Numerical investigation of PCM melting process in sleeve tube with internal fins

Energy Conversion and Management 110 (2016) 428–435

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Numerical investigation of PCM melting process in sleeve tube with internal fins Peilun Wang a,b, Hua Yao b, Zhipeng Lan b, Zhijian Peng a,⇑, Yun Huang b,⇑, Yulong Ding c a

School of Engineering and Technology, China University of Geosciences, Beijing 100083, China State Key Laboratory of Multiphase Complex Systems, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China c Birmingham Centre for Thermal Energy Storage, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK b

a r t i c l e

i n f o

Article history: Received 5 September 2015 Accepted 16 December 2015 Available online 31 December 2015 Keywords: Fins arrangement Phase change material (PCM) Natural convection Outer tube

a b s t r a c t Due to the poor thermal conductivity of the Phase Change Materials (PCMs), heat transfer performance of Latent Thermal Energy Storage (LTES) systems is usually unsatisfactory. In this work, a detailed numerical study is carried out to analyze the impact of fin geometry (including fin-length, fin-ratio and the angle between neighbor fins) and outer tube conductivity on PCM melting process; the influence of the natural convection in the horizontal sleeve-tube unit within the longitudinal fins is further examined. Results shows that small fin-ratio can reduce melting time, but not remarkably; the angle between neighbor fins has little impact on melting process, however, there is an optimization of the angle between neighbor fins to reduce melting time in the full-scale unit. The outer tube conductivity has great impact on melting process whether considering the natural convection or not. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction Over the last three decades, many studies are carried out on the Thermal Energy Storage (TES) system employed in solar, refrigeration and temperature control system to store the surplus energy when the supply and consumption do not match. Compared with Sensible Thermal Energy Storage (STES), LTES with phase change materials offers a number of advantages such as quasi-isothermal charging/discharging process and high energy density. Thus, the LTES has great potential in the field of solar energy [1,2], building applications [3,4], heat load shifting [5] and electronics cooling components [6,7]. Though LTES unit serves as a better energy storage device, the PCMs loaded in the unit possesses a relatively low thermal conductivity, which limits the heat exchange performance. There are several methods to enhance heat transfer, such as extending surfaces, employing multiple PCMs, increasing thermal conductivity, and using micro-encapsulation of PCM [8]. Due to the simple construction and easy processing, the sleeve-tube LTES unit has drawn great attention in the past decades [9–13]. And extending fin surface is considered as an ideal way to enhance heat transfer, not only in the traditional heat transfer unit [14,15], but also in the LTES unit. ⇑ Corresponding authors. Tel.: +86 15910889256 (Z. Peng), +86 82544814 (Y. Huang). E-mail addresses: [email protected] (Z. Peng), [email protected] (Y. Huang). http://dx.doi.org/10.1016/j.enconman.2015.12.042 0196-8904/Ó 2015 Elsevier Ltd. All rights reserved.

Ismail et al. [16] studied the effects of fin number, length, thickness and the annular aspect ratio on the solidified mass fraction, complete solidification time and the energy storage capacity. They found that the fin thickness has small impact on the solidification, while the fin length as well as the number of fins have strong impact on the solidification. They also pointed out that the fins had undesirable effects on the natural convection during the phase change process. Seeniraj et al. [10] reported that the addition of fins enhanced the energy storage process, and the fin and inner tube material with high thermal conductivity resulted in stronger enhancement in the sleeve-tube LTES unit. Kayansayan and Ali Acar [17] investigated the effect of density and size of fins on the dynamic performance of the sleeve-tube unit and found that there was almost no variation in the storage capacity in laminar flow conditions but a remarkable acceleration on the solidification. Besides, there was a jump in the stored energy when the denser and longer fins were used. Agyenim et al. [18] studied the heat transfer enhancement of circular and longitudinal fins on discharging process of the sleeve-tube LTES unit and found that the longitudinal fins had better performance than circular fins both in charging and discharging process. Ravi et al. [19] studied the heat transfer behavior of PCMs in circular tube within internal longitudinal fins. The fin ratio and thermal conductivity of fin had strong impact on the Nusselt number. Pakrouh et al. [20] optimized the number, height and thickness of the pin fins, which could affect the phase change process. It is founded that the optimal case

