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Numerical investigations of unconstrained melting of nano-enhanced phase change material (NEPCM) inside a spherical container
International Journal of Thermal Sciences 51 (2012) 77e83
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International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts
Numerical investigations of unconstrained melting of nano-enhanced phase change material (NEPCM) inside a spherical container S.F. Hosseinizadeh a, A.A. Rabienataj Darzi b, F.L. Tan c, * a
Department of Mechanical Engineering, Babol University of Technology, Babol, Islamic Republic of Iran Faculty of Mechanical Engineering, Babol University of Technology, Babol, Islamic Republic of Iran c Nanyang Technological University, School of Mechanical & Aerospace Engineering, 50 Nanyang Avenue, 639798, Singapore b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 27 May 2011 Received in revised form 11 August 2011 Accepted 12 August 2011 Available online 6 September 2011
This paper presents a numerical study of unconstrained melting of nano-enhanced phase change materials (NEPCM) inside a spherical container using RT27 and copper particles as base material and nano-particle, respectively. Numerical studies are performed for three different Stefan number and volume fraction of nano-particles with an initial sub-cooling of 6 C. Transient numerical simulations are performed for axi-symmetric melting inside a sphere. The simulation results show that the nanoparticles cause an increase in thermal conductivity of NEPCM compared to conventional PCM. The enhancement in thermal conductivity with a decrease in latent heat results in higher melting rate of NEPCM. Ó 2011 Elsevier Masson SAS. All rights reserved.
Keywords: Unconstrained melting NEPCM Nano-particle Phase change material Melting inside sphere
1. Introduction Several studies are carried out on phase change materials over the last three decades. Phase change materials are very interesting due to their absorbing of large amount of energy as latent heat at a constant phase transition temperature. These materials can be used for passive heat storage. Major disadvantage of the PCM is related to their low thermal conductivity which impedes high rate of charge and discharge of heat flux. These types of materials have many useful properties including heat source at constant temperature, heat recovery with small temperature drop, high storage density, melting point which matches the applications, low vapor pressure (1 bar) at the operational temperature, and chemical stability and non-corrosiveness. These properties allow the PCM to be used in many industrial applications such as thermal storage of solar energy [1e6], thermal management of electronic devices [5e7], thermal storage in buildings [8,9], cooling of engines [10,11]. Following the literature review according to Telkes and Raymond [12], the first study of phase change materials was carried out in the 1940s. There are few work reported until the 1970s. After
* Corresponding author. Tel.: þ65 6790 5541; fax: þ65 6791 1859. E-mail addresses: [email protected] (S.F. Hosseinizadeh), Rabienataj@stu. nit.ac.ir (A.A. R. Darzi), mfl[email protected] (F.L. Tan). 1290-0729/$ e see front matter Ó 2011 Elsevier Masson SAS. All rights reserved. doi:10.1016/j.ijthermalsci.2011.08.006
that, the first study on PCM was presented by Barkmann and Wessling [13] for use in buildings, and later by other researchers [14e16]. Sokolov and Keizman [17] presented the applications of PCM in a solar collector for first time at 1991, and later by others, e.g. Rabin et al. [18], Enibe [19,20], and Tey et al. [21]. Also, there are a few review papers on energy thermal storage and phase change material [22,23]. Following them, a beneficial review of thermal energy storage based on PCM was presented by Zalba et al. [24]. They classified types of PCM based on material properties, heat transfer and its applications. In the recent years, many researchers have shown great interest in using PCM because of greenhouse gas emission and increasing cost of fossil fuels. Majority of their experimental and numerical studies are related to saving of energy in building structures and solar collectors. Wang et al. [25] investigated numerically the effect of orientation for PCM based on hybrid heat sinks for electronic devices (plate fin heat sink that immerse in PCM). They found that the orientation of the heat sink limited the effect of thermal performance for hybrid cooling system. Khodadadi and Zhang [26] studied the effect of buoyancy-driven convection on constrained melting of PCM in a spherical container numerically. They used the single-domain enthalpy formulation and the Darcy’s law for simulation of phase change phenomenon and porous media treatment. Their results showed the rate of melting in top region of sphere was faster than in bottom region
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Nomenclature C C0 CP ds g h H k L T u
Mushy zone constant [kg/m3s] constant Specific heat [J/kg K] Diameter of nano-particle [m] Gravitational acceleration [m/s2] Sensible enthalpy [J/kg] Enthalpy [J/kg] Thermal conductivity [W/m K] Latent heat fusion [J/kg] Temperature [K] velocity [m/s]
due to the increasing conduction heat transfer. They also investigated the effect of the Prandtl number on the flow and melting patterns. Alawadhi [27] carried out a numerical study on transient laminar flow past an in-line cylinders array containing phase change material (PCM) using the finite-element method. He investigated a parametric study of heat exchanges between the PCM and flow at different Reynolds numbers and pitch to diameter ratios whereas Prandtl number was fixed at 0.71. His numerical results showed that the Reynolds number had a significant effect on the PCM melting time, whereas the pitch to diameter ratio had an insignificant effect. Assis et al. [28] investigated both numerically and experimentally on melting in a spherical shell. They performed their numerical studies using the commercial code Fluent 6.0. Computational results had good agreement with experimental results for different wall temperatures and different shell diameters. They presented a correlation for the melting fraction based on the Grashof, Stefan and Fourier numbers. They performed another combined experimental and numerical study on the solidification of PCM inside a spherical shell with various diameters [29]. Tan and Leong [30] carried out an experimental study of solidification of pure n-Octadecane within two rectangular cells with different aspect ratios and three different constant heat fluxes. Their results showed that a faster rate of solidification occurred at higher heat rates and smaller aspect ratios. They