal conductivity is 337 W m1K1 when the density of the sample is 831 kg m3. It is almost one hundred times higher compared to the values for the consolidated plates of ENG [18], and almost 50 times higher than the samples of disk with similar density. For the samples with density higher than 900 kg m3, accurate results cannot be obtained because the thermal resistance of sample is much lower than the range of the equipment, which should be greater than 2 · 104 m2 K W1, and also the influence on the measuring error of the interfacial resistance becomes increasingly significant, possibly as high as 30%. For the samples of plate, the compacting pressure increases almost linearly with the density whilst density is lower than 600 kg m3. The trend is similar to that of consolidated samples of disk with density lower than 600 kg m3. It increases rapidly when the density is higher than 600 kg m3. Fig. 9 also shows that the density beyond
Fig. 9 – Thermal conductivity and compacting pressure vs. density for plates of consolidated ENG-TSA.
Permeability
Five consolidated samples of disk and five consolidated samples of plate were chosen for the permeability measurements, and the results are shown in Table 2. In Table 2 the permeability decreases rapidly with increased density for both samples of disk and plate. The permeability of samples of plate (perpendicular to the direction of compression) is at least 30 times higher than those of the disk (parallel to compression). When the density is lower than 200 kg m3, the permeability of the samples of plate is more than 200 times higher than that of the disk.
3.4. Scanning electronic microscope (SEM) pictures of consolidated samples Measurement shows that the consolidated samples of plate (perpendicular to compression) not only have higher thermal conductivity, but also have higher permeability than those of the disks (parallel to compression). These results are mainly due to the micro layers formed by the compressive force. SEM pictures of consolidated samples of disk and consolidated samples of plate are shown in Fig. 10. All magnifications in Fig. 10 fall within 90–130·. Fig. 10 shows that when the density of the samples is lower, for example Fig. 10a and d, the micro structure of the samples has a worm-like structure, which is similar to that of consolidated ENG. But when the density is higher, for example when the density is higher than 300 kg m3, the worm structure of the samples is replaced by layers, and the layers of graphite appear to be distributed much more uniformly than ENG with similar density [18]. It is suggested that this uniformity accounts for consolidated ENG-TSA showing a much higher thermal conductivity compared to consolidated ENG. The SEM pictures indicate possible reasons for the trend of thermal conductivity in Figs. 6 and 9. For the disk samples (Figs. 6 and 10a–c), the thermal conductivity is influenced by two factors. One is the contact resistance between layers and the other is conduction through the layers, both parallel and perpendicular to the graphite flakes. It is suggested that as the disk density increases (up to 250 kg m3) there is an initial rise in conductivity because the contact resistance is reduced. Within the layers there is not complete alignment of flakes perpendicular to the compression direction and so a significant contribution to the total conductivity is made by conduction in the plane of the flakes, many of which are still oriented not completely perpendicular to the compression direction. With further compression (density 250–650 kg m3), the thermal conductivity keeps at a stabilized value about 8– 9 W m1K1 because the positive influence of reduced resistance between flakes balances with negative influence of layers aligning perpendicular to the heat transfer direction. With almost complete alignment (density above 650 kg m3), the
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Table 2 – Permeability of different samples. Type of block
Density (kg m3)
Permeability (m2)
Direction of gas flow
Consolidated samples of disk
75 164 212 309 475
5.30 · 1014 1.12 · 1015 3.89 · 1016 9.15 · 1017 1.49 · 1017
Parallel to the compressive direction
Consolidated samples of plate
111 211 303 487 539
1.12 · 1011 1.17 · 1014 2.01 · 1015 3.96 · 1016 1.64 · 1016
Perpendicular to the compressive direction
Fig. 10 – SEM pictures for consolidated samples with different values of density, (a) sample of disk, 65 kg m3, 110·, (b) sample of disk, 379 kg m3, 104·, (c) sample of disk, 1084 kg m3, 106·, (d) sample of plate, 65 kg m3, 90.8·, (e) sample of plate, 363 kg m3, 128·, (f) sample of plate, 702 kg m3, 116·.
thermal resistance stabilises at a lower level with all heat transfer in the graphite perpendicular to the plane of the flakes. For the plate samples (Fig. 10d–f) the thermal conductivity always increases with increasing compacting pressure because the heat transfer is all in the plane of the graphite flakes and the better the alignment the better the heat transfer (Fig. 9). For the permeability in Table 2, the samples of both disk and plate have lower permeability with higher density since there is less void space available to allow the passage of gas. The samples with highest density would be unsuitable for use as heat adsorbent matrices because of the poor mass transfer.
3.5. Specific heat and overview of ENG-TSA as a heat transfer enhancing matrix for adsorbents As explained above, if the intention is to enhance thermal conductivity in adsorbent beds by use of a conducting matrix
of graphite or other material it is important that the matrix should have small thermal capacity compared with that of the adsorbent. The specific heat of ENG-TSA was measured using a Seteram SENSYS DSC, and the specific heat of AC manufactured by the Chemviron with the size of 80–100 mesh was also measured. The composite adsorbent with two different types of heat transfer matrix, i.e. ENG-TSA and aluminum powder, are calculated and compared to confirm the good performance of ENG-TSA using Eq. (5), in which Cp is calculated based on 1 kg adsorbent, i.e. 1 kg AC. This is simply to reflect that the function of the composite material is to adsorb and that from the point of view of thermodynamic cycle efficiency the conductive matrix represents a wasteful thermal mass. The use of the conductivity enhancing matrix improves the power density but decreases the efficiency as the specific heat per unit of adsorbing material increases. 1 ½ð1 rÞ Cp;AC þ r Cp;matrix ð5Þ Cp ¼ ð1 rÞ where Cp is the specific heat capacity for the composite adsorbent with 1 kg AC (J kg1 K1), r is the ratio of ENG-TSA or
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3.6.