P. Wang et al. / Energy Conversion and Management 110 (2016) 428–435

429

Nomenclature Symbols Amush cp g h H k l L P Ra Sh Si Sb t T

mush room constant specific heat, J/(kg K) acceleration of gravity, m/s2 sensible enthalpy, J/(kg K) enthalpy/fin length, J/m conductivity, W/(m k) feature size, m latent heat, J/kg pressure, Pa Rayleigh number hates related source term momentum sink buoyancy source term time, s temperature, K


u W

velocity vector, m/s fin thickness, mm

Greek symbols the angle between neighbor fins b thermal expansion, 1/K/liquid fraction q density, kg/m3 l viscosity, m2/s

a

Subscripts ref reference value ini initial value f HTF value PCM PCM value s/l the physical property of PCM in solid/liquid phase

strongly depended on the fins’ number, height and thickness. Mat et al. [21] studied the impact of fins on the melting process in a triplex-tube unit with PCM. They founded that there were no significant difference among internal fin, external fin and internal–external fin in terms of the heat transfer enhancement, but compared with unit without fins, the complete melting time using internal–external fin was reduced by 43.3%. All above studies about the utilization of fins to enhance heat transfer was in the same length with uniform arrangement in the sleeve-tube LTES unit. Even with nonuniform fins arrangement, only the number of fins in the half bottom was studied [22]. Besides, almost all of the studies about the sleeve-tube LTES unit did not take into account the conductivity of outer tube, which means that the thickness of outer tube had been neglected and treated as adiabatic wall. In this article, the impact of fin arrangement and length-ratio on the melting rate of PCM was studied.

For the phase-change of the PCM, enthalpy-porosity approach is used, by which the porosity in each cell is set equal to its liquid fraction. The continuity equation:

2. Numerical modeling of the two-dimensional melting problem

H ¼ h þ DH Z h ¼ href þ

2.1. Physical model The computational domain of the symmetric model in twodimensional is shown in Fig. 1. The sleeve-tube LTES unit is placed horizontally. The inner radiuses of internal and external tubes are 25 mm and 73.2 mm with the thickness of 2 mm and 3 mm respectively and the thickness of fins is 1 mm. As shown in Fig. 1 (b) and (c), the fins scale has the relationship of H1 + H3 = 2H2 = 69.3 mm and H2 = H3 = 46.2 mm for the four half-scale fins and the three full-scale fins respectively. Due to the symmetry of the sleeve-tube unit, only half of the unit is calculated. The grid figure is shown in Fig. 2 and the grid number of no fin, four half-scale fins and three full-scale fins units are 4732, 4731 and 4764 respectively. The material properties of the tube and fins are shown in Table 1 and the thermophysical properties of PCMs are shown in Table 2. 2.2. Simulation model A computational domain, based on the axial symmetry of the physical model, is defined, as shown in Fig. 2. The melting/solidification model is adopted to simulate the melting process of the PCMs considering natural convection in the fined sleeve-tube unit.

@q ! þ r  ðq u Þ ¼ 0 @t

ð1Þ

The momentum equation: @ðquÞ þ @t @ðqv Þ þ @t

rðq! u uÞ ¼ rðlr  uÞ  @P þ Sx @x

rðq! u v Þ ¼ rðlr  v Þ  @P þ Sy þ Sb @y

ð2Þ

The energy equation:


 @ ! ðqHÞ þ r  q u H ¼ r  ðkrTÞ þ Sh @t

ð3Þ

The enthalpy of the material is computed as the sum of the sensible enthalpy, h, and the latent heat, DH:

ð4Þ T

cp dT

ð5Þ

T ref

8 T > Tl > T > T s > : 0 T < Ts

ð6Þ

where href, Tref, cp, L and h are reference enthalpy, reference temper! ature, specific heat, latent heat and sensitive heat of the PCM, and u is the fluid velocity, b is the liquid fraction defined as b ¼ 0 if T < T s , b ¼ 1, if T > T l , and b ¼ ðT  T s Þ=ðT l  T s Þ; a, l and q are thermal conductivity, viscosity and density of PCM respectively; ! Sh ¼ @ðq@tDHÞ þ rðq u DHÞ is a phase related source term, Sb ¼ qgbðh  href Þ=cp is buoyance source term; Sx, and Sy, are momentum sink in the form of Si ¼ Amush ui ð1  bÞ2 =ðb3 þ eÞ, with Amush = 105 in this study. The small constant e < 0.0001 is to prevent division by zero. The CFD software FLUENT was used to solve and calculate the governing equations. The power law differencing scheme and the SIMPLE method for pressure–velocity coupling are used to solve the momentum and energy equations. Also the PRESTO scheme is adopted for the pressure correction equation [23]. After a careful examination of the preliminary calculations, the time step was set as small as 0.05 s. The convergence criterion was 105 for velocity

430

P. Wang et al. / Energy Conversion and Management 110 (2016) 428–435

Fig. 1. Schematic of the sleeve-tube LTES units (a) no fin; (b) four half-scale fins; (c) three full-scale fins.

