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paraffin phase change composite
International Journal of Thermal Sciences 88 (2015) 128e135
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International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts
Investigation of a graphite/paraffin phase change composite Albouchi Fethi a, *, Lachheb Mohamed a, Karkri Mustapha b, Ben ameurTarek c, Ben Nasrallah Sassi a Laboratoire d'Etudes des Syst emes Thermiques et Energ etiques, University of Monastir, Monastir, Tunisia Centre d'Etude et de Recherche en Thermique, Environnement et Syst emes (CERTES), University of Paris-Est France c Laboratoire de G enie M ecanique (LGM), ENIM, University of Monastir, Tunisia a
b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 1 January 2014 Received in revised form 14 September 2014 Accepted 14 September 2014 Available online
Latent heat thermal storage of graphite/PCM composite was investigated numerically and experimentally. Graphite, as a highly-conductive, is an excellent candidate for forming thermal energy storage composites with improved effective thermal conductivity. For numerical simulation, the graphite/ paraffin composite was modeled as a two dimensional system. Three modes of graphite addition were analyzed. Graphite was added as fibers, as fins or as foam. For every case, the thermal heat storage/ release cycle is evaluated versus different graphite mass fraction. For experimental verification, the effective thermal conductivity of graphite/paraffin composites was measured using an electrothermal sensor based on a Wheatstone bridge. The results indicate a noticeable improvement in the effective thermal conductivity of composites compared to the PCM. The latent heat is measured using the differential scanning calorimeter (DSC). Our results are consistent with reported literature results. © 2014 Published by Elsevier Masson SAS.
Keywords: Latent heat thermal storage Graphite/PCM composite Numerical simulation Experimental analysis Thermal conductivity
1. Introduction The production and consumption of energy contribute to the change in thermal equilibrium at the surface of the earth by producing greenhouse gas emissions. One of the major challenges facing our society is the management of our natural resources without causing depletion without altering the environment of the planet. Therefore, reducing consumption is the most effective way not only to save energy but also to reduce pollution. Indeed, the limited reserves of fossil fuels and the increase of the use of energy are the main driving forces behind efforts to search a new and renewable energy. During these years, scientists from all over the world are in search of an efficient and economical technology that can be used to save energy. One of these technologies, the thermal energy storage (TES) is a technique with a high potential for different thermal applications. It is well known that TES could be the most appropriate way and method to correct the gap between the demand and supply of energy and therefore it has become a very attractive technology, used in different areas, such as building heating/cooling systems and solar energy collector's power [1e10]. Three major methods for thermal storage are currently considered:
* Corresponding author. E-mail addresses: [email protected], [email protected] (A. Fethi). http://dx.doi.org/10.1016/j.ijthermalsci.2014.09.008 1290-0729/© 2014 Published by Elsevier Masson SAS.
sensible heat, latent heat and thermochemical heat. The latent thermal energy storage method uses phase change materials (PCM), which store heat when they go from solid to liquid, from liquid to gas or from solid to solid. Then they release energy when they have the reverse phase change. It must be mentioned that, until now the PCM studies and applications have been mainly focused on the solideliquid phase change because of its important enthalpy variation and simultaneous weak volume variation unlike solidegas or liquidegas [11]. These systems are used in order to store thermal energy for a period while the supply is sufficient or cheaper, to be discharged when the supply becomes insufficient or expensive. In some applications, the thermal energy must be absorbed or released at a very fast rate. However, most phase change materials have a low thermal conductivity [12,13]. Various methods have been investigated for increasing the thermal conductivity of PCMs. These techniques include dispersing high conductivity particles within the PCM, inserting a metallic matrix, adding chunks of metal tubing into the PCM and impregnating a porous graphite matrix with PCM [14e23]. The most promising of these methods was the graphite matrix due to its high thermal conductivity and its mechanical properties. Although some studies have been developed to investigate the heat storage through graphite/PCM composites, few detailed information on the heat storage rate and storage efficiency of these materials are known. This paper aims to investigate a numerical and experimental study of graphite/PCM latent heat thermal
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Nomenclature Cp h H q p L t T x,y u
heat capacity, J kg1 K1 heat transfer coefficient, W m2 K1 total volumetric enthalpy of the PCM, J m3 density of heat flow, W m2 static pressure Pa latent heat of the PCM, J kg1 time, s temperature, K space coordinate, m velocity, m s1
Greek symbols r density, kg m3 l thermal conductivity, W/m K b liquid fraction t stress tensor
energy storage composites. The influences of the amount of graphite and its nature (fibers, fins, and foams) on the heat storage and the heat release are investigated. The heat storage/release properties were analyzed by comparing the temperature variation during storage and release phases as function of the nature of the added graphite and graphite mass fraction. Experimentally, graphite/PCM composites are elaborated using two different methods. Their thermal conductivity is measured by an electrothermal sensor based on a Wheatstone bridge. The latent heat of composites is measured using the Differential scanning calorimetry method (DSC). The obtained results show a decrease of the latent heat versus the graphite mass fraction. 2. Experimental 2.1. Graphite/paraffin composite elaboration For this study, two different methods have been used for the elaboration of graphite/PCM composites: The first method involves the dispersion of graphite in the PCM. This is achieved above the melting temperature by mechanical dispersion within the molten PCM. In this case, the stirring rate is of great importance to obtain a homogeneous dispersion and avoid a local concentration of the graphite. Above the melting temperature, the obtained composite can be poured into a stainless steel mould to obtain a desired external shape. The second method is based on the cold uni-axial compression, in which paraffin powders and graphite particles are mixed together, and then the obtained mixture (paraffin þ graphite) is poured into a stainless steel mould followed by an uni-axial compression (80 bar) at ambient temperature. A series of
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graphite/paraffin composite PCMs with different mass fractions of graphite and paraffin were prepared. The used graphite is an industrial graphite ‘‘graphite waste’’. It was obtained from damaged Tubular graphite Heat Exchangers. It is a form of carbon with crystalline structure; it has good thermal and mass transfer characteristics that have led to its use for thermal conductivity enhancement. The average size of graphite particles is about 85 mm. Moreover, graphite has strong resistance to corrosion and chemical attacks, which makes it compatible with most PCM. The recycling of graphite has a lot of benefits, it can preserve natural resources of graphite for future generations i.e. recycling graphite reduces the need for raw materials; it also uses less energy, and it have economic benefits. The thermal properties of the used graphite are: thermal conductivity l ¼ 23 W/m K, density r ¼ 1936 kg/m3 and specific heat Cp ¼ 650 J/kg K. Fig. 1 presents examples of elaborated composites. 2.2. Thermal conductivity measurement The thermal conductivity of the elaborated composites is measured using the experimental setup illustrated in Fig. 2 and constituted by an electrothermal sensor sandwiched between two composites graphite/paraffin. The sensor is connected with a current generator and an Agilent acquisition card. The recorded signal from the output of the Agilent card is transferred to a computer using the RS 232 serial interface. The sensor is based on a Wheatstone bridge. As long as the sample temperature is uniform, the bridge is inherently balanced. A constant current is passed through the bridge to heat the resistances, thus resulting in unbalancing the bridge due to the hot-wire's temperature and therefore resistance change. The bridge input Vin and output Vout voltages are measured using a computerized data acquisition system (Agilent card). The bridge voltage output and time are measured and stored simultaneously. Post-processing of the acquired data is then performed in order to calculate the resistance change, temperature change and then thermal conductivity of the test sample. The thermal conductivity is deduced from the expression as follow:
l¼
q$Lnðtiþ1 =ti Þ $x 4p$dðDTmax Þ
(1)
where q is the heated flux and x is the slope of the experimental signal. The intensification of the thermal conductivity is given by:
I¼
lcomposite lparaffin lparaffin
(2)
The composites graphite/paraffin with different mass fraction (5%, 10%, 15%, and 20%) were elaborated using the two different methods cited above. For each sample different measures are effectuated and a mean value of thermal conductivity is calculated.
Fig. 1. Example of graphite/PCM composite samples elaborated by uni-axial compression and dispersion methods.
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Fig. 2. The apparatus used for thermal conductivity measurement.
The obtained results for all elaborated composites are illustrated in Table 1. Table 1 indicates that the thermal conductivity of the composites increased with increasing the mass fraction of graphite. An amount of 20% graphite can provides intensification of the thermal conductivity about 319.2% for dispersion method. Whereas; the thermal intensification is lower for composites elaborated using the compression method. This intensification difference between dispersion and compression composites is due to the porosity. Increase in graphite mass fraction over 20 wt% will result in an increase in thermal conductivity of the composite due to a decrease in the mass fraction of paraffin (below 80 wt%) in the composite. The high thermal conductivity of composite PCM makes it much more attractive than pure paraffin for many applications. Looking in Table 1, our measured thermal conductivity appear in good agreement with results given by Min et al. [24]. Moreover, the experimental thermal conductivities are compared with the calculated values using the analytical model given by Lewis & Nielsen [25].
leff ¼ lm
where :
1 þ ALN BLN 4 1 BLN j4
(3)
8 lf lf > > ¼ 1 þ ALN B > LN < lm lm > > > :
j¼1þ
2.3. DSC analysis The phase change behavior of graphite/paraffin composite PCMs includes two parameters: the latent heat and the phase change temperature, which can be measured by DSC analysis. The principle of DSC, described in Ref. [26] is based on the measurement of the difference of the heat flows between the reference cell and the measured PCM cell. By integrating the heat flow during phase change, the melting/freezing temperatures, the peak temperatures and the latent heat can be obtained [27,28]. DSC analysis was conducted to investigate the influence of graphite addition on thermal properties such as melting temperature and the latent heat storage capacity of paraffin and the composite PCMs. Fig. 4(a) shows the typical DSC curves of the pure paraffin used in the preparation of the composites. These DSC curves present reference data to evaluate the changes in the thermal properties of the composite PCM, depending on the amount of paraffin. It can be seen from Fig. 4(a) that there are two peaks in the DSC curve of the pure paraffin. The sharp or main peak represents the solideliquid phase change of the paraffin and the minor peak at the left side of the main peak corresponds to the solidesolid phase transition of paraffin (transition temperature Tt ¼ 39.84 C). Fig. 4(a) indicates that the peak temperature in the heat storage process (T ¼ 58 C) is different from this in the heat release process (T ¼ 55.57 C). The deviations of the melting and freezing temperatures can be explained by the fact that the PCM used is a mix of different alcanes.
ð1 4max Þ4 42max
And 4max is the maximum packing fraction of fillers. The parameter ALN depend on the shape, the distribution and the orientation of fillers. In this case, we use 4max ¼ 74% and ALN ¼ 1.5. The comparison between calculated and measured values for the composites elaborated by compression is presented on Fig. 3. We remark that our measurements agree with analytical values.
Table 1 Measured thermal conductivity as function of graphite mass fraction. Samples
ld
Paraffin 5% (Graphite) 10% (Graphite) 15% (Graphite) 20% (Graphite)
0.208 0.377 0.539 0.713 0.874
lC ± ± ± ± ±
0.004 0.015 0.022 0.008 0.014
0.208 0.286 0.312 0.362 0.401
± ± ± ± ±
0.01 0.011 0.008 0.012 0.02
Id
IC
Ref. [24]
0 0.808 1.583 2.418 3.192
0 0.375 0.5 0.74 0.927
0.205 0.372 (4%) 0.510 (10%) 0.747 (16%) e
Fig. 3. Comparison between experimental and analytical thermal conductivities.
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Fig. 4. a- DSC curve of pure paraffin, b- DSC curve of 20% graphite/paraffin composite.