Fig. 11 – Specific heat vs. temperature for ENG-TSA, AC and composite adsorbents.
aluminium inside the composite adsorbents, Cp,AC and Cp, matrix are the specific heat capacity of AC and heat transfer matrix (J kg1 K1), respectively. The C p, matrix for aluminium is obtained from [20]. The results are shown in Fig. 11. The specific heat of ENGTSA and AC all increase with increasing temperature and the values of ENG-TSA are much lower than that of AC. The average values of specific heat in the range of 20–150 C are 0.89 and 1.01 kJ kg1 K1 for ENG-TSA and AC, respectively, and the value of ENG-TSA is 12% less than the value of AC. The average specific heat of ENG-TSA is slightly lower than the average value of aluminium [20] in the temperature range of 20–150 C, which is 0.92 kJ kg1 K1. The high thermal conductivity and low specific heat of compact ENG-TSA indicate that ENG-TSA is a promising heat transfer matrix, even better than some metals. Two types of composite adsorbents are compared in Fig. 11, and the sample with ENG-TSA as matrix is slightly lower than the value of the sample with aluminium as a matrix.An appropriate figure of the merit of thermal conductivity and specific heat is the thermal diffusivity of the matrix material: a ¼ kðq Cp Þ
ð6Þ 2
1
where a is the thermal diffusivity (m s ), q is density (kg m3). Pure aluminium has a thermal diffusivity of 9.4 · 105 m2 1 s for the temperature range of 30–150 C, whereas ENGTSA conducting perpendicular to the compression direction with a density of 831 kg m3 and thermal conductivity of 337 W m1K1 has a thermal diffusivity of 4.6 · 104 m2 s1, which is about five times higher. Compared with the consolidated active carbon sorbent LM8 of reference [19] that was intended for adsorption refrigeration and heat pump applications, the thermal conductivity of ENG-TSA is 100 times higher whilst the permeability is similar.
Analysis of experimental error
For the thermal resistance of samples higher than 2 · 104 m2 K W1, the accuracy of the Quickline-10 is 3–8%. When the thermal resistance of the samples is lower than 2 · 104 m2 K W1, the interfacial thermal resistance will greatly influence the results. In order to obtain accurate results, firstly the surface of the samples was machined with the same finishing process for calibrated samples of aluminium 6082. Secondly the samples with density higher than 600 kg m3 are machined to different thicknesses, and then the thermal conductivity was measured for these samples, and the results are shown in Table 3. The test results are compared with the data in Fig. 9, and the relative difference was calculated by j
Dk kdt k j¼j j k k
ð7Þ
where Dk is the relative difference of thermal conductivity for the samples with same density, k is the thermal conductivity of samples shown in Fig. 9, kdt is the thermal conductivity shown in Table 3.Results showed that the largest relative difference is 4.1%. The error for the permeability measurements is: j
dK dW BdX dW BdX j¼j j6j jþj j K W BX W BX W BX
ð8Þ
The pressure is calculated from the atmospheric pressure and the pressure drop is measured by the differential pressure transducer with an error of ±0.5%. The air flowrate is measured by a Rotameter with an error of ±4% when testing the samples with large permeability at high flowrate. When the flowrate is smaller, it is tested by a timer and measuring cylinder and the error is mainly caused by the difference of time for the last bubble to rise from the bottom of the measuring cylinder. The largest error of 9.2% occurs for the disk sample of 475 kg m3, which has the smallest permeability and longest testing time. The relative error of K is calculated, and its average error is 9.6%, and the largest error is 15.7%. For the specific heat, the largest error expected from the Seteram SENSYS DSC for the calibration of heat is 1.8%, and the corresponding largest uncertainty in the temperature is 0.011%. Then the total largest error calculated for Cp is 1.811%.
4.
Conclusions
Expanded graphite treated with acid, which has proved promising for electrical conducting process, had been evaluated for heat and mass transfer applications in adsorbent beds. Results show that expanded natural graphite treated with sulphuric acid (ENG-TSA) is a promising heat transfer matrix,
Table 3 – Thermal conductivity of different samples for the comparison of error. No. of sample Thickness (mm) Density (kg m3) kdt (W m1 K1) Relative difference of k
1
2
3
4
5
6
35 831 325 3.5%
28 831 342 1.4%
35 754 242 3.8%
28 754 251 0.4%
35 679 199 2.1%
28 679 195 4.1%
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even better than pure aluminium. The conclusions are as follows: (1) The direction parallel to the direction of compression has poorer heat and mass transfer performance. The maximum value of thermal conductivity is 8.9 W m1 K1. The permeability varies from 10 14 to 10 17 m2 as the density varies from 75 to 475 kg m3. (2) The optimal heat and mass transfer direction is perpendicular to the direction of compression used to produce the consolidated samples. The highest thermal conductivity is 337 W m1K1 when the density is 831 kg m3, and the permeability varies from 1011 to 1016 m2 for samples of plate as the density varies between 111 and 539 kg m3. (3) The SEM micrographs show that the consolidated ENGTSA has different characteristics compared with that of consolidated ENG [18] when the density is higher than 300 kg m3. A worm-like structure exists in consolidated ENG even when the density is as high as 700 kg m3, but for consolidated ENG-TSA, the wormlike structure only exists for samples with lower density. When the samples have density higher than 300 kg m3, the micro structure is composed of organised layers. Such a phenomenon leads to a much higher thermal conductivity than that of ENG. (4) In the temperature range of 30–150 C the specific heat of ENG-TSA is 12% lower than the AC adsorbent. Taking thermal diffusivity as a figure of merit for performance as a thermally enhancing matrix, it is approximately five times better than aluminium. Compared to the monolithic AC if the permeability is kept at the same permitted level then the conductivity is about 100 times higher.
Acknowledgements This work was supported by a Royal Society Incoming Fellowship, the AWM Science City Energy Efficiency Project, the Natural Science Foundation of China under the contract No. 50736004 and contract No. 50806043, and the National 100 Outstanding PhD thesis Foundation in China.
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[2] El-Sharkawy II, Hassan M, Saha BB, Koyama S, Nasr MM. Study on adsorption of methanol onto carbon based adsorbents. Int J Refrig 2009;32:1579–86. [3] Perrin A, Celzard A, Mareche JF, Furdin G. Improved methane storage capacities by sorption on wet active carbons. Carbon 2004;42:1249–56. [4] Mauran S, Coudevylle O, Lu HB. Optimization of porous reactive media for solid sorption heat pumps, Inter sorption heat pump confer (ISHPC). Canada: Montreal; 1996. p. 3–8. [5] Han JH, Lee KH. Gas permeability of expanded graphitemetallic salt composite. Appl Therm Eng 2001;21:453–63. [6] Fujioka K, Hatanaka K, Hirata Y. Composite reactants of calcium chloride combined with functional carbon materials for chemical heat pumps. Appl Therm Eng 2008;28:304–10. [7] Kim KJ, Montoya B, Razani A, Lee KH. Metal hydride compacts of improved thermal conductivity. Int J Hydrogen Energ 2001;26:609–13. [8] Klein HP, Groll M. Heat transfer characteristics of expanded graphite matrices in metal hydride beds. Int J of Hydrogen Energ 2004;29:1503–11. [9] Menard D, Py X, Mazet N. Activated carbon monolith of high thermal conductivity for adsorption processes improvement, Part A: Adsorption step. Chem Eng Process 2005;44:1029–38. [10] Ahmet S, Ali K. Thermal conductivity and latent heat thermal energy storage characteristics of paraffin/expanded graphite composite as phase change material. Appl Therm Eng 2007;27:1271–7. [11] Py X, Daguerre E, Menard D. Composites of expanded natural graphite and in situ prepared activated carbons. Carbon 2002;40:1255–65. [12] Inagaki M, Iwashita N, Kouno E. Potential change with intercalation of sulphuric acid into graphite by chemical oxidation. Carbon 1990;28:49–55. [13] Metrot A. Charge transfer reactions during anodic oxidation of graphite in H2SO4. Synthetic Met 1981;3:201–7. [14] Bottomley MJ, Parry GS, Ubbelohde AR, Young DA. Electrochemical preparation of salts from well-oriented graphite. J Chem Soc 1963;1083:5674–80. [15] Dhakate SR, Sharm S, Borah M, Mathur RB, Dhami TL. Expanded graphite-based electrically conductive composites as bipolar plate for PEM fuel cell. Int J Hydrogen Energy 2008;33:7146–52. [16] Zhao HP, Ren J, He XM, Li JJ, Jiang CY, Wan CR. Modification of natural graphite for lithium ion batteries. Solid State Sci 2008;10:612–7. [17] Mills A, Farid M, Selman JR, Al-Hallaj S. Thermal conductivity enhancement of phase change materials using a graphite matrix. Appl Therm Energy 2006;26:1652–61. [18] Wang LW, Tamainot-Telto Z, Metcalf SJ, Critoph RE, Wang RZ. Anisotropic thermal conductivity and permeability of consolidated expanded natural graphite. Appl Therm Energy 2010;30(13):1805–11. [19] Tamainot-Telto Z, Critoph RE. Monolithic carbon for sorption refrigeration and heat pump applications. Appl Therm Energy 2001;21:37–52. [20] Takahashi Y, Azumi T, Sekine Y. Heat capacity of aluminum from 80 to 880 K. Thermochim Acta 1989;139:133–7.
4 9 ( 2 0 1 1 ) 4 8 1 2 –4 8 1 9
available at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/carbon
Thermal conductivity and permeability of consolidated expanded natural graphite treated with sulphuric acid L.W. Wang a b
a,b
, S.J. Metcalf b, R.E. Critoph
b,* ,
R. Thorpe b, Z. Tamainot-Telto
b
Institute of Refrigeration and Cryogenics, Shanghai Jiao Tong University, Shanghai 200240, China School of Engineering, University of Warwick, Coventry CV4 7AL, UK
A R T I C L E I N F O
A B S T R A C T
Article history:
The thermal conductivity and permeability of consolidated expanded natural graphite trea-
Received 29 October 2010
ted with sulphuric acid (ENG-TSA) were measured both parallel and perpendicular to the
Accepted 29 June 2011
direction of compression used to produce the samples. Results showed that the thermal
Available online 3 July 2011
conductivity and permeability were highly anisotropic. The thermal conductivity perpendicular to the direction of compression was 50 times higher than that parallel to the direction of compression and the permeability was 200 times higher. The maximum thermal conductivity measured was 337 W m1K1 at a bulk density of 831 kg m3. The permeability perpendicular to the direction of compression varied in the range of 1011 to 1016 m2 as the density increased from 111 to 539 kg m3. The specific heat was measured, and the average value is 0.89 kJ kg1K1 in the temperature range 30–150 C. As a type of heat transfer matrix the thermal diffusivity was about five times higher than that of, for example, pure aluminium due to the combination of improved thermal conductivity with comparatively low density and reasonable specific heat. 2011 Elsevier Ltd. All rights reserved.
1.
Introduction
Adsorbents such as active carbons, zeolites etc. are used in adsorption cycles for refrigeration, heat pumping or energy storage. The cycles are all discontinuous batch process involving periodic adsorption and desorption. A major technical challenge is to achieve high thermal conductivity within the bed without a correspondingly large increase in the thermal capacity. For example, activated carbon (AC) is mainly utilised for adsorbates such as ammonia or methanol for refrigeration [1,2] and methane for energy storage [3], and poor heat transfer performance will lead to longer cycle time and smaller refrigeration power or low energy storage and discharge rate. The greatest heat transfer resistance is a result of the poor thermal conductivity of granular adsorbent, which is typically 0.2 W m1K1. In order to improve the thermal conductivity of adsorbents, compressed mixtures of expanded natural graphite (ENG) and
adsorbent in which the graphite forms a highly conductive matrix around the particles of adsorbent have been studied. For example, ENG impregnated with CaCl2, termed IMPEX [4] was evaluated as an adsorbent for ammonia. Later, Han and Lee studied the permeability of composites of ENG-metallic salt for heat pumps, and found that the permeability of gas was in the range of 1016 to 1012 m2, depending on the reacting pair, bulk density and mass fraction of the ENG [5]. Fujioka et al. developed a composite adsorbent composed of CaCl2, ENG, and AC fibre, which improves the thermal conductivity of the adsorbent from less than 0.15 to over 0.6 W m1K1 [6]. Consolidated composites of LaNi5 and compressed ENG improved the thermal conductivity of the metal hydride from 0.1 to 3–6 W m1K1 showing a good potential for the development of devices for the storage of hydrogen with high power density [7]. However, the thermal conductivity of ENG is limited – a pure pellet of ENG with a porosity of 79.1% only
* Corresponding author: Fax: +44 2476 418922. E-mail address: [email protected] (R.E. Critoph). 0008-6223/$ - see front matter 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.carbon.2011.06.093
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has a conductivity of 8 W m1K1 when the density of ENG is 1250 kg m3 [8]. Thus in applications of ENG to enhanced conductivity of adsorbent beds the thermal conductivity is always lower than 6–7 W m1K1 [7,9,10]. Py et al. proposed a new method to improve thermal conductivity [11], which is a little complex, requiring that the precursor and the activation agent for composite preparation for AC and ENG were pre-mixed, followed by compression and activation (physical or chemical). Such methods achieved a thermal conductivity as high as 32 W m1K1 [11], but the composites were only evaluated for CO2 adsorption for gas purification [9]. Chemical and electrochemical oxidation of graphite in acid leads to the formation of salt-like intercalated compounds [12–14]. Such materials are mainly utilised for the improvement of performance in PEM fuel cells [15] or batteries [16]. One type of expanded graphite previously evaluated as an enhancer of thermal conductivity for phase change materials was produced by consolidating graphite flakes that had been impregnated with sulphuric and nitric acid and then heattreated at 900 C. The results showed that the thermal conductivity of the consolidated material was as high as 16.6 W m1K1 [17] when the density of the graphite was 220 kg m3. However, there is no research on the permeability and thermal conductivity of consolidated pure ENG treated with acid. In order to have an overview of the suitability of consolidated expanded natural graphite treated with acid for enhancing heat transfer performance, the thermal conductivity, permeability and specific heat of consolidated expanded natural graphite treated by sulphuric acid (ENG-TSA) with different density (obtained by using different compaction pressures) have been measured. Since thermal conductivity and permeability are anisotropic in consolidated ENG [18] they are measured both parallel and perpendicular to the direction of compression.
2.
Experiments
2.1.
Production of the consolidated blocks
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The ENG-TSA was manufactured by Mersen (previously Carbone Lorraine) in France. The sample was made from natural graphite that was soaked in sulphuric acid, which became intercalated in the layered structure of the graphite. Finally the sample was exfoliated by heating in a flame, forming expanded graphite with much lower density than normal ENG whilst the intercalated acid was removed. The composition of this material, as supplied by Mersen, is shown in Table 1. The carbon content in the material is greater than 99.8%,
and the ash content is less than 0.2%. The density of the material is only 5–6 kg m3, which is about three times less than that of ENG. In order to measure the anisotropic properties, two moulds were used to produce samples with the compression direction either in the plane of a disk or along its axis, as shown in Fig. 1. Fig. 1a shows a disk for which the direction of compression was parallel to the axis. Fig. 1b shows a sample of plate, which was compressed in a rectangular section tube, and a circular disk was then cut from the plate as shown. For the disk sample in Fig. 1a the diameter is 50.8 mm. The plate is 72 mm in width and 95 mm in length. The diameter of the disk cut from it is also 50.8 mm. The two types of sample were both heated in an oven at 150 C for 4 h to make sure there was no retained water before they were compressed.
2.2.
Measurement of thermal conductivity
Thermal conductivity was measured by an Anter Quickline-10 using the ASTM E1530 guarded thermal flow meter method. The principle is shown in Fig. 2. The instrument includes a heater, upper plate, lower plate, reference calorimeter, and heat sink. The sample was placed between the upper plate and lower plate, and the temperatures of the upper plate, lower plate and heat sink were measured by thermistors.The thermal conductivity is calculated as follows: k¼
d Rs
ð1Þ
where k is the thermal conductivity (W m1 K1), d is the thickness of the sample (m), and Rs is the thermal resistance of the sample (m2 K W1). d ðTu Tl Þ F ðTu Tl Þ Rint ¼ ¼ Rint Q k ðTl Th Þ DTs ¼F Rint DTr
Rs ¼
ð2Þ
where Tu, Tl and Th are values of temperature for upper plate, lower plate and heat sink (K), respectively, as shown in Fig. 2; Q is the thermal flux through the sample (W m2); Rint is the interfacial thermal resistance (m2 K W1) between the surface of sample and plates; F is the reference thermal resistance (m2 K W1); DTs is the temperature difference across the sample (K), and DTr is the temperature difference across the referenced sample (K). Before the thermal conductivity of samples was measured the apparatus must be calibrated with three samples with known thermal conductivity to determine reliable values for Rint and F in Eq. (2).
Table 1 – The composition of ENG-TSA. Carbon content (%) >99.8
Ash content (%) <0.2 Average ash content (ppm) Fe 150
Si 230
Mg 60
Al 20
Ca 10
Cr 10
Mn 10
Cu 10
Resistance to temperature in oxidising atmosphere
Density kg m3
500 C
5–6
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Since the samples to be tested were porous media with very low gas velocity, the Ergun model is applicable. Assuming the gas to be ideal and no accumulation of gas inside the sample, for axial flow of gas, the intrinsic characteristic of the material is given by the following expression [19]: W¼
1 þ BX K
ð3Þ
In which W¼ Fig. 1 – Consolidated ENG-TSA, (a) sample of disk, (b) sample of plate.
Heater Upper plate
•
Tu
Sample Lower plate
•
Tl
Reference
Heat flux
calorimeter
transducer
•
X¼
ma ; lS
ma ¼ qSva
ð4Þ
where K is permeability (m2), B is the shape factor of the sample, p1 and p2 are the pressure of inlet and outlet air (Pa), obtained from the measured outlet pressure and the pressure drop. S is the cross sectional area of sample (m2), R is the gas constant (J kg1 K1), T is the temperature of sample (K), which does not change significantly through the sample, l and q are the viscosity (Pa s) and density (kg m3), respectively, of gas; ma is the mass flowrate of gas (kg s1), and va is the mean free stream axial velocity of the gas (m s1). To measure the permeability, W and X were calculated using the experimental data of flowrate, pressure drop, ambient temperature, and pressure of outlet gas, etc., and then K was obtained from the relationship between W and X, which was linear with 1/K being the intercept.
Th
Heat sink
Fig. 2 – Thermal conductivity test principle.
2.3.
ðp21 p22 ÞS ; 2RTlma Dz
Measurement of permeability
The permeability of the samples was measured using a specially designed unit shown in Fig. 3. The main components are a sample holder, a differential pressure transducer to measure the pressure drop in the flow of gas through the sample and a flow meter. The sample is placed between the steel ring and steel step inside the sample holder with PTFE tape to prevent leakage of gas around the outside. The permeability experiments comprised measurement of the pressure drop Dp across the block when compressed air was flowing through it with flowrate qv. Two methods were used to measure the flowrate; higher flowrates were measured using a Rotameter, and low flowrates was measured by air collection in an inverted measuring cylinder initially full of water.
Fig. 3 – The permeability test unit.
3.
Results and discussion
3.1. Thermal conductivity of disks (parallel to the compacting direction) of consolidated ENG-TSA The thermal conductivity of the disks of consolidated ENGTSA was measured as described above. The three calibration samples were: a steel cylinder with diameter 50.8 · 12.7 mm thickness and two Vespel disks with diameter 50.8 · 3.175 mm thickness and diameter 50.8 · 6.35 mm thickness. The calibration results are shown in Fig. 4, in which point A is the steel sample, point B is the Vespel sample with thickness of 3.175 mm, and point C is the Vespel sample with thickness of 6.35 mm. From Fig. 4 the values of F and Rint in Eq. (2) were calculated as 2.26 · 103 m2 K W1 and 5.99 · 104 m2 K W1 respectively. Then the thermal conductivity of the samples was obtained by measurement of Tu, Tl, and Th. For the test results to be accurate, the thermal resistance obtained must fall
Fig. 4 – Characteristic line for calibration samples.
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within the range of samples used for calibration, which were from 8.74 · 104 to 1.6759 · 102 m2 K W1. 31 Consolidated samples of disk were tested, and the density, thickness, and thermal resistance of samples are shown in Fig. 5. Their density ranged from 42 to 1263 kg m3. As Eq. (2) shows, the thermal resistance is larger when the thickness of the sample is larger. Because the thermal resistance must lie within the range of the calibrated experiments, i.e. 8.74 · 104 to 1.68 · 102 m2 K W1, in the experiments the thickness of the samples was controlled to give a thermal resistance within the desired range. The highest and lowest values of resistance obtained from different samples were 4.84 · 103 and 8.80 · 104 m2 K W1, respectively. The thermal conductivity of the consolidated samples of disk is shown in Fig. 6. The thermal conductivity increases rapidly as density increases, then stabilises, and finally decreases. The thermal conductivity stabilises at a value of about 5–6 W m1K1 when the density is between 1000 and 1200 kg m3. The thermal conductivity of the consolidated disks of ENG-TSA is much higher than that of consolidated disks of ENG [18], and the highest value for ENG-TSA is 8.9 W m1K1, which is about five times more than the highest value for ENG [18]. The corresponding compacting pressure needed for producing consolidated disks of ENGTSA is shown in Fig. 6. We can see there is a relationship between thermal conductivity and compacting pressure or density. The thermal conductivity of the material decreases when the density is higher than 600 kg m3. The relationship between compacting pressure and density is roughly linear when the density is lower than 600 kg m3, and increases rapidly and non-linearly when the density is higher than 600 kg m3. It means that the consolidated ENG-TSA is much more difficult to compress when the density is higher than 600 kg m3. Fig. 6 also shows that the density beyond which compaction pressure increases rapidly is the same density beyond which conductivity decreases.
3.2. Thermal conductivity (perpendicular to direction of compression) of consolidated plates of ENG-TSA The consolidated plates of ENG-TSA had much higher thermal conductivity than disks of consolidated ENG-TSA due to the orientation of the micro layers. Three calibration lines were needed for the samples of plate in order to enable the thermal resistance obtained to fall within the range of calibration. One was the calibration line shown in Fig. 4, and the other two lines are shown in Fig. 7. Four samples are utilised for the calibration experiments in Fig. 7. Point of A is for
Fig. 5 – Thermal resistance and thickness vs. density of the consolidated samples of disk.
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Fig. 6 – Thermal conductivity and compacting pressure vs. density of consolidated disks of ENG-TSA.
a stainless steel sample with 50.8 mm diameter · 12.7 mm thickness. Points of D, E, F are aluminium 6082 samples with 50.8 diameter · 39 mm thickness, 50.8 diameter · 18 mm thickness, and 50.8 mm diameter · 14 mm thickness, respectively. For the calibration line of RsL, values of F and Rint in Eq. (2) are calculated from the slope of 1.621 · 103 and the intercept of 3.31 · 104 m2 K W1 of the line of best fit, and the calibrated range is from 7.8 · 105 to 2.17 · 104 m2 K W 1 . For the calibration line of RsH, values of F and Rint in Eq. (2) are calculated from the slope of 1.769 · 103 and the intercept of 3.74 · 104 m2 K W1 of the line of best fit, respectively, and the calibrated range is from 1.0 · 104 to 8.74 · 10 4 m2 K W1. 10 Samples were tested, and density, thickness, and thermal resistance of the samples are shown in Fig. 8. The thermal resistance decreases very rapidly with increasing density. For the samples with density equal to or lower than 204 kg m3 the thermal resistance is between 9.15 · 104 and 4.87 · 103 m2 K W1, and the calibration line of Fig. 4 is utilised for the calculation of the thermal resistance of the samples. For the samples with density higher than 204 kg m3 and equal to or lower than 679 kg m3, Fig. 8 shows that the thermal resistance is between 2.11 · 104 and 5.20 · 104 m2 K W 1 , and the calibration line of RsH in Fig. 7 is used For the samples with density of 754 and 831 kg m3, the thermal resistance is 1.71 · 104 and 1.28 · 104 m2 K W1, respectively, and the calibration line of RsL in Fig. 7 is used. When the thermal resistance is lower than 5 · 104 m2 K W1, the measuring error due to the interfacial thermal resistance will greatly influence the accuracy if the surface of the samples is much different from that of the calibration samples. In order to obtain accurate data, the surface of the samples with density equal to or higher than 259 kg m3 was machined
Fig. 7 – Calibration results for consolidated plates of ENGTSA.
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which the compacting pressure required increases rapidly is somewhat higher than the density beyond which conductivity increases rapidly. This is in complete contrast to the trends shown for disk samples (conductivity parallel to direction of compression) above.
3.3.
Fig. 8 – Thermal resistance and thickness vs. density of consolidated plates.
with same finishing process as the surface of aluminium 6082 calibrated samples. The measurement error will be smaller when the thermal resistance of sample is larger, thus for the samples with smaller thermal resistance, i.e. for the samples with density larger than 600 kg m3, the largest thickness of 43 mm for experiments is utilised in order to maximise the thermal resistance and reduce the measurement error. The thermal conductivity of the consolidated plates is shown in Fig. 9. Thermal conductivity increases rapidly as the density increases. The highest thermal conductivity is 337 W m1K1 when the density of the sample is 831 kg m3. It is almost one hundred times higher compared to the values for the consolidated plates of ENG [18], and almost 50 times higher than the samples of disk with similar density. For the samples with density higher than 900 kg m3, accurate results cannot be obtained because the thermal resistance of sample is much lower than the range of the equipment, which should be greater than 2 · 104 m2 K W1, and also the influence on the measuring error of the interfacial resistance becomes increasingly significant, possibly as high as 30%. For the samples of plate, the compacting pressure increases almost linearly with the density whilst density is lower than 600 kg m3. The trend is similar to that of consolidated samples of disk with density lower than 600 kg m3. It increases rapidly when the density is higher than 600 kg m3. Fig. 9 also shows that the density beyond
Fig. 9 – Thermal conductivity and compacting pressure vs. density for plates of consolidated ENG-TSA.
Permeability
Five consolidated samples of disk and five consolidated samples of plate were chosen for the permeability measurements, and the results are shown in Table 2. In Table 2 the permeability decreases rapidly with increased density for both samples of disk and plate. The permeability of samples of plate (perpendicular to the direction of compression) is at least 30 times higher than those of the disk (parallel to compression). When the density is lower than 200 kg m3, the permeability of the samples of plate is more than 200 times higher than that of the disk.
3.4. Scanning electronic microscope (SEM) pictures of consolidated samples Measurement shows that the consolidated samples of plate (perpendicular to compression) not only have higher thermal conductivity, but also have higher permeability than those of the disks (parallel to compression). These results are mainly due to the micro layers formed by the compressive force. SEM pictures of consolidated samples of disk and consolidated samples of plate are shown in Fig. 10. All magnifications in Fig. 10 fall within 90–130·. Fig. 10 shows that when the density of the samples is lower, for example Fig. 10a and d, the micro structure of the samples has a worm-like structure, which is similar to that of consolidated ENG. But when the density is higher, for example when the density is higher than 300 kg m3, the worm structure of the samples is replaced by layers, and the layers of graphite appear to be distributed much more uniformly than ENG with similar density [18]. It is suggested that this uniformity accounts for consolidated ENG-TSA showing a much higher thermal conductivity compared to consolidated ENG. The SEM pictures indicate possible reasons for the trend of thermal conductivity in Figs. 6 and 9. For the disk samples (Figs. 6 and 10a–c), the thermal conductivity is influenced by two factors. One is the contact resistance between layers and the other is conduction through the layers, both parallel and perpendicular to the graphite flakes. It is suggested that as the disk density increases (up to 250 kg m3) there is an initial rise in conductivity because the contact resistance is reduced. Within the layers there is not complete alignment of flakes perpendicular to the compression direction and so a significant contribution to the total conductivity is made by conduction in the plane of the flakes, many of which are still oriented not completely perpendicular to the compression direction. With further compression (density 250–650 kg m3), the thermal conductivity keeps at a stabilized value about 8– 9 W m1K1 because the positive influence of reduced resistance between flakes balances with negative influence of layers aligning perpendicular to the heat transfer direction. With almost complete alignment (density above 650 kg m3), the
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Table 2 – Permeability of different samples. Type of block
Density (kg m3)
Permeability (m2)
Direction of gas flow
Consolidated samples of disk
75 164 212 309 475
5.30 · 1014 1.12 · 1015 3.89 · 1016 9.15 · 1017 1.49 · 1017
Parallel to the compressive direction
Consolidated samples of plate
111 211 303 487 539
1.12 · 1011 1.17 · 1014 2.01 · 1015 3.96 · 1016 1.64 · 1016
Perpendicular to the compressive direction
Fig. 10 – SEM pictures for consolidated samples with different values of density, (a) sample of disk, 65 kg m3, 110·, (b) sample of disk, 379 kg m3, 104·, (c) sample of disk, 1084 kg m3, 106·, (d) sample of plate, 65 kg m3, 90.8·, (e) sample of plate, 363 kg m3, 128·, (f) sample of plate, 702 kg m3, 116·.
thermal resistance stabilises at a lower level with all heat transfer in the graphite perpendicular to the plane of the flakes. For the plate samples (Fig. 10d–f) the thermal conductivity always increases with increasing compacting pressure because the heat transfer is all in the plane of the graphite flakes and the better the alignment the better the heat transfer (Fig. 9). For the permeability in Table 2, the samples of both disk and plate have lower permeability with higher density since there is less void space available to allow the passage of gas. The samples with highest density would be unsuitable for use as heat adsorbent matrices because of the poor mass transfer.
3.5. Specific heat and overview of ENG-TSA as a heat transfer enhancing matrix for adsorbents As explained above, if the intention is to enhance thermal conductivity in adsorbent beds by use of a conducting matrix
of graphite or other material it is important that the matrix should have small thermal capacity compared with that of the adsorbent. The specific heat of ENG-TSA was measured using a Seteram SENSYS DSC, and the specific heat of AC manufactured by the Chemviron with the size of 80–100 mesh was also measured. The composite adsorbent with two different types of heat transfer matrix, i.e. ENG-TSA and aluminum powder, are calculated and compared to confirm the good performance of ENG-TSA using Eq. (5), in which Cp is calculated based on 1 kg adsorbent, i.e. 1 kg AC. This is simply to reflect that the function of the composite material is to adsorb and that from the point of view of thermodynamic cycle efficiency the conductive matrix represents a wasteful thermal mass. The use of the conductivity enhancing matrix improves the power density but decreases the efficiency as the specific heat per unit of adsorbing material increases. 1 ½ð1 rÞ Cp;AC þ r Cp;matrix ð5Þ Cp ¼ ð1 rÞ where Cp is the specific heat capacity for the composite adsorbent with 1 kg AC (J kg1 K1), r is the ratio of ENG-TSA or
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3.6.
Fig. 11 – Specific heat vs. temperature for ENG-TSA, AC and composite adsorbents.
aluminium inside the composite adsorbents, Cp,AC and Cp, matrix are the specific heat capacity of AC and heat transfer matrix (J kg1 K1), respectively. The C p, matrix for aluminium is obtained from [20]. The results are shown in Fig. 11. The specific heat of ENGTSA and AC all increase with increasing temperature and the values of ENG-TSA are much lower than that of AC. The average values of specific heat in the range of 20–150 C are 0.89 and 1.01 kJ kg1 K1 for ENG-TSA and AC, respectively, and the value of ENG-TSA is 12% less than the value of AC. The average specific heat of ENG-TSA is slightly lower than the average value of aluminium [20] in the temperature range of 20–150 C, which is 0.92 kJ kg1 K1. The high thermal conductivity and low specific heat of compact ENG-TSA indicate that ENG-TSA is a promising heat transfer matrix, even better than some metals. Two types of composite adsorbents are compared in Fig. 11, and the sample with ENG-TSA as matrix is slightly lower than the value of the sample with aluminium as a matrix.An appropriate figure of the merit of thermal conductivity and specific heat is the thermal diffusivity of the matrix material: a ¼ kðq Cp Þ
ð6Þ 2
1
where a is the thermal diffusivity (m s ), q is density (kg m3). Pure aluminium has a thermal diffusivity of 9.4 · 105 m2 1 s for the temperature range of 30–150 C, whereas ENGTSA conducting perpendicular to the compression direction with a density of 831 kg m3 and thermal conductivity of 337 W m1K1 has a thermal diffusivity of 4.6 · 104 m2 s1, which is about five times higher. Compared with the consolidated active carbon sorbent LM8 of reference [19] that was intended for adsorption refrigeration and heat pump applications, the thermal conductivity of ENG-TSA is 100 times higher whilst the permeability is similar.
Analysis of experimental error
For the thermal resistance of samples higher than 2 · 104 m2 K W1, the accuracy of the Quickline-10 is 3–8%. When the thermal resistance of the samples is lower than 2 · 104 m2 K W1, the interfacial thermal resistance will greatly influence the results. In order to obtain accurate results, firstly the surface of the samples was machined with the same finishing process for calibrated samples of aluminium 6082. Secondly the samples with density higher than 600 kg m3 are machined to different thicknesses, and then the thermal conductivity was measured for these samples, and the results are shown in Table 3. The test results are compared with the data in Fig. 9, and the relative difference was calculated by j
Dk kdt k j¼j j k k
ð7Þ
where Dk is the relative difference of thermal conductivity for the samples with same density, k is the thermal conductivity of samples shown in Fig. 9, kdt is the thermal conductivity shown in Table 3.Results showed that the largest relative difference is 4.1%. The error for the permeability measurements is: j
dK dW BdX dW BdX j¼j j6j jþj j K W BX W BX W BX
ð8Þ
The pressure is calculated from the atmospheric pressure and the pressure drop is measured by the differential pressure transducer with an error of ±0.5%. The air flowrate is measured by a Rotameter with an error of ±4% when testing the samples with large permeability at high flowrate. When the flowrate is smaller, it is tested by a timer and measuring cylinder and the error is mainly caused by the difference of time for the last bubble to rise from the bottom of the measuring cylinder. The largest error of 9.2% occurs for the disk sample of 475 kg m3, which has the smallest permeability and longest testing time. The relative error of K is calculated, and its average error is 9.6%, and the largest error is 15.7%. For the specific heat, the largest error expected from the Seteram SENSYS DSC for the calibration of heat is 1.8%, and the corresponding largest uncertainty in the temperature is 0.011%. Then the total largest error calculated for Cp is 1.811%.
4.
Conclusions
Expanded graphite treated with acid, which has proved promising for electrical conducting process, had been evaluated for heat and mass transfer applications in adsorbent beds. Results show that expanded natural graphite treated with sulphuric acid (ENG-TSA) is a promising heat transfer matrix,
Table 3 – Thermal conductivity of different samples for the comparison of error. No. of sample Thickness (mm) Density (kg m3) kdt (W m1 K1) Relative difference of k
1
2
3
4
5
6
35 831 325 3.5%
28 831 342 1.4%
35 754 242 3.8%
28 754 251 0.4%
35 679 199 2.1%
28 679 195 4.1%
CARBON
4 9 ( 20 1 1 ) 4 8 1 2–48 1 9
even better than pure aluminium. The conclusions are as follows: (1) The direction parallel to the direction of compression has poorer heat and mass transfer performance. The maximum value of thermal conductivity is 8.9 W m1 K1. The permeability varies from 10 14 to 10 17 m2 as the density varies from 75 to 475 kg m3. (2) The optimal heat and mass transfer direction is perpendicular to the direction of compression used to produce the consolidated samples. The highest thermal conductivity is 337 W m1K1 when the density is 831 kg m3, and the permeability varies from 1011 to 1016 m2 for samples of plate as the density varies between 111 and 539 kg m3. (3) The SEM micrographs show that the consolidated ENGTSA has different characteristics compared with that of consolidated ENG [18] when the density is higher than 300 kg m3. A worm-like structure exists in consolidated ENG even when the density is as high as 700 kg m3, but for consolidated ENG-TSA, the wormlike structure only exists for samples with lower density. When the samples have density higher than 300 kg m3, the micro structure is composed of organised layers. Such a phenomenon leads to a much higher thermal conductivity than that of ENG. (4) In the temperature range of 30–150 C the specific heat of ENG-TSA is 12% lower than the AC adsorbent. Taking thermal diffusivity as a figure of merit for performance as a thermally enhancing matrix, it is approximately five times better than aluminium. Compared to the monolithic AC if the permeability is kept at the same permitted level then the conductivity is about 100 times higher.
Acknowledgements This work was supported by a Royal Society Incoming Fellowship, the AWM Science City Energy Efficiency Project, the Natural Science Foundation of China under the contract No. 50736004 and contract No. 50806043, and the National 100 Outstanding PhD thesis Foundation in China.
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