Fig. 2. Grid figure ((a) no fin; (b) four half-scale fins; (c) three full-scale fins).

Table 1 Material properties of tube and fins. Property

Aluminum (outer tube)

Copper (inner tube and fins)

Density, p (kg/m3) Thermal conductivity, k (W/(m K)) Specific heat, Cp (J/(kg K))

2719 202.4 871

8978 387.6 381

The interface between PCM and inner tube is coupled – wall boundary condition for heat transfer: T f ;wall ¼ T PCM ð7Þ     @T f @T f  @T PCM @T PCM  þy þy kf x ¼ kPCM x ð8Þ @x @y pxffiffiffiffiffiffiffiffiffi @x @x pxffiffiffiffiffiffiffiffiffi 2 þy2 ¼27 mm 2 þy2 ¼27 mm

A constant temperature of the heating wall is prescribed as:

T ¼ Tjpxffiffiffiffiffiffiffiffiffi 2 þy2 ¼25

Table 2 Thermophysical properties of PCMs. Property

Value

Phase change temperature, Ts/Tl (K) Heat of fusion, L (kJ/(kg K)) Specific heat of PCM, cp (kJ/(kg K)) Thermal conductivity of PCM, k (W/(m K)) Density of PCM, p (kg/m3) Thermal expansion, b (1/K)

393/394 339.8 2.3 0.326 1350 0.001

and continuity components and 109 for energy equation respectively.

mm

¼ 413:15 K

ð9Þ

The condition of outer surface of the external tube is insulated boundary conditions as:

  @T @T  x þy @x @y pxffiffiffiffiffiffiffiffiffi 2 þy2 ¼76:2

¼0

ð10Þ

mm

The center line of the sleeve-tube unit is symmetric boundary condition which is used in fins, PCM and inner and outer tubes:

@T @T ! u ¼ 0; x þy ¼0 @x @y

ð11Þ

2.3. Boundary and initial conditions

In the simulation, the initial temperature of the whole system is 383.15 K, i.e. the PCM is slightly subcooled. In the computational domain:

In the present simulations, the melting process of the sleeve-tube with inter fins heating from inner tube are presented.

! T ini ¼ 383:15 K; uini ¼ 0

ð12Þ

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P. Wang et al. / Energy Conversion and Management 110 (2016) 428–435

3. Verification and grid independence study

1.0

4. Result and discussion The solid PCM was initially subcooled at 383.15 K and the temperature difference between inner tube-wall and melting

(a)

1.0

Liquid fraction

0.8

0.6 T=333K:5 fins[24]

0.4

T=333K:1 fins[24] T=333K:no fins[24] T=333K:5 fins(simulation)

0.2

T=333K:1 fins(simulation) T=333K:no fins(simulation)

0.0 0

2000

4000

6000

8000

10000

12000

0.8

Liquid fraction

The present numerical code has been validated by many simulation scenarios [24,25]. As shown in Fig 3, two works depict the reasonable agreement between the experiment and numerical simulations. Thus, the present method is validated to simulate the latent thermal storage unit. The power law differencing scheme and the SIMPLE method for pressure–velocity coupling are used to solve the momentum and energy equations and the PRESTO scheme is adopted for the pressure correction equation. The relaxation factors for the momentum, pressure correction, energy, body forces and liquid fraction are 0.7, 0.3, 1, 1 and 0.9, respectively. The grid size independence study has been performed. Five sizes of grids were compared with fine structured mesh near the outer surface of inner tube to resolve the thermal boundary layer, ranging as 0.7 mm, 0.8 mm, 1 mm, 1.2 mm and 1.4 mm, with the total number of grids 7132, 6292, 5452, 4732 and 3892. As seen from Fig. 4, the differences of the simulation results in liquid fraction for five different grid sizes are almost coincident with each other as the number of grids from 3892 to 7132. In presented study, the grid size of 1.2 mm, which can be regarded as grid independent, was chosen for further numerical investigation.