Table 2 Measured latent heat as function of graphite mass fraction. Measured latent heat (J/g) Paraffin Paraffin Paraffin Paraffin Paraffin
þ þ þ þ
5% graphite 10% graphite 15% graphite 20% graphite
142.163 135.744 133.758 120.293 114.899
The melting point of paraffin is given by the value of the onset temperature (51.81 C). Fig. 4(b) presents the DSC curves of a composite 20% graphite/ paraffin. We remark that the melting and the freezing points of the composite (57.21 and 55.37 C) were slightly different than those of the pure paraffin (58 and 55.57 C). This is because there is no interaction between the paraffin and the graphite. In addition, the latent heat of the composite PCMs is measured for different amount of graphite. The obtained results are illustrated in Table 2 for different graphite mass fraction. We remark that the latent heat decreases with increase in graphite mass faction. Physically, the latent heat can be attributed to the intermolecular van der Waals forces. Therefore, with increase in the mass fraction of the graphite, the volume expansion of the melted paraffin will be confined and the pressure in the pores increases continuously during melting, which restricts the molecular thermal motion of the paraffin and consequently decreases the latent heat. By comparing our results with literature, we remark that ours values are close to these given by Xia et al. [29]. 2.4. Energy storage The energy storage of different composites is analyzed experimentally. Temperatures variation are illustrated in Fig. 5(a and b)
versus time for paraffin, graphite/PCM and graphite foam/PCM composites. It can be seen that the melting phase starts at a temperature 51.8 C in agreement with DSC results. From Fig. 5(a), we remark that the addition of graphite accelerate the heat storage/release of the PCM. The heat storage and retrieval durations were both considerably reduced for graphite/ paraffin composite which was attributed to the addition of graphite. However, it can also be seen that the effect of graphite was more significant in heat retrieval than in heat storage. These phenomena can be attributed to the melting/freezing characteristic of each PCM. The melting of pure paraffin was accelerated during heat storage (melting) because of the intensive natural convection in the melted paraffin, whereas the natural convection did not play significant role in the heat transfer during heat retrieval (freezing). 3. Numerical 3.1. Thermal model A two-dimensional finite-element study is developed to solve the transient heat conduction problems with phase change. The numerical model uses different thermophysical properties for the liquid and solid phases. Solideliquid phase-change (melting or solidification) heat transfer phenomena are accompanied by a phase transformation of the medium and by either absorption or release of thermal energy in the active zone. The energy absorbed or released from the surrounding system is commonly transferred by conduction or convection. Because of the motion of the solideliquid interface, the problems posed are nonlinear, so that few exact analytical solutions are available, and those that do exist are primarily for one-dimensional planar geometry. The PCM used in the simulations is a commercially paraffin, and the enhanced thermal conductivity material is the graphite. The geometry studied in this case is presented in Fig. 6.
Fig. 5. a- Experimental heat storage curves of paraffin and graphite/paraffin composite; b- Experimental heat storage curves of paraffin and graphite foam/paraffin composite.
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For the graphite, only 2D conduction is considered. Accordingly, the energy equation is:
! vTðtÞ ; div lg gradðTÞ ¼ rg Cg vt
lg
(5)
Momentum equation
! ! vðrPCM u Þ !! ! þ V$ðrPCM u u Þ ¼ Vp þ rPCM g þ V$t þ F vt
(6)
where p is the static pressure, u is the velocity, t is the stress tensor, ! ! r g , F are the gravitational body force and external body forces, respectively. Energy equation
! vH þ div lPCM gradðTÞ ¼ 0 vt
(7)
where H is the total volumetric enthalpy of the PCM, written as follows.
H ¼ rPCM Cp; PCM T þ rPCM Lb
(8)
with L is the latent heat of the PCM and b is the liquid fraction defined as:
8 b¼0 > > > > > T Ts > > :b ¼ Tl Ts
if T < Tsolidus if T > Tliquid
(9)
if Tsolidus < T < Tliquid
Considering the Equation (8), Equation (7) can be written as follows.
vT ! rPCM Cp; PCM eff þ div lPCM gradðTÞ ¼ 0 vt where ðrPCM Cp; PCM Þeff ¼ rPCM Cp; PCM þ rPCM LvðbÞ=vT The initial conditions is taken as:
at t ¼ 0
(11)
The boundary conditions are as follows:
(4)
where lg, rg and Cg are the thermal conductivity, the density and the specific heat of the graphite. For the paraffin (PCM), the governing equations are as follows: The continuity equation:
vrPCM ! þ V$ðrPCM u Þ ¼ 0 vt
Ti ¼ 298 K
(10)
vTðtÞ ¼ qðtÞ hðTðtÞ Ti Þ vx
at y ¼ 0
(12)
with q is the heat flux at the bottom surface and h ¼ 10 W m2 K1 is the convective heat coefficient. The lateral and the top surfaces are isolated (adiabatic). The thermophysical properties of the paraffin used in the numerical calculations are presented in Table 3. The difference in the solidus and liquidus temperatures defines the transition from solid to liquid phases during the melting of PCM. The effective density, specific heat capacity and thermal conductivity of the PCM are defined as follows.
rPCM ¼ ð1 bÞrPCM; s þ brPCM; l
(13)
CP; PCM ¼ ð1 bÞCP; PCM; s þ bCP; PCM; l
(14)
lPCM ¼ ð1 bÞlPCM; s þ blPCM; l
(15)
3.2. Results and discussion The numerical simulations of different amount of graphite have been conducted with variable parameters including variable shape of graphite (fibers, fins, foams). In such composites, the direction of fibers or fins is crucial [30]. The equation system is solved using the finite element scheme. Different meshes are tested to study the influence of grid dimension on the solution. 3.2.1. Heat storage rate of the graphite fiber/PCM composite First, for the graphite/paraffin composite, the graphite is added as fibers into the PCM. The fibers have small dimensions, so we can supposed that we use isotropic graphite fibers, the conduction is almost the same in transverse or parallel directions. In this case, we choose the heat flow perpendicular to fibers. The effect of fibers on the transient thermal storage cycle is examined. The PCM temperatures variations are shown in Fig. 7a and b for different fiber section and graphite mass fraction. It can be seen that decreasing the section of fiber increases the heat transfer inside the composite. The melting time decreases with the decrease of fiber section. Compared with pure paraffin, we remark that addition of graphite improve the thermal conductivity, which accelerates the storage/release cycle. This indicated that the heat transfer rate was increased with the additional surface area provided by the fibers. The heat from the source was conducted by the fibers to the surface of the PCM. By increasing the graphite mass fraction from 10% to 20% (Fig. 7b), we note that the influence of fiber section becomes small, but the melting time decreases with increase of graphite amount. Consequently, the heat rate increases with graphite mass fraction. 3.2.2. Heat storage rate of the graphite fin/PCM composite Secondly, the graphite is added as fins into the PCM and the heat flow is parallel to fins. The temperature variations during storage Table 3 Thermophysical properties of PCM used in the numerical calculations. Material l (W/m K) Paraffin
Fig. 6. Physical model.
r (kg/m3)
Cp (J/kg K)
Ts (K) Tl (K) Latent heat (J g1)
0.21 (solid) 920 (solid) 1900 (solid) 331 0.12 (liquid) 795 (liquid) 2200 (liquid)
332
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Fig. 7. The heat storage/release curve of paraffin and the graphite/paraffin composites: a- graphite fiber/PCM with 10% of graphite, b- graphite fiber/PCM with 20% of graphite.
and release phases are presented on Fig. 8a and b). From these curves, we can conclude that the melting time of the sample decreases considerably, not only by increasing the percentage of graphite but also by decreasing the thickness of graphite fin structure. In addition, we noticed that the operating time decreases comparing to the case of graphite fiber/PCM composite. Thus, reducing the cycle time amounts to physically increasing the contact area and thermal conduction. In addition, the thermal conductivity of the matrix composite plays an important role in the heat absorption rate. The higher the value of the thermal conductivity of the matrix composite, the higher the value of the heat absorption rate but through a smaller time interval. 3.2.3. Heat storage rate of the graphite foam/PCM composite To further improve the thermal storage of the PCM, we introduce the paraffin into graphite foam with porosity 75%. The effects of the porosity and thermal properties of a porous medium filled with PCM were studied numerically. Fig. 9 illustrates a comparison between storage cycle relative to pure paraffin, graphite fiber/PCM, graphite fin/PCM and graphite foam/PCM composites. It can be seen that at approximately 368 s, the foam/PCM composite material initiated the change from solid to liquid phase. At this time, the energy absorption was mainly due to the phase change process. At approximately 1256 s, the phase change process was complete. As seen from the figure, without the use of graphite foam, pure paraffin initiated the change from solid to liquid phase at 1094 s and takes around 3492 s to melt completely. For the composite graphite fin/PCM, the onset of melting is at 457 s and the end of melting phase is at 2028 s. Whereas, graphite fiber/PCM composite initiated the melting phase at 836 s. From these results, we can conclude that, the time required to melt approximately the same amount of paraffin when using graphite foams is reduced to 37% of that necessary without graphite foam.
Moreover, we remark that the foam/PCM composite solidifies more uniformly than the pure paraffin. As discussed earlier, the effective thermal conductivity of foam/PCM composite is significantly higher than that of pure PCM, which in turn reduces the thermal resistance to heat transfer and so the temperature gradient is small. The addition of high porosity graphite foam provides a large solid-to-fluid surface area, combined with a high thermal conducting phase, would allow for enhanced heat transfer by conducting heat inside the graphite struts. The results, illustrated above, showed that the porosity of the matrix composite play important roles in its thermal performance. The higher, the active porosity of the PCM inside the matrix pores, the more stable of the thermal performance of the matrix composite is. On the other hand, the dispersed and the continuous form of the matrix composite matrix acts sharply to increase or decrease its heat absorption rate. 3.2.4. Enhancement of the melting rate The rate of melting is an important factor in many engineering applications, such as in the latent heat thermal energy storage systems. The melting rate is plotted against time for graphite fin/ PCM and graphite foam/PCM composites in Fig. 10. It can be seen that the melting rate of the graphite foam/PCM is greater than this of graphite fin/PCM composite. For duration of storage/release cycle, we remark that graphite foam/PCM composite give reduced cycle. At 5500 s, the paraffin returns to the solid state and completes the cycle storage. Whereas, in the graphite fin/PCM composite, the paraffin is in the liquid state during the storage phase. 4. Comparison between numerical and experimental results Regarding, the plateau during the solid to liquid phase change, for numerical results, we note an idealized phase change at a
Fig. 8. The heat storage/release curve of paraffin and the graphite/paraffin composites: a- graphite fin/PCM with 10% of graphite, b- graphite fin/PCM with 20% of graphite.
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5. Conclusion In conclusion; this work investigated the use of graphite with different configuration designs to improve the thermal storage of PCM systems. The transient thermal behavior of graphite fiber/ PCM, graphite fin/PCM and graphite foam/PCM composites were analyzed and compared to the transient thermal behavior of the pure paraffin. It was found that the selection of enhancement method has a significant effect on the thermal response of the system. The numerical results are validated experimentally and a good agreement was obtained. The rate of energy storage and release is highly depended on the nature of the solid matrix.
References Fig. 9. The heat storage/release curves of PCM and graphite foam/PCM composites.
constant temperature (Figs. 7e9). Whereas, for the experimental curves, there was a continuous ramp up of temperature during the phase change for PCM and graphite/PCM composites (Fig. 5a and b). This behavior includes a reality-based temperature range for the phase change in contrast with theoretical model which considers a melting point. In addition, the modeled graphite/PCM composites were treated as homogenous materials. As a consequence, the numerical results (Figs. 7e9) indicated a flatter response during melt when compared to the experimental data (Fig. 5a and b). From the curves given above (Fig. 5), we note that the experimental melting time is 403 s for foam/PCM composite and 989 s for PCM. Compared with numerical values (368 s and 1094 s), the relative uncertainty is 8.6% for foam/PCM composite and 9.5% for PCM. This small difference between numerical and experimental values is due essentially to natural convection, which therefore suggests that natural convection played an important role in the heat transfer during heat storage. Due to intensive natural convection in the melted paraffin, so the melting of the paraffin is accelerated.
Fig. 10. Liquid fraction in melting process of graphite foam/paraffin and graphite fin/ paraffin composites.
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International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts
Investigation of a graphite/paraffin phase change composite Albouchi Fethi a, *, Lachheb Mohamed a, Karkri Mustapha b, Ben ameurTarek c, Ben Nasrallah Sassi a Laboratoire d'Etudes des Syst emes Thermiques et Energ etiques, University of Monastir, Monastir, Tunisia Centre d'Etude et de Recherche en Thermique, Environnement et Syst emes (CERTES), University of Paris-Est France c Laboratoire de G enie M ecanique (LGM), ENIM, University of Monastir, Tunisia a
b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 1 January 2014 Received in revised form 14 September 2014 Accepted 14 September 2014 Available online
Latent heat thermal storage of graphite/PCM composite was investigated numerically and experimentally. Graphite, as a highly-conductive, is an excellent candidate for forming thermal energy storage composites with improved effective thermal conductivity. For numerical simulation, the graphite/ paraffin composite was modeled as a two dimensional system. Three modes of graphite addition were analyzed. Graphite was added as fibers, as fins or as foam. For every case, the thermal heat storage/ release cycle is evaluated versus different graphite mass fraction. For experimental verification, the effective thermal conductivity of graphite/paraffin composites was measured using an electrothermal sensor based on a Wheatstone bridge. The results indicate a noticeable improvement in the effective thermal conductivity of composites compared to the PCM. The latent heat is measured using the differential scanning calorimeter (DSC). Our results are consistent with reported literature results. © 2014 Published by Elsevier Masson SAS.
Keywords: Latent heat thermal storage Graphite/PCM composite Numerical simulation Experimental analysis Thermal conductivity
1. Introduction The production and consumption of energy contribute to the change in thermal equilibrium at the surface of the earth by producing greenhouse gas emissions. One of the major challenges facing our society is the management of our natural resources without causing depletion without altering the environment of the planet. Therefore, reducing consumption is the most effective way not only to save energy but also to reduce pollution. Indeed, the limited reserves of fossil fuels and the increase of the use of energy are the main driving forces behind efforts to search a new and renewable energy. During these years, scientists from all over the world are in search of an efficient and economical technology that can be used to save energy. One of these technologies, the thermal energy storage (TES) is a technique with a high potential for different thermal applications. It is well known that TES could be the most appropriate way and method to correct the gap between the demand and supply of energy and therefore it has become a very attractive technology, used in different areas, such as building heating/cooling systems and solar energy collector's power [1e10]. Three major methods for thermal storage are currently considered:
* Corresponding author. E-mail addresses: [email protected], [email protected] (A. Fethi). http://dx.doi.org/10.1016/j.ijthermalsci.2014.09.008 1290-0729/© 2014 Published by Elsevier Masson SAS.
sensible heat, latent heat and thermochemical heat. The latent thermal energy storage method uses phase change materials (PCM), which store heat when they go from solid to liquid, from liquid to gas or from solid to solid. Then they release energy when they have the reverse phase change. It must be mentioned that, until now the PCM studies and applications have been mainly focused on the solideliquid phase change because of its important enthalpy variation and simultaneous weak volume variation unlike solidegas or liquidegas [11]. These systems are used in order to store thermal energy for a period while the supply is sufficient or cheaper, to be discharged when the supply becomes insufficient or expensive. In some applications, the thermal energy must be absorbed or released at a very fast rate. However, most phase change materials have a low thermal conductivity [12,13]. Various methods have been investigated for increasing the thermal conductivity of PCMs. These techniques include dispersing high conductivity particles within the PCM, inserting a metallic matrix, adding chunks of metal tubing into the PCM and impregnating a porous graphite matrix with PCM [14e23]. The most promising of these methods was the graphite matrix due to its high thermal conductivity and its mechanical properties. Although some studies have been developed to investigate the heat storage through graphite/PCM composites, few detailed information on the heat storage rate and storage efficiency of these materials are known. This paper aims to investigate a numerical and experimental study of graphite/PCM latent heat thermal
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Nomenclature Cp h H q p L t T x,y u
heat capacity, J kg1 K1 heat transfer coefficient, W m2 K1 total volumetric enthalpy of the PCM, J m3 density of heat flow, W m2 static pressure Pa latent heat of the PCM, J kg1 time, s temperature, K space coordinate, m velocity, m s1
Greek symbols r density, kg m3 l thermal conductivity, W/m K b liquid fraction t stress tensor
energy storage composites. The influences of the amount of graphite and its nature (fibers, fins, and foams) on the heat storage and the heat release are investigated. The heat storage/release properties were analyzed by comparing the temperature variation during storage and release phases as function of the nature of the added graphite and graphite mass fraction. Experimentally, graphite/PCM composites are elaborated using two different methods. Their thermal conductivity is measured by an electrothermal sensor based on a Wheatstone bridge. The latent heat of composites is measured using the Differential scanning calorimetry method (DSC). The obtained results show a decrease of the latent heat versus the graphite mass fraction. 2. Experimental 2.1. Graphite/paraffin composite elaboration For this study, two different methods have been used for the elaboration of graphite/PCM composites: The first method involves the dispersion of graphite in the PCM. This is achieved above the melting temperature by mechanical dispersion within the molten PCM. In this case, the stirring rate is of great importance to obtain a homogeneous dispersion and avoid a local concentration of the graphite. Above the melting temperature, the obtained composite can be poured into a stainless steel mould to obtain a desired external shape. The second method is based on the cold uni-axial compression, in which paraffin powders and graphite particles are mixed together, and then the obtained mixture (paraffin þ graphite) is poured into a stainless steel mould followed by an uni-axial compression (80 bar) at ambient temperature. A series of
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graphite/paraffin composite PCMs with different mass fractions of graphite and paraffin were prepared. The used graphite is an industrial graphite ‘‘graphite waste’’. It was obtained from damaged Tubular graphite Heat Exchangers. It is a form of carbon with crystalline structure; it has good thermal and mass transfer characteristics that have led to its use for thermal conductivity enhancement. The average size of graphite particles is about 85 mm. Moreover, graphite has strong resistance to corrosion and chemical attacks, which makes it compatible with most PCM. The recycling of graphite has a lot of benefits, it can preserve natural resources of graphite for future generations i.e. recycling graphite reduces the need for raw materials; it also uses less energy, and it have economic benefits. The thermal properties of the used graphite are: thermal conductivity l ¼ 23 W/m K, density r ¼ 1936 kg/m3 and specific heat Cp ¼ 650 J/kg K. Fig. 1 presents examples of elaborated composites. 2.2. Thermal conductivity measurement The thermal conductivity of the elaborated composites is measured using the experimental setup illustrated in Fig. 2 and constituted by an electrothermal sensor sandwiched between two composites graphite/paraffin. The sensor is connected with a current generator and an Agilent acquisition card. The recorded signal from the output of the Agilent card is transferred to a computer using the RS 232 serial interface. The sensor is based on a Wheatstone bridge. As long as the sample temperature is uniform, the bridge is inherently balanced. A constant current is passed through the bridge to heat the resistances, thus resulting in unbalancing the bridge due to the hot-wire's temperature and therefore resistance change. The bridge input Vin and output Vout voltages are measured using a computerized data acquisition system (Agilent card). The bridge voltage output and time are measured and stored simultaneously. Post-processing of the acquired data is then performed in order to calculate the resistance change, temperature change and then thermal conductivity of the test sample. The thermal conductivity is deduced from the expression as follow:
l¼
q$Lnðtiþ1 =ti Þ $x 4p$dðDTmax Þ
(1)
where q is the heated flux and x is the slope of the experimental signal. The intensification of the thermal conductivity is given by:
I¼
lcomposite lparaffin lparaffin
(2)
The composites graphite/paraffin with different mass fraction (5%, 10%, 15%, and 20%) were elaborated using the two different methods cited above. For each sample different measures are effectuated and a mean value of thermal conductivity is calculated.
Fig. 1. Example of graphite/PCM composite samples elaborated by uni-axial compression and dispersion methods.
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Fig. 2. The apparatus used for thermal conductivity measurement.
The obtained results for all elaborated composites are illustrated in Table 1. Table 1 indicates that the thermal conductivity of the composites increased with increasing the mass fraction of graphite. An amount of 20% graphite can provides intensification of the thermal conductivity about 319.2% for dispersion method. Whereas; the thermal intensification is lower for composites elaborated using the compression method. This intensification difference between dispersion and compression composites is due to the porosity. Increase in graphite mass fraction over 20 wt% will result in an increase in thermal conductivity of the composite due to a decrease in the mass fraction of paraffin (below 80 wt%) in the composite. The high thermal conductivity of composite PCM makes it much more attractive than pure paraffin for many applications. Looking in Table 1, our measured thermal conductivity appear in good agreement with results given by Min et al. [24]. Moreover, the experimental thermal conductivities are compared with the calculated values using the analytical model given by Lewis & Nielsen [25].
leff ¼ lm
where :
1 þ ALN BLN 4 1 BLN j4
(3)
8 lf lf > > ¼ 1 þ ALN B > LN < lm lm > > > :
j¼1þ
2.3. DSC analysis The phase change behavior of graphite/paraffin composite PCMs includes two parameters: the latent heat and the phase change temperature, which can be measured by DSC analysis. The principle of DSC, described in Ref. [26] is based on the measurement of the difference of the heat flows between the reference cell and the measured PCM cell. By integrating the heat flow during phase change, the melting/freezing temperatures, the peak temperatures and the latent heat can be obtained [27,28]. DSC analysis was conducted to investigate the influence of graphite addition on thermal properties such as melting temperature and the latent heat storage capacity of paraffin and the composite PCMs. Fig. 4(a) shows the typical DSC curves of the pure paraffin used in the preparation of the composites. These DSC curves present reference data to evaluate the changes in the thermal properties of the composite PCM, depending on the amount of paraffin. It can be seen from Fig. 4(a) that there are two peaks in the DSC curve of the pure paraffin. The sharp or main peak represents the solideliquid phase change of the paraffin and the minor peak at the left side of the main peak corresponds to the solidesolid phase transition of paraffin (transition temperature Tt ¼ 39.84 C). Fig. 4(a) indicates that the peak temperature in the heat storage process (T ¼ 58 C) is different from this in the heat release process (T ¼ 55.57 C). The deviations of the melting and freezing temperatures can be explained by the fact that the PCM used is a mix of different alcanes.
ð1 4max Þ4 42max
And 4max is the maximum packing fraction of fillers. The parameter ALN depend on the shape, the distribution and the orientation of fillers. In this case, we use 4max ¼ 74% and ALN ¼ 1.5. The comparison between calculated and measured values for the composites elaborated by compression is presented on Fig. 3. We remark that our measurements agree with analytical values.
Table 1 Measured thermal conductivity as function of graphite mass fraction. Samples
ld
Paraffin 5% (Graphite) 10% (Graphite) 15% (Graphite) 20% (Graphite)
0.208 0.377 0.539 0.713 0.874
lC ± ± ± ± ±
0.004 0.015 0.022 0.008 0.014
0.208 0.286 0.312 0.362 0.401
± ± ± ± ±
0.01 0.011 0.008 0.012 0.02
Id
IC
Ref. [24]
0 0.808 1.583 2.418 3.192
0 0.375 0.5 0.74 0.927
0.205 0.372 (4%) 0.510 (10%) 0.747 (16%) e
Fig. 3. Comparison between experimental and analytical thermal conductivities.
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Fig. 4. a- DSC curve of pure paraffin, b- DSC curve of 20% graphite/paraffin composite.
Table 2 Measured latent heat as function of graphite mass fraction. Measured latent heat (J/g) Paraffin Paraffin Paraffin Paraffin Paraffin
þ þ þ þ
5% graphite 10% graphite 15% graphite 20% graphite
142.163 135.744 133.758 120.293 114.899
The melting point of paraffin is given by the value of the onset temperature (51.81 C). Fig. 4(b) presents the DSC curves of a composite 20% graphite/ paraffin. We remark that the melting and the freezing points of the composite (57.21 and 55.37 C) were slightly different than those of the pure paraffin (58 and 55.57 C). This is because there is no interaction between the paraffin and the graphite. In addition, the latent heat of the composite PCMs is measured for different amount of graphite. The obtained results are illustrated in Table 2 for different graphite mass fraction. We remark that the latent heat decreases with increase in graphite mass faction. Physically, the latent heat can be attributed to the intermolecular van der Waals forces. Therefore, with increase in the mass fraction of the graphite, the volume expansion of the melted paraffin will be confined and the pressure in the pores increases continuously during melting, which restricts the molecular thermal motion of the paraffin and consequently decreases the latent heat. By comparing our results with literature, we remark that ours values are close to these given by Xia et al. [29]. 2.4. Energy storage The energy storage of different composites is analyzed experimentally. Temperatures variation are illustrated in Fig. 5(a and b)
versus time for paraffin, graphite/PCM and graphite foam/PCM composites. It can be seen that the melting phase starts at a temperature 51.8 C in agreement with DSC results. From Fig. 5(a), we remark that the addition of graphite accelerate the heat storage/release of the PCM. The heat storage and retrieval durations were both considerably reduced for graphite/ paraffin composite which was attributed to the addition of graphite. However, it can also be seen that the effect of graphite was more significant in heat retrieval than in heat storage. These phenomena can be attributed to the melting/freezing characteristic of each PCM. The melting of pure paraffin was accelerated during heat storage (melting) because of the intensive natural convection in the melted paraffin, whereas the natural convection did not play significant role in the heat transfer during heat retrieval (freezing). 3. Numerical 3.1. Thermal model A two-dimensional finite-element study is developed to solve the transient heat conduction problems with phase change. The numerical model uses different thermophysical properties for the liquid and solid phases. Solideliquid phase-change (melting or solidification) heat transfer phenomena are accompanied by a phase transformation of the medium and by either absorption or release of thermal energy in the active zone. The energy absorbed or released from the surrounding system is commonly transferred by conduction or convection. Because of the motion of the solideliquid interface, the problems posed are nonlinear, so that few exact analytical solutions are available, and those that do exist are primarily for one-dimensional planar geometry. The PCM used in the simulations is a commercially paraffin, and the enhanced thermal conductivity material is the graphite. The geometry studied in this case is presented in Fig. 6.
Fig. 5. a- Experimental heat storage curves of paraffin and graphite/paraffin composite; b- Experimental heat storage curves of paraffin and graphite foam/paraffin composite.
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For the graphite, only 2D conduction is considered. Accordingly, the energy equation is:
! vTðtÞ ; div lg gradðTÞ ¼ rg Cg vt
lg
(5)
Momentum equation
! ! vðrPCM u Þ !! ! þ V$ðrPCM u u Þ ¼ Vp þ rPCM g þ V$t þ F vt
(6)
where p is the static pressure, u is the velocity, t is the stress tensor, ! ! r g , F are the gravitational body force and external body forces, respectively. Energy equation
! vH þ div lPCM gradðTÞ ¼ 0 vt
(7)
where H is the total volumetric enthalpy of the PCM, written as follows.
H ¼ rPCM Cp; PCM T þ rPCM Lb
(8)
with L is the latent heat of the PCM and b is the liquid fraction defined as:
8 b¼0 > > > >
if T < Tsolidus if T > Tliquid
(9)
if Tsolidus < T < Tliquid
Considering the Equation (8), Equation (7) can be written as follows.
vT ! rPCM Cp; PCM eff þ div lPCM gradðTÞ ¼ 0 vt where ðrPCM Cp; PCM Þeff ¼ rPCM Cp; PCM þ rPCM LvðbÞ=vT The initial conditions is taken as:
at t ¼ 0
(11)
The boundary conditions are as follows:
(4)
where lg, rg and Cg are the thermal conductivity, the density and the specific heat of the graphite. For the paraffin (PCM), the governing equations are as follows: The continuity equation:
vrPCM ! þ V$ðrPCM u Þ ¼ 0 vt
Ti ¼ 298 K
(10)
vTðtÞ ¼ qðtÞ hðTðtÞ Ti Þ vx
at y ¼ 0
(12)
with q is the heat flux at the bottom surface and h ¼ 10 W m2 K1 is the convective heat coefficient. The lateral and the top surfaces are isolated (adiabatic). The thermophysical properties of the paraffin used in the numerical calculations are presented in Table 3. The difference in the solidus and liquidus temperatures defines the transition from solid to liquid phases during the melting of PCM. The effective density, specific heat capacity and thermal conductivity of the PCM are defined as follows.
rPCM ¼ ð1 bÞrPCM; s þ brPCM; l
(13)
CP; PCM ¼ ð1 bÞCP; PCM; s þ bCP; PCM; l
(14)
lPCM ¼ ð1 bÞlPCM; s þ blPCM; l
(15)
3.2. Results and discussion The numerical simulations of different amount of graphite have been conducted with variable parameters including variable shape of graphite (fibers, fins, foams). In such composites, the direction of fibers or fins is crucial [30]. The equation system is solved using the finite element scheme. Different meshes are tested to study the influence of grid dimension on the solution. 3.2.1. Heat storage rate of the graphite fiber/PCM composite First, for the graphite/paraffin composite, the graphite is added as fibers into the PCM. The fibers have small dimensions, so we can supposed that we use isotropic graphite fibers, the conduction is almost the same in transverse or parallel directions. In this case, we choose the heat flow perpendicular to fibers. The effect of fibers on the transient thermal storage cycle is examined. The PCM temperatures variations are shown in Fig. 7a and b for different fiber section and graphite mass fraction. It can be seen that decreasing the section of fiber increases the heat transfer inside the composite. The melting time decreases with the decrease of fiber section. Compared with pure paraffin, we remark that addition of graphite improve the thermal conductivity, which accelerates the storage/release cycle. This indicated that the heat transfer rate was increased with the additional surface area provided by the fibers. The heat from the source was conducted by the fibers to the surface of the PCM. By increasing the graphite mass fraction from 10% to 20% (Fig. 7b), we note that the influence of fiber section becomes small, but the melting time decreases with increase of graphite amount. Consequently, the heat rate increases with graphite mass fraction. 3.2.2. Heat storage rate of the graphite fin/PCM composite Secondly, the graphite is added as fins into the PCM and the heat flow is parallel to fins. The temperature variations during storage Table 3 Thermophysical properties of PCM used in the numerical calculations. Material l (W/m K) Paraffin
Fig. 6. Physical model.
r (kg/m3)
Cp (J/kg K)
Ts (K) Tl (K) Latent heat (J g1)
0.21 (solid) 920 (solid) 1900 (solid) 331 0.12 (liquid) 795 (liquid) 2200 (liquid)
332
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Fig. 7. The heat storage/release curve of paraffin and the graphite/paraffin composites: a- graphite fiber/PCM with 10% of graphite, b- graphite fiber/PCM with 20% of graphite.
and release phases are presented on Fig. 8a and b). From these curves, we can conclude that the melting time of the sample decreases considerably, not only by increasing the percentage of graphite but also by decreasing the thickness of graphite fin structure. In addition, we noticed that the operating time decreases comparing to the case of graphite fiber/PCM composite. Thus, reducing the cycle time amounts to physically increasing the contact area and thermal conduction. In addition, the thermal conductivity of the matrix composite plays an important role in the heat absorption rate. The higher the value of the thermal conductivity of the matrix composite, the higher the value of the heat absorption rate but through a smaller time interval. 3.2.3. Heat storage rate of the graphite foam/PCM composite To further improve the thermal storage of the PCM, we introduce the paraffin into graphite foam with porosity 75%. The effects of the porosity and thermal properties of a porous medium filled with PCM were studied numerically. Fig. 9 illustrates a comparison between storage cycle relative to pure paraffin, graphite fiber/PCM, graphite fin/PCM and graphite foam/PCM composites. It can be seen that at approximately 368 s, the foam/PCM composite material initiated the change from solid to liquid phase. At this time, the energy absorption was mainly due to the phase change process. At approximately 1256 s, the phase change process was complete. As seen from the figure, without the use of graphite foam, pure paraffin initiated the change from solid to liquid phase at 1094 s and takes around 3492 s to melt completely. For the composite graphite fin/PCM, the onset of melting is at 457 s and the end of melting phase is at 2028 s. Whereas, graphite fiber/PCM composite initiated the melting phase at 836 s. From these results, we can conclude that, the time required to melt approximately the same amount of paraffin when using graphite foams is reduced to 37% of that necessary without graphite foam.
Moreover, we remark that the foam/PCM composite solidifies more uniformly than the pure paraffin. As discussed earlier, the effective thermal conductivity of foam/PCM composite is significantly higher than that of pure PCM, which in turn reduces the thermal resistance to heat transfer and so the temperature gradient is small. The addition of high porosity graphite foam provides a large solid-to-fluid surface area, combined with a high thermal conducting phase, would allow for enhanced heat transfer by conducting heat inside the graphite struts. The results, illustrated above, showed that the porosity of the matrix composite play important roles in its thermal performance. The higher, the active porosity of the PCM inside the matrix pores, the more stable of the thermal performance of the matrix composite is. On the other hand, the dispersed and the continuous form of the matrix composite matrix acts sharply to increase or decrease its heat absorption rate. 3.2.4. Enhancement of the melting rate The rate of melting is an important factor in many engineering applications, such as in the latent heat thermal energy storage systems. The melting rate is plotted against time for graphite fin/ PCM and graphite foam/PCM composites in Fig. 10. It can be seen that the melting rate of the graphite foam/PCM is greater than this of graphite fin/PCM composite. For duration of storage/release cycle, we remark that graphite foam/PCM composite give reduced cycle. At 5500 s, the paraffin returns to the solid state and completes the cycle storage. Whereas, in the graphite fin/PCM composite, the paraffin is in the liquid state during the storage phase. 4. Comparison between numerical and experimental results Regarding, the plateau during the solid to liquid phase change, for numerical results, we note an idealized phase change at a
Fig. 8. The heat storage/release curve of paraffin and the graphite/paraffin composites: a- graphite fin/PCM with 10% of graphite, b- graphite fin/PCM with 20% of graphite.
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5. Conclusion In conclusion; this work investigated the use of graphite with different configuration designs to improve the thermal storage of PCM systems. The transient thermal behavior of graphite fiber/ PCM, graphite fin/PCM and graphite foam/PCM composites were analyzed and compared to the transient thermal behavior of the pure paraffin. It was found that the selection of enhancement method has a significant effect on the thermal response of the system. The numerical results are validated experimentally and a good agreement was obtained. The rate of energy storage and release is highly depended on the nature of the solid matrix.
References Fig. 9. The heat storage/release curves of PCM and graphite foam/PCM composites.
constant temperature (Figs. 7e9). Whereas, for the experimental curves, there was a continuous ramp up of temperature during the phase change for PCM and graphite/PCM composites (Fig. 5a and b). This behavior includes a reality-based temperature range for the phase change in contrast with theoretical model which considers a melting point. In addition, the modeled graphite/PCM composites were treated as homogenous materials. As a consequence, the numerical results (Figs. 7e9) indicated a flatter response during melt when compared to the experimental data (Fig. 5a and b). From the curves given above (Fig. 5), we note that the experimental melting time is 403 s for foam/PCM composite and 989 s for PCM. Compared with numerical values (368 s and 1094 s), the relative uncertainty is 8.6% for foam/PCM composite and 9.5% for PCM. This small difference between numerical and experimental values is due essentially to natural convection, which therefore suggests that natural convection played an important role in the heat transfer during heat storage. Due to intensive natural convection in the melted paraffin, so the melting of the paraffin is accelerated.
Fig. 10. Liquid fraction in melting process of graphite foam/paraffin and graphite fin/ paraffin composites.
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