carried out another experimental investigation of conjugate solidification inside a thick mold [31]. They used n-Octadecane as PCM that was superheated initially. Their experiments were carried out for subcooled and non-subcooled walls. They found that the solidification fraction was directly proportional to cubic root of time and changes linearly with time for subcooled and non-subcooled wall conditions, respectively. Khodadadi and Hosseinizadeh [32] performed a numerical study on improvement of thermal storage energy using nanoparticleenhanced phase change material (NEPCM). They used water and copper nonoparticle as nanofluid that enhanced the thermal conductivity of base material. They obtained higher heat release rate using NEPCM instead of conventional PCM. Tan et al. [33] presented an experimental and computational study of constrained melting of PCM inside a spherical capsule. Their investigations showed that the numerical results had some delay compared to the experimental finding. They found that this delay could be related to the thermal stratification within the constant temperature bath that enclosed the capsule. Tan [34] investigated an experimental study of constrained and unconstrained melting in a spherical container using n-Octadecane as PCM that was initially subcooled to 1 C. He indicated that the
Greece symbols m Dynamic viscosity of fluid [kg/ms] r Density [kg/m3] n Kinematics viscosity [m2/s] b Thermal expansion coefficient [1/K] l Liquid fraction f Volume fraction of nano-particle subscripts f Base fluid nf nanofluid s Solid (nano-particle) 0 stagnant
solid PCM sinks to the bottom of sphere due to gravity whereas the PCM was restrained from sinking under the constrained condition. Bagheri et al. [35] studied the transient behavior of a thermal storage module numerically. The module was composed of a concentric tube, in which the annulus contains the phase-change material (PCM) and the inner tube carried the heat transfer fluid. They used three different PCM. They measured the charging time for every PCM at the same condition. A numerical study of unconstrained melting of nano-enhanced phase change materials (NEPCM) in a spherical container following the work of [28] is presented in this paper. The effect of various volume fractions of nano-particles (0, 0.02 and 0.04) on melting rate for three temperature difference is investigated. Details of computational procedures are discussed in following sections. 2. Problem statement The computational domain of the axi-symmetric model is shown in Fig. 1. The sphere’s inner radius and wall thickness are 40 mm and 2 mm, respectively. In the initial state, the NEPCM fills 85% of the enclosed space. This is due to the large difference between solid and liquid density that causes a significant increase in the NEPCM volume during the melting. The NEPCM is exposed to air from above. In the simulations, the initial temperature of the whole system is 23 C, i.e. the PCM is slightly subcooled. The thermal conductivity of Plexiglas is equal to 0.18 (W/m K). The properties of the PCM based on a commercially available
Fig. 1. The computational domain.
S.F. Hosseinizadeh et al. / International Journal of Thermal Sciences 51 (2012) 77e83
79
where DH being the latent heat content may vary between zero (solid) and L (liquid), the latent heat of the PCM. Therefore, the liquid fraction, l, can be defined as following:
Table 1 Thermophysical Properties of RT27. Properties
Values
Melting temperature Density (solid/liquid) Kinematics Viscosity Specific Heat (solid/liquid) Thermal Conductivity (solid/liquid) Latent Heat of Fusion Thermal Expansion Coefficient
28/30 C 870/760 kg/m3 3.42 103 m2/s 2400/1800 J/kg K 0.24/0.15 W/m K 179 kJ/kg 0.0005 K1
material, RT27 (Rubitherm GmbH), is shown in Table 1. In addition, variable density was defined in the liquid state as r ¼ rl(b(T Tl) þ 1)1 for 30 C < T < 100 C, with linearly varying density in the “mushy” state, from 870 kg/m3 at 28 C to 760 kg/m3 at 30 C. It is assumed that both solid and liquid phases are homogeneous and isotropic. Also a densityetemperature relation is used for air: r ¼ 1.2 105T2 0.01134T þ 3.4978. The type of nano-particles is a key factor for the heat transfer enhancement. Nemati et al. [38] found that copper nanoparticles further increase heat transfer against Al2O3 and CuO. Due to this reason and based on the work of Khodadadi and Hosseinizadeh [32], the copper nano-particles are used in the present study. The properties of copper nano-particles are shown in Table 2.
8 DH > > ¼ > > Lf > > > < DH ¼ l ¼ L > > > f > > DH > > ¼ : Lf
0
if
T < Ts
1
if
T>Tl
T Ts Tl Ts
if
(6) T < T < Tl
In Eq. (2), Si is the Darcy’s law damping terms (as source term) that are added to the momentum equation due to phase change effect on convection. It is defined as:
Cð1 lÞ
Si ¼
l3
2
ui
(7)
That coefficient C is a mushy zone constant that is fixed to 105 kg/m3s for the present study [36]. The density of the nanofluid is given by:
rnf ¼ ð1 fÞrf þ frs
(8)
The heat capacity of the nanofluid and part of the Boussinesq term are:
rcp
nf
¼ ð1 fÞ rcp f þf rcp s
(9)
3. Governing equations The flow is considered unsteady, laminar, incompressible and two-dimensional. The viscous dissipation term is considered negligible, so that the viscous incompressible flow and the temperature distribution inside the sphere are described by the NaviereStokes and thermal energy equations, respectively. Consequently, the continuity, momentum, and thermal energy equations for NEPCM can be expressed as follows: Continuity:
vt rnf þ vi rnf ui ¼ 0
(1)
Momentum:
vi rnf ui þ vj rnf ui uj ¼ meff vjj ui vi P þ rnf gi þ Si
ðrbÞnf ¼ ð1 fÞðrbÞf þfðrbÞs
(10)
In these equation f is the volume fraction of the solid particles and subscripts f, nf and s stand for base fluid, nanofluid and solid particle, respectively. The viscosity of nanofluid which containing suspension with low concentration factor and include small rigid spherical particles is given by:
meff ¼
mf
ð1 fÞ2:5
(11)
The thermal conductivity of the stagnant (subscript 0) nanofluid is given as follows:
(2)
Thermal Energy:
vt rnf h þ vt rnf DH þ vi rnf ui h ¼ vi keff vi T
(3)
In these relations ui is the fluid velocity, rnf is the NEPCM’s density, meff is the dynamics viscosity of NEPCM, P is the pressure, g is the gravitational acceleration, keff is the effective thermal conductivity and h is sensible enthalpy that is defined as following [36]:
ZT
h ¼ href þ
Cp dT
(4)
Tref
The enthalpy, H, is therefore:
H ¼ h þ DH
(5)
Table 2 Properties of copper nano-particle. Properties
Values
Density Specific Heat Thermal Conductivity Thermal Expansion Coefficient
8954 kg/m3 383 J/kg K 400 W/m K 1.67 105 K1
Fig. 2. Comparison of liquid fraction versus time between present study and Assis et al. [28] work.
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knf 0 kf
ks þ 2kf 2f kf ks ¼ ks þ kf þ f kf ks
(12)
Ra ¼
The effective thermal conductivity of the nanofluid is:
keff ¼ knf 0 þ kd
(13)
And the thermal conductivity enhancement term due to thermal dispersion is given by:
kd ¼ C r cp nf ui f ds 0
g bnf DTR3
nnf anf
¼
ðrbÞnf rcp nf DTR3
meff keff
(16)
meff cp nnf Pr ¼ ¼ anf keff
nf
(17)
(14)
The empirically-determined constant C0 is evaluated following the work of Wakao and Kaguei [37]. The latent heat that is evaluated using:
ðrLÞnf ¼ ð1 fÞðrLÞf
NEPCM. The Rayleigh and Prandtl numbers for the NEPCM are given in the following equations:
(15)
It is obvious that Eqs. of (10) and (11) are employed in liquid region of NEPCM while other relations are applied in all region of
4. Initial and boundary condition At the initial time stage (t ¼ 0), the NEPCM is taken to be a motionless solid that is maintained at a constant temperature 6 K below the melting temperature of the NEPCM, i.e. T0 ¼ 296 K where l ¼ 0. Also the no-slip boundary condition is applied at container wall, i.e. ui ¼ 0 and the temperature of container wall is maintained at 307.15, 312.15 and 317.15 K for temperature difference (DT) of 5,
Fig. 3. Unconstrained melting phase for various volume fraction of nano-particle when DT ¼ 10 C.
S.F. Hosseinizadeh et al. / International Journal of Thermal Sciences 51 (2012) 77e83
10 and 15, respectively. The boundary for the opening to air is considered as pressure outlet boundary with gauge pressure of zero. 5. Numerical procedure and validation In order to describe the PCMeair system with a moving internal interface but without inter-penetration of the two media, the socalled “volume-of-fluid” (VOF) model has been used. In order to solve the momentum and energy equations, the power law scheme and the PISO method for pressureevelocity coupling are used. Also the PRESTO scheme is adopted for the pressure correction equation. The under-relaxation factors for the velocity components, pressure correction, thermal energy and
81
liquid fraction are 0.7, 0.3, 1 and 0.9, respectively. Different grid densities are selected and tested to ensure independency of solution from the adopted grid density based on comparison of melting fraction and streamline contours. An arrangement of 4326 grids is found sufficient for present study. Adoption of fine grid distribution in the radial direction allows the use of longer time steps. The time duration to achieve full melting is a good indicator of time step dependence. The PCM melted after 10.54, 11.18 and 12.39 min with time step increments of 0.002, 0.005 and 0.01 s for temperature difference of 10 C, respectively. Therefore, the time step is set to 0.005 s. It should be mentioned that in all cases, the time step is fixed at 0.0005 at the start time. The time step is changed to higher values when the NEPCM melts up to 10%. The number of iterations for every time step is fixed at 70 and it is found sufficient to satisfy
Fig. 4. Detailed temperature contour for various volume fraction of nano-particle when DT ¼ 10 C.
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S.F. Hosseinizadeh et al. / International Journal of Thermal Sciences 51 (2012) 77e83
the convergence criteria of 106 for the continuity and momentum equations and at 108 for the energy equation. In order to validate the present work, initial run is performed and compared with those of Assis et al. [28] for temperature difference of 10 C (Ste ¼ 0.1) and shell diameter of 40 (mm). Fig. 2 shows the comparison of liquid fraction versus time between two works. It can be seen that the present study shows a good agreement with those of Assis et al. [28]. 6. Results and discussions The colorized contours of solideliquid front at various time instants for different volume fraction of nano-particle are presented in Fig. 3. The solid was subcooled to 296.15 C and the difference between wall temperature and melting temperature of NEPCM was 10 C. It can be seen that solid NEPCM sinks to the bottom of sphere due to gravity force since it is heavier in relation to the liquid NEPCM. Thus, the solid PCM is in contact with the bottom hot surface of sphere at these times. But, this is not a full perfect contact as a thin layer is seen between the inner wall and the solid PCM at every time during the melting. At the start, the outer surface of solid PCM is in contact with the inner wall of sphere so that heat conduction dominates between solid NEPCM and wall. This causes the formation of a thin layer of liquid between the solid PCM and sphere. As time progresses, the molten zone expands and the liquid layer grows. The liquid film formed at the bottom of the solid PCM is squeezed down by the sinking heavier solid. The squeezed liquid film is then pushed upward along the inner surface of the sphere, occupying the region above the solid PCM. As the warm liquid rises to the top portion of the sphere, the cooler liquid is replaced and forced to sink toward the solid PCM. Thus, natural convection in combination with a hot rising curved wall jet dominates in the top and side regions of the sphere, while heat conduction occurs at the bottom region of sphere between inner wall and the solid NEPCM. The temperature of air above NEPCM increases very fast and subsequently, it causes to increase in the melting rate of top region. However this effect diminishes when the interface between air and molten NEPCM rises and the volume of air reduced. The oblate shape of the solid NEPCM that can be seen after 6 min is distinctly indicative of the intensity of buoyancy-driven convection responsible for expedited melting in the top and bottom zone. Another phenomenon that can be observed in Fig. 3 is an increment of melting rate of NEPCM with increasing the volume fraction of nano-particle. This increment becomes obvious when we consider the solideliquid front of PCM for f ¼ 0:04 after 6 min and for f ¼ 0 after 8 min. It can be readily distinguishable that those two have approximately same solid PCM (and/or melting zone). The temperature contour of NEPCM for temperature difference of 10 C and different volume fraction of nano-particles are shown in Fig. 4. PCM is solid/liquid where temperature is lesser/more than 301.15 C and 303.15 C respectively. Also it is in mushy zone where temperature is between 301.15 C and 303.15 C. The figure reveals that most regions between NEPCM and inner wall of sphere (except very thin layer near hot wall) are in the mushy zone. It can be observed that this region is expanded with increasing volume fraction of nano-particles due to increasing in thermal conductivity of NEPCM (especially mushy zone). The computed variations of the liquid fraction versus time for three Stefan numbers of 0.05, 0.1 and 0.15 (temperature difference of 5 C, 10 C and 15 C, respectively) are shown in Fig. 5. The Stefan number (Ste) describes the operating condition of the sphere undergoing melting, given that the surface temperature TS directly affects the value of the Stefan number and is defined as:
Fig. 5. Variation of liquid fraction versus time for various volume fraction of nanoparticle and different wall temperature.
S.F. Hosseinizadeh et al. / International Journal of Thermal Sciences 51 (2012) 77e83
Ste ¼
cpl ðTs Tm Þ L
(18)
where Cpl is the specific heat of the liquid PCM, L is the latent heat of PCM and Tm is the melting temperature of PCM. Using the same PCM inside the sphere, a higher surface temperature gives rise to a higher Stefan number. The liquid fraction of PCM is defined as current melted mass divided by the total mass of the PCM. It can be observed that the duration of full melting of NEPCM decreases when volume fraction increases. It occurs 5, 3 and 2 min earlier when volume fraction changes from 0 to 0.04 for temperature difference of 5, 10 and 15, respectively. It is due to an increase in thermal conductivity of NEPCM and lowering of the latent heat of fusion (according to Eq. [13]) in comparison with the conventional PCM. 7. Conclusion Numerical study of melting of nano-enhanced phase change material is presented in this paper. Transient simulation of axisymmetric unconstrained melting inside a spherical shell is performed and is validated with other author work (Assis et al. [28]). The simulation results show an enhancement of melting rate of NEPCM respect to conventional PCM due to the increase in thermal conductivity and the lowering of latent heat of fusion. This simulation study shows a great potential of utilizing nano-particles in phase change material in thermal energy storage application. Acknowledgment This work is a remembrance of Seyed Farid Hosseinizadeh, who unfortunately had passed away in a car accident in January 2011. His youth and talent in computational modeling and simulation work would be forever remembered by the co-authors and others who may be inspired by his research work. References [1] G.A. Lane, Solar Heat Storage: Latent Heat Material, in: Technology, vol. II. CRC Press, Florida, 1986. [2] M. Kamimoto, Y. Abe, S. Sawata, T. Tani, T. Ozawa, Latent heat storage unit using form-stable high density polyethylene for solar thermal applications, in: Proceedings of the International Symposium on Thermal Application of Solar Energy (1985) Hakone (Kanagawa, Japan). [3] M. Hadjieva, S. Kanev, J. Argirov, Thermo physical properties of some paraffins applicable to thermal energy storage, Sol. Energ. Mater. 27 (1992) 181e187. [4] V.H. Morcos, Investigation of a latent heat thermal energy storage system, Solar Wind Technol. 7 (2/3) (1990) 197e202. [5] M.A. Cuevas-Diarte, T. Calvet-Pallas, J.L. Tamarit, H.A.J. Oonk, D. Mondieig, Y. Haget, Nuevos materials termoajustables, Mundo Cientifico (2000) June. [6] D. Pal, Y. Joshi, Application of phase change materials for passive thermal control of plastic quad flat packages: a computational study, Numer. Heat Trans. Part A 30 (1996) 19e34. [7] L.F. Cabeza, J. Roca, M. Nogues, B. Zalba, J.M. Marın, Transportation And Conservation of Temperature Sensitive Materials with Phase Change Materials: State of the Art. IEA ECES IA Annex 17 2nd Workshop, Ljubljana (Slovenia), 2002. [8] M. Koschenz, B. Lehmann, Development of a thermally activated ceiling panel with PCM for application in lightweight and retrofitted buildings, Energy Build. 36 (2002) 567e578. [9] J.K. Kissock, J.M. Hannig, T.I. Whitney, M.L. Drake, Testing and simulation of phase change wallboard for thermal storage in buildings, in: Proceedings of 1998 International Solar Energy Conference (1998), pp. 45e52 New York, USA.
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[10] J. Bellettre, V. Sartre, F. Biais, A. Lallemand, Transient state study of electric motor heating and phase change solideliquid cooling, Appl. Therm. Eng. 17 (1) (1997) 17e31. [11] L.L. Vasiliev, V.S. Burak, A.G. Kulakov, D.A. Mishkinis, P.V. Bohan, Latent heat storage modules for preheating internal combustion engines: application to a bus petrol engine, Appl. Therm. Eng. 20 (2000) 913e923. [12] M. Telkes, E. Raymond, Storing solar heat in chemicals-a report on the Dover house, Heat Vent. 46 (11) (1949) 80e86. [13] H.G. Barkmann, F.C. Wessling, Use of buildings structural components for thermal storage, in: Proceedings of the Workshop on Solar Energy Storage Subsystems for the Heating and Cooling of Buildings. Charlottesville, Virginia, USA, 1975. [14] D.W. Hawes, D. Feldman, D. Banu, Latent heat storage in building materials, Energy Build. 20 (1993) 77e86. [15] Y. Morikama, H. Suzuki, F. Okagawa, K.A. Kanki, development of building elements using PCM, in: Proceedings of the International Symposium on Thermal Application of Solar Energy (1985) Hakone (Kanagawa, Japan). [16] C.H. Lee, H.K. Choi, Crystalline morphology in high-density polyethylene/ paraffin blend for thermal energy storage, Polym. Compos. 19 (6) (1998) 704e708. [17] M. Sokolov, Y. Keizman, Performance indicators for solar pipes with phase change storage, Sol. Energy 47 (1991) 339e346. [18] Y. Rabin, I. Bar-Niv, E. Korin, B. Mikic, Integrated solar collector storage system based on a salt-hydrate phase change material, Sol. Energy 55 (1995) 435e444. [19] S.O. Enibe, Parametric effects on the performance of a passive solar air heater with storage, in: Proceedings of the World Renewable Energy Congress WII (2002) Cologne, Germany. [20] S.O. Enibe, Performance of a natural circulation air heating system with phase change material energy storage, Renew. Energ. 27 (2002) 69e86. [21] J. Tey, R. Fernandez, J. Rosell, M. Ibanez, Solar collector with integrated storage and transparent insulation cover, in: Proceedings of Eurosun. Bologna, Italy, 2002. [22] F. Agyenim, N. Hewitt, P. Eames, M. Smyth, A review of materials, heat transfer and phase change problem formulation for latent heat thermal energy storage systems (LHTESS), Renew. Sust. Energ. Rev. 14 (2010) 615e628. [23] M.M. Farid, A.M. Khudhair, S.A.K. Razack, S. Al-Hallaj, A review on phase change energy storage: materials and applications, Energ. Convers. Manage. 45 (2004) 1597e1615. [24] B. Zalba, J.M. Marın, L.F. Cabeza, H. Mehling, Review on thermal energy storage with phase change: materials, heat transfer analysis and applications, Appl. Therm. Eng. 23 (2003) 251e283. [25] X.Q. Wang, A.S. Mujumdar, C. Yap, Effect of orientation for phase change material (PCM)-based heat sinks for transient thermal management of electric components, Int. Commun. Heat Mass Trans. 34 (2007) 801e808. [26] J.M. Khodadadi, Y. Zhang, Effects of buoyancy-driven convection on melting within spherical containers, Int. J. Heat Mass Trans. 44 (2001) 1605e1618. [27] E.M. Alawadhi, Thermal analysis of transient laminar flow past an in-line cylinders array containing phase change material, Proc. IMechE, Part A: J. Power Energy 223 (4) (2009) 349e360. [28] E. Assis, L. Katsman, G. Ziskind, R. Letan, Numerical and experimental study of melting in a spherical shell, Int. J. Heat Mass Trans. 50 (2007) 1790e1804. [29] E. Assis, G. Ziskind, R. Letan, Numerical and experimental study of solidification in a spherical shell, J. Heat Trans. 31 (1) (2009) 24502e24507. [30] F.L. Tan, K.C. Leong, an experimental investigation of solidification in a rectangular enclosure under constant heat rate conditions, Int. Commun. Heat Mass Trans. 26 (7) (1999) 925e934. [31] F.L. Tan, K.C. Leong, Conjugate solidification inside a thick mold, J. Mater. Process. Technol. 89e90 (1999) 159e164. [32] J.M. Khodadadi, S.F. Hosseinizadeh, Nanoparticle-enhanced phase change materials (NEPCM) with great potential for improved thermal energy storage, Int. Commun. Heat Mass Trans. 34 (2007) 534e543. [33] F.L. Tan, S.F. Hosseinizadeh, J.M. Khodadadi, L. Fan, Experimental and computational study of constrained melting of phase change materials (PCM) inside a spherical capsule, Int. J. Heat Mass Trans. 52 (2009) 3464e3472. [34] F.L. Tan, Constrained and unconstrained melting inside a sphere, Int. Commun. Heat Mass Trans. 35 (2008) 466e475. [35] G.H. Bagheri, M.A. Mehrabian, K. Hooman, Numerical study of the transient behaviour of a thermal storage module containing phase-change material, Proc. IMechE, Part A: J. Power Energy 224 (4) (2010) 349e360. [36] www.FLUENT.com. [37] N. Wakao, S. Kaguei, Heat and Mass Transfer in Packed Beds. Gordon and Breach Science Publishers, New York, 1982, pp. 175e205. [38] H. Nemati, M. Farhadi, K. Sedighi, E. Fattahi, A.A.R. Darzi, Lattice Boltzmann simulation of nanofluid in lid-driven cavity, Int. Commun. Heat Mass Trans. 37 (2010) 1528e1534.
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International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts
Numerical investigations of unconstrained melting of nano-enhanced phase change material (NEPCM) inside a spherical container S.F. Hosseinizadeh a, A.A. Rabienataj Darzi b, F.L. Tan c, * a
Department of Mechanical Engineering, Babol University of Technology, Babol, Islamic Republic of Iran Faculty of Mechanical Engineering, Babol University of Technology, Babol, Islamic Republic of Iran c Nanyang Technological University, School of Mechanical & Aerospace Engineering, 50 Nanyang Avenue, 639798, Singapore b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 27 May 2011 Received in revised form 11 August 2011 Accepted 12 August 2011 Available online 6 September 2011
This paper presents a numerical study of unconstrained melting of nano-enhanced phase change materials (NEPCM) inside a spherical container using RT27 and copper particles as base material and nano-particle, respectively. Numerical studies are performed for three different Stefan number and volume fraction of nano-particles with an initial sub-cooling of 6 C. Transient numerical simulations are performed for axi-symmetric melting inside a sphere. The simulation results show that the nanoparticles cause an increase in thermal conductivity of NEPCM compared to conventional PCM. The enhancement in thermal conductivity with a decrease in latent heat results in higher melting rate of NEPCM. Ó 2011 Elsevier Masson SAS. All rights reserved.
Keywords: Unconstrained melting NEPCM Nano-particle Phase change material Melting inside sphere
1. Introduction Several studies are carried out on phase change materials over the last three decades. Phase change materials are very interesting due to their absorbing of large amount of energy as latent heat at a constant phase transition temperature. These materials can be used for passive heat storage. Major disadvantage of the PCM is related to their low thermal conductivity which impedes high rate of charge and discharge of heat flux. These types of materials have many useful properties including heat source at constant temperature, heat recovery with small temperature drop, high storage density, melting point which matches the applications, low vapor pressure (1 bar) at the operational temperature, and chemical stability and non-corrosiveness. These properties allow the PCM to be used in many industrial applications such as thermal storage of solar energy [1e6], thermal management of electronic devices [5e7], thermal storage in buildings [8,9], cooling of engines [10,11]. Following the literature review according to Telkes and Raymond [12], the first study of phase change materials was carried out in the 1940s. There are few work reported until the 1970s. After
* Corresponding author. Tel.: þ65 6790 5541; fax: þ65 6791 1859. E-mail addresses: [email protected] (S.F. Hosseinizadeh), Rabienataj@stu. nit.ac.ir (A.A. R. Darzi), mfl[email protected] (F.L. Tan). 1290-0729/$ e see front matter Ó 2011 Elsevier Masson SAS. All rights reserved. doi:10.1016/j.ijthermalsci.2011.08.006
that, the first study on PCM was presented by Barkmann and Wessling [13] for use in buildings, and later by other researchers [14e16]. Sokolov and Keizman [17] presented the applications of PCM in a solar collector for first time at 1991, and later by others, e.g. Rabin et al. [18], Enibe [19,20], and Tey et al. [21]. Also, there are a few review papers on energy thermal storage and phase change material [22,23]. Following them, a beneficial review of thermal energy storage based on PCM was presented by Zalba et al. [24]. They classified types of PCM based on material properties, heat transfer and its applications. In the recent years, many researchers have shown great interest in using PCM because of greenhouse gas emission and increasing cost of fossil fuels. Majority of their experimental and numerical studies are related to saving of energy in building structures and solar collectors. Wang et al. [25] investigated numerically the effect of orientation for PCM based on hybrid heat sinks for electronic devices (plate fin heat sink that immerse in PCM). They found that the orientation of the heat sink limited the effect of thermal performance for hybrid cooling system. Khodadadi and Zhang [26] studied the effect of buoyancy-driven convection on constrained melting of PCM in a spherical container numerically. They used the single-domain enthalpy formulation and the Darcy’s law for simulation of phase change phenomenon and porous media treatment. Their results showed the rate of melting in top region of sphere was faster than in bottom region
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Nomenclature C C0 CP ds g h H k L T u
Mushy zone constant [kg/m3s] constant Specific heat [J/kg K] Diameter of nano-particle [m] Gravitational acceleration [m/s2] Sensible enthalpy [J/kg] Enthalpy [J/kg] Thermal conductivity [W/m K] Latent heat fusion [J/kg] Temperature [K] velocity [m/s]
due to the increasing conduction heat transfer. They also investigated the effect of the Prandtl number on the flow and melting patterns. Alawadhi [27] carried out a numerical study on transient laminar flow past an in-line cylinders array containing phase change material (PCM) using the finite-element method. He investigated a parametric study of heat exchanges between the PCM and flow at different Reynolds numbers and pitch to diameter ratios whereas Prandtl number was fixed at 0.71. His numerical results showed that the Reynolds number had a significant effect on the PCM melting time, whereas the pitch to diameter ratio had an insignificant effect. Assis et al. [28] investigated both numerically and experimentally on melting in a spherical shell. They performed their numerical studies using the commercial code Fluent 6.0. Computational results had good agreement with experimental results for different wall temperatures and different shell diameters. They presented a correlation for the melting fraction based on the Grashof, Stefan and Fourier numbers. They performed another combined experimental and numerical study on the solidification of PCM inside a spherical shell with various diameters [29]. Tan and Leong [30] carried out an experimental study of solidification of pure n-Octadecane within two rectangular cells with different aspect ratios and three different constant heat fluxes. Their results showed that a faster rate of solidification occurred at higher heat rates and smaller aspect ratios. They carried out another experimental investigation of conjugate solidification inside a thick mold [31]. They used n-Octadecane as PCM that was superheated initially. Their experiments were carried out for subcooled and non-subcooled walls. They found that the solidification fraction was directly proportional to cubic root of time and changes linearly with time for subcooled and non-subcooled wall conditions, respectively. Khodadadi and Hosseinizadeh [32] performed a numerical study on improvement of thermal storage energy using nanoparticleenhanced phase change material (NEPCM). They used water and copper nonoparticle as nanofluid that enhanced the thermal conductivity of base material. They obtained higher heat release rate using NEPCM instead of conventional PCM. Tan et al. [33] presented an experimental and computational study of constrained melting of PCM inside a spherical capsule. Their investigations showed that the numerical results had some delay compared to the experimental finding. They found that this delay could be related to the thermal stratification within the constant temperature bath that enclosed the capsule. Tan [34] investigated an experimental study of constrained and unconstrained melting in a spherical container using n-Octadecane as PCM that was initially subcooled to 1 C. He indicated that the
Greece symbols m Dynamic viscosity of fluid [kg/ms] r Density [kg/m3] n Kinematics viscosity [m2/s] b Thermal expansion coefficient [1/K] l Liquid fraction f Volume fraction of nano-particle subscripts f Base fluid nf nanofluid s Solid (nano-particle) 0 stagnant
solid PCM sinks to the bottom of sphere due to gravity whereas the PCM was restrained from sinking under the constrained condition. Bagheri et al. [35] studied the transient behavior of a thermal storage module numerically. The module was composed of a concentric tube, in which the annulus contains the phase-change material (PCM) and the inner tube carried the heat transfer fluid. They used three different PCM. They measured the charging time for every PCM at the same condition. A numerical study of unconstrained melting of nano-enhanced phase change materials (NEPCM) in a spherical container following the work of [28] is presented in this paper. The effect of various volume fractions of nano-particles (0, 0.02 and 0.04) on melting rate for three temperature difference is investigated. Details of computational procedures are discussed in following sections. 2. Problem statement The computational domain of the axi-symmetric model is shown in Fig. 1. The sphere’s inner radius and wall thickness are 40 mm and 2 mm, respectively. In the initial state, the NEPCM fills 85% of the enclosed space. This is due to the large difference between solid and liquid density that causes a significant increase in the NEPCM volume during the melting. The NEPCM is exposed to air from above. In the simulations, the initial temperature of the whole system is 23 C, i.e. the PCM is slightly subcooled. The thermal conductivity of Plexiglas is equal to 0.18 (W/m K). The properties of the PCM based on a commercially available
Fig. 1. The computational domain.
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where DH being the latent heat content may vary between zero (solid) and L (liquid), the latent heat of the PCM. Therefore, the liquid fraction, l, can be defined as following:
Table 1 Thermophysical Properties of RT27. Properties
Values
Melting temperature Density (solid/liquid) Kinematics Viscosity Specific Heat (solid/liquid) Thermal Conductivity (solid/liquid) Latent Heat of Fusion Thermal Expansion Coefficient
28/30 C 870/760 kg/m3 3.42 103 m2/s 2400/1800 J/kg K 0.24/0.15 W/m K 179 kJ/kg 0.0005 K1
material, RT27 (Rubitherm GmbH), is shown in Table 1. In addition, variable density was defined in the liquid state as r ¼ rl(b(T Tl) þ 1)1 for 30 C < T < 100 C, with linearly varying density in the “mushy” state, from 870 kg/m3 at 28 C to 760 kg/m3 at 30 C. It is assumed that both solid and liquid phases are homogeneous and isotropic. Also a densityetemperature relation is used for air: r ¼ 1.2 105T2 0.01134T þ 3.4978. The type of nano-particles is a key factor for the heat transfer enhancement. Nemati et al. [38] found that copper nanoparticles further increase heat transfer against Al2O3 and CuO. Due to this reason and based on the work of Khodadadi and Hosseinizadeh [32], the copper nano-particles are used in the present study. The properties of copper nano-particles are shown in Table 2.
8 DH > > ¼ > > Lf > > > < DH ¼ l ¼ L > > > f > > DH > > ¼ : Lf
0
if
T < Ts
1
if
T>Tl
T Ts Tl Ts
if
(6) T < T < Tl
In Eq. (2), Si is the Darcy’s law damping terms (as source term) that are added to the momentum equation due to phase change effect on convection. It is defined as:
Cð1 lÞ
Si ¼
l3
2
ui
(7)
That coefficient C is a mushy zone constant that is fixed to 105 kg/m3s for the present study [36]. The density of the nanofluid is given by:
rnf ¼ ð1 fÞrf þ frs
(8)
The heat capacity of the nanofluid and part of the Boussinesq term are:
rcp
nf
¼ ð1 fÞ rcp f þf rcp s
(9)
3. Governing equations The flow is considered unsteady, laminar, incompressible and two-dimensional. The viscous dissipation term is considered negligible, so that the viscous incompressible flow and the temperature distribution inside the sphere are described by the NaviereStokes and thermal energy equations, respectively. Consequently, the continuity, momentum, and thermal energy equations for NEPCM can be expressed as follows: Continuity:
vt rnf þ vi rnf ui ¼ 0
(1)
Momentum:
vi rnf ui þ vj rnf ui uj ¼ meff vjj ui vi P þ rnf gi þ Si
ðrbÞnf ¼ ð1 fÞðrbÞf þfðrbÞs
(10)
In these equation f is the volume fraction of the solid particles and subscripts f, nf and s stand for base fluid, nanofluid and solid particle, respectively. The viscosity of nanofluid which containing suspension with low concentration factor and include small rigid spherical particles is given by:
meff ¼
mf
ð1 fÞ2:5
(11)
The thermal conductivity of the stagnant (subscript 0) nanofluid is given as follows:
(2)
Thermal Energy:
vt rnf h þ vt rnf DH þ vi rnf ui h ¼ vi keff vi T
(3)
In these relations ui is the fluid velocity, rnf is the NEPCM’s density, meff is the dynamics viscosity of NEPCM, P is the pressure, g is the gravitational acceleration, keff is the effective thermal conductivity and h is sensible enthalpy that is defined as following [36]:
ZT
h ¼ href þ
Cp dT
(4)
Tref
The enthalpy, H, is therefore:
H ¼ h þ DH
(5)
Table 2 Properties of copper nano-particle. Properties
Values
Density Specific Heat Thermal Conductivity Thermal Expansion Coefficient
8954 kg/m3 383 J/kg K 400 W/m K 1.67 105 K1
Fig. 2. Comparison of liquid fraction versus time between present study and Assis et al. [28] work.
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knf 0 kf
ks þ 2kf 2f kf ks ¼ ks þ kf þ f kf ks
(12)
Ra ¼
The effective thermal conductivity of the nanofluid is:
keff ¼ knf 0 þ kd
(13)
And the thermal conductivity enhancement term due to thermal dispersion is given by:
kd ¼ C r cp nf ui f ds 0
g bnf DTR3
nnf anf
¼
ðrbÞnf rcp nf DTR3
meff keff
(16)
meff cp nnf Pr ¼ ¼ anf keff
nf
(17)
(14)
The empirically-determined constant C0 is evaluated following the work of Wakao and Kaguei [37]. The latent heat that is evaluated using:
ðrLÞnf ¼ ð1 fÞðrLÞf
NEPCM. The Rayleigh and Prandtl numbers for the NEPCM are given in the following equations:
(15)
It is obvious that Eqs. of (10) and (11) are employed in liquid region of NEPCM while other relations are applied in all region of
4. Initial and boundary condition At the initial time stage (t ¼ 0), the NEPCM is taken to be a motionless solid that is maintained at a constant temperature 6 K below the melting temperature of the NEPCM, i.e. T0 ¼ 296 K where l ¼ 0. Also the no-slip boundary condition is applied at container wall, i.e. ui ¼ 0 and the temperature of container wall is maintained at 307.15, 312.15 and 317.15 K for temperature difference (DT) of 5,
Fig. 3. Unconstrained melting phase for various volume fraction of nano-particle when DT ¼ 10 C.
S.F. Hosseinizadeh et al. / International Journal of Thermal Sciences 51 (2012) 77e83
10 and 15, respectively. The boundary for the opening to air is considered as pressure outlet boundary with gauge pressure of zero. 5. Numerical procedure and validation In order to describe the PCMeair system with a moving internal interface but without inter-penetration of the two media, the socalled “volume-of-fluid” (VOF) model has been used. In order to solve the momentum and energy equations, the power law scheme and the PISO method for pressureevelocity coupling are used. Also the PRESTO scheme is adopted for the pressure correction equation. The under-relaxation factors for the velocity components, pressure correction, thermal energy and
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liquid fraction are 0.7, 0.3, 1 and 0.9, respectively. Different grid densities are selected and tested to ensure independency of solution from the adopted grid density based on comparison of melting fraction and streamline contours. An arrangement of 4326 grids is found sufficient for present study. Adoption of fine grid distribution in the radial direction allows the use of longer time steps. The time duration to achieve full melting is a good indicator of time step dependence. The PCM melted after 10.54, 11.18 and 12.39 min with time step increments of 0.002, 0.005 and 0.01 s for temperature difference of 10 C, respectively. Therefore, the time step is set to 0.005 s. It should be mentioned that in all cases, the time step is fixed at 0.0005 at the start time. The time step is changed to higher values when the NEPCM melts up to 10%. The number of iterations for every time step is fixed at 70 and it is found sufficient to satisfy
Fig. 4. Detailed temperature contour for various volume fraction of nano-particle when DT ¼ 10 C.
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the convergence criteria of 106 for the continuity and momentum equations and at 108 for the energy equation. In order to validate the present work, initial run is performed and compared with those of Assis et al. [28] for temperature difference of 10 C (Ste ¼ 0.1) and shell diameter of 40 (mm). Fig. 2 shows the comparison of liquid fraction versus time between two works. It can be seen that the present study shows a good agreement with those of Assis et al. [28]. 6. Results and discussions The colorized contours of solideliquid front at various time instants for different volume fraction of nano-particle are presented in Fig. 3. The solid was subcooled to 296.15 C and the difference between wall temperature and melting temperature of NEPCM was 10 C. It can be seen that solid NEPCM sinks to the bottom of sphere due to gravity force since it is heavier in relation to the liquid NEPCM. Thus, the solid PCM is in contact with the bottom hot surface of sphere at these times. But, this is not a full perfect contact as a thin layer is seen between the inner wall and the solid PCM at every time during the melting. At the start, the outer surface of solid PCM is in contact with the inner wall of sphere so that heat conduction dominates between solid NEPCM and wall. This causes the formation of a thin layer of liquid between the solid PCM and sphere. As time progresses, the molten zone expands and the liquid layer grows. The liquid film formed at the bottom of the solid PCM is squeezed down by the sinking heavier solid. The squeezed liquid film is then pushed upward along the inner surface of the sphere, occupying the region above the solid PCM. As the warm liquid rises to the top portion of the sphere, the cooler liquid is replaced and forced to sink toward the solid PCM. Thus, natural convection in combination with a hot rising curved wall jet dominates in the top and side regions of the sphere, while heat conduction occurs at the bottom region of sphere between inner wall and the solid NEPCM. The temperature of air above NEPCM increases very fast and subsequently, it causes to increase in the melting rate of top region. However this effect diminishes when the interface between air and molten NEPCM rises and the volume of air reduced. The oblate shape of the solid NEPCM that can be seen after 6 min is distinctly indicative of the intensity of buoyancy-driven convection responsible for expedited melting in the top and bottom zone. Another phenomenon that can be observed in Fig. 3 is an increment of melting rate of NEPCM with increasing the volume fraction of nano-particle. This increment becomes obvious when we consider the solideliquid front of PCM for f ¼ 0:04 after 6 min and for f ¼ 0 after 8 min. It can be readily distinguishable that those two have approximately same solid PCM (and/or melting zone). The temperature contour of NEPCM for temperature difference of 10 C and different volume fraction of nano-particles are shown in Fig. 4. PCM is solid/liquid where temperature is lesser/more than 301.15 C and 303.15 C respectively. Also it is in mushy zone where temperature is between 301.15 C and 303.15 C. The figure reveals that most regions between NEPCM and inner wall of sphere (except very thin layer near hot wall) are in the mushy zone. It can be observed that this region is expanded with increasing volume fraction of nano-particles due to increasing in thermal conductivity of NEPCM (especially mushy zone). The computed variations of the liquid fraction versus time for three Stefan numbers of 0.05, 0.1 and 0.15 (temperature difference of 5 C, 10 C and 15 C, respectively) are shown in Fig. 5. The Stefan number (Ste) describes the operating condition of the sphere undergoing melting, given that the surface temperature TS directly affects the value of the Stefan number and is defined as:
Fig. 5. Variation of liquid fraction versus time for various volume fraction of nanoparticle and different wall temperature.
S.F. Hosseinizadeh et al. / International Journal of Thermal Sciences 51 (2012) 77e83
Ste ¼
cpl ðTs Tm Þ L
(18)
where Cpl is the specific heat of the liquid PCM, L is the latent heat of PCM and Tm is the melting temperature of PCM. Using the same PCM inside the sphere, a higher surface temperature gives rise to a higher Stefan number. The liquid fraction of PCM is defined as current melted mass divided by the total mass of the PCM. It can be observed that the duration of full melting of NEPCM decreases when volume fraction increases. It occurs 5, 3 and 2 min earlier when volume fraction changes from 0 to 0.04 for temperature difference of 5, 10 and 15, respectively. It is due to an increase in thermal conductivity of NEPCM and lowering of the latent heat of fusion (according to Eq. [13]) in comparison with the conventional PCM. 7. Conclusion Numerical study of melting of nano-enhanced phase change material is presented in this paper. Transient simulation of axisymmetric unconstrained melting inside a spherical shell is performed and is validated with other author work (Assis et al. [28]). The simulation results show an enhancement of melting rate of NEPCM respect to conventional PCM due to the increase in thermal conductivity and the lowering of latent heat of fusion. This simulation study shows a great potential of utilizing nano-particles in phase change material in thermal energy storage application. Acknowledgment This work is a remembrance of Seyed Farid Hosseinizadeh, who unfortunately had passed away in a car accident in January 2011. His youth and talent in computational modeling and simulation work would be forever remembered by the co-authors and others who may be inspired by his research work. References [1] G.A. Lane, Solar Heat Storage: Latent Heat Material, in: Technology, vol. II. CRC Press, Florida, 1986. [2] M. Kamimoto, Y. Abe, S. Sawata, T. Tani, T. Ozawa, Latent heat storage unit using form-stable high density polyethylene for solar thermal applications, in: Proceedings of the International Symposium on Thermal Application of Solar Energy (1985) Hakone (Kanagawa, Japan). [3] M. Hadjieva, S. Kanev, J. Argirov, Thermo physical properties of some paraffins applicable to thermal energy storage, Sol. Energ. Mater. 27 (1992) 181e187. [4] V.H. Morcos, Investigation of a latent heat thermal energy storage system, Solar Wind Technol. 7 (2/3) (1990) 197e202. [5] M.A. Cuevas-Diarte, T. Calvet-Pallas, J.L. Tamarit, H.A.J. Oonk, D. Mondieig, Y. Haget, Nuevos materials termoajustables, Mundo Cientifico (2000) June. [6] D. Pal, Y. Joshi, Application of phase change materials for passive thermal control of plastic quad flat packages: a computational study, Numer. Heat Trans. Part A 30 (1996) 19e34. [7] L.F. Cabeza, J. Roca, M. Nogues, B. Zalba, J.M. Marın, Transportation And Conservation of Temperature Sensitive Materials with Phase Change Materials: State of the Art. IEA ECES IA Annex 17 2nd Workshop, Ljubljana (Slovenia), 2002. [8] M. Koschenz, B. Lehmann, Development of a thermally activated ceiling panel with PCM for application in lightweight and retrofitted buildings, Energy Build. 36 (2002) 567e578. [9] J.K. Kissock, J.M. Hannig, T.I. Whitney, M.L. Drake, Testing and simulation of phase change wallboard for thermal storage in buildings, in: Proceedings of 1998 International Solar Energy Conference (1998), pp. 45e52 New York, USA.
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