0.6

0.4

grid size=0.7 grid size=0.8 grid size=1 grid size=1.2 grid size=1.4

0.2

0.0

0

50

100

150

200

250

Time (min) Fig. 4. Grid size independence.

temperature of PCM was 30 °C. To reduce computational cost, only a half of intersecting surface of the sleeve-tube was calculated.

4.1. Effect of adding fins on melting process Fig. 5 compares the liquid fraction of PCM as a function of time in the LTES units with no fin and 4 half-scale fins. It shows that adding the fins have a remarkable effect on heat transfer enhancement in the melting process, which was also given in Ref. [18] that the utilization of fins has great impact on the reducing phase change process, especially for the longitudinal finned unit. As shown in Fig. 6 that the melted region is near the wall of inner tube and fins in the early time, but the melted region expands outward as time goes on, and more PCM melt in the 4 half-scale fins unit than no fins unit due to the heat transfer enhancement. As seen in Fig. 6, there appear vortices in both LTES units at 2000 s. Because of more melted PCM in the 4 fins unit, the natural convection is more intensified than that in no fin unit. The PCM in the upper region has been melted completely at 10,000 s. The temperature gradient near the phase change interface is large at that moment, but the melting speed slows down as time going by because the heat conduction to dominate the heat transfer has instead of natural convection. The inflection point, of the four half-scale fins LTES unit in Fig. 5, represents the point when the total melting speed slows down as the upper region is almost melted completely. However, there is no inflection point with no fins. This is because the melting speed of the no fins unit in up region is slower than that

Time (s) 1.0

(b)

1.0 0.8

0.6

y/H

2 min(simulation) 5 min(simulation) 8 min(simulation) 14 min(simulation) 2 min[25] 5 min[25] 8 min[25] 14 min[25]

0.4

0.2

0.2

0.4

0.6

0.8

1.0

x/W Fig. 3. Comparison of the numerical predictions with experimental results.

Liquid fraction

0.8

0.0 0.0

no fins 4 fins inflection point

0.6

0.4

0.2

0.0

0

50

100

150

Time (min) Fig. 5. Liquid fraction of PCM.

200

250

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P. Wang et al. / Energy Conversion and Management 110 (2016) 428–435

Fig. 6. Contours of liquid fraction and temperature gradient for no fins and 4 fins sleeve-tube LTES unit.

of the 4-fins unit as shown in Fig. 6, resulting in the liquid fraction curve of no fins unit is more smooth than that of the 4-fins unit. 4.2. Effect of fin-ratio on melting process As discussed in Section 4.1, the reason of the slowing down of melting speed is that the conduction starts to dominate the heat transfer instead of the natural convection. Therefore, in order to increase melting speed of PCM, it is reasonable to prolong the fins length in the bottom to increase heat transfer area. In this section, a fins-ratio is defined as n = H1/H3 while the total length of fins H = H1 + H3 fixed (except for n = 0). Five cases of n which are 1, 0.705, 0.486, 0.316, 0.182 and 0, were studied to find its impact on the melting process. Fig. 7 shows that the complete melting time increases monotonically with n. Decrease n represents the increasement of H3 which increases surface area and enhances heat transfer at the bottom of LTES unit. The complete melting time is reduced 23 min as n decreases from 1 to 0.182. There is a sudden increasement when the value of n increases from 0 to 0.182 and this is due to the n value increasing heat transfer area (H = H3 when n = 0 which results in the decrease of the total length of fins).

Table 3 Conditions of three LTES unit groups. Fins number

Fin length (mm)

Outer tube conductivity

a

Group 1

3

46.2

No

Group 2

3

46.2

Yes

Group 3

4

34.65

Yes

30°, 60°, 90°, 120° 30°, 60°, 90°, 120° 30°, 45°, 60°, 90°

4.3. Effect of outer tube on melting with full-scale-fins at different a values In this section, three groups of LTES unit are studied numerically, as in Table 3: The three groups LTES unit have the same total fins length (L = single fin length  fin number) which 34.65  4 = 46.2  3 mm. Fig. 8 presents the time evolution of the liquid fraction of group 1 and 2 (3 full-scale fins unit). As shown in Fig. 8, the melting rate of PCM is higher in the 3 full-scale fins unit than 4 half-scale fins unit. When the fins connect with the outer tube, the heat can

0.8

240

Liquid fraction

Complete melting time (min)

1.0

230

220

0.6

o

α = 30

0.4

o

α = 45

o

α = 60

0.2

210

o

α = 90

o

α = 120

0.0 200 0.0

0.2

0.4

0.6

0.8

1.0

0

50

100

150

200

250

Time (min)

Fins-ratio Fig. 7. Melting time at different fin ratios.

Fig. 8. The time evolution of liquid fraction of group 1 and 2 (the open and solid interior represent the LTES units of group 1 and 2 respectively).

P. Wang et al. / Energy Conversion and Management 110 (2016) 428–435

433

Fig. 9. Cloud picture of the melting process of group 1 (left) and 3 (right) with 2 full-scale-fins.

transfer from the fins to the outer tube through conduction, which drives the outer tube temperature higher than the phase change temperature in the early melting period. Thus, as shown in Fig. 9, the PCM near the outer tube melts in the early time. Fig. 9 presents the time evolution of the PCM melting process of group 1 and 2 and the left hand side of the liquid fraction contours is group 1 (neglecting the conductivity of the outer tube) and the right hand side is group 3 (considering the conductivity of the outer tube). As shown in Fig. 9, the PCM between the fins melts completely at 7500 s when a equals to 60°, but the PCM at upper side does not melt completely when a equals to 90° at that moment in grope 2 in the right hand side. That is to say, the best value of a is between

60° and 90° to enhance heat transfer, when the conductivity of outer tube is considered. As seen in Fig. 10, the melting ratio is also affected by a values when the fins connect with the outer tube and the best a value is 60° both for group 1 and 2. However, as shown in Fig. 10 of group 1 (4 half-scale fins), there is no noticeable change in the completely melting time even the conductivity of outer tube is considered, which means the a value almost has no impact on the melting process. It takes less time for group 1 to melt completely than group 3, even if all of them have the same total fins length. That is to say, long fins are far more efficient in enhancing heat transfer than several short fins.

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P. Wang et al. / Energy Conversion and Management 110 (2016) 428–435

80

Group 1 Group 2 Group 3 HTE

240

60

180 40 120 20 60

Heat transfer enhancement/%

Comleted melting time (min)

300

0

0 20

40

60

80

100

120

Degree (o) Fig. 10. Completed melting time for three group 1, 2 and 3 and heat transfer enhancement between group 1 and 2.

As shown in Fig. 10, the HTE values varies with a values, which means the heat transfer enhancement of outer tube is different for different angle between neighbor fins. The highest HTE values equal to 39.9% at a = 90° for the four a values in group 1 and 2. However, HTE value equals to 49.9% for group 1 at a = 120° comparing with group 2 at a = 60°. So, the conductivity of out tube and a values has great impact on melting process in the sleevetube unit. Fig. 11 shows the change trend of the liquid fraction at different fins thickness in the full-scale sleeve unit. Four kinds of thickness, which are 1 mm, 1.5 mm, 2 mm and 2.5 mm, are studied to find the impact of fins on PCM melting process. As shown in Fig. 11, the melting speed increases with fins thickness, but an increase in fin thickness has only a slight improvement in the melting process even considering the conductivity of the out tube but more effective than the result form Ref. [26]. As discussed in Ref. [26], the liquid fraction curve of different fins thickness almost coincide with each other and there was also no effect of fins thickness on the melting process.

1.0

4.4. Effect of a value on melting process without taking account of gravity

Liquid fraction

0.8

0.8

Fig. 12 shows the trend of liquid fraction for different a with 3 full-scale fins in LTES unit. As shown in Fig. 12, the melting speed increases with a and a = 120° is the best fins arrangement when the natural convection is not considered. However, it is opposite when the natural convection is considered. As shown in Fig. 8, when the natural convection is considered, a = 120° is the worst value whether considering the heat conductivity of outer tube or not. In general, PCM takes much more time to melt when the natural convection is neglected. This is because that the key to accelerate melting process is to modify the melting process in bottom part of the sleeve tube unit when the natural convection is being considered. It is also shown in Fig. 12 that the outer tube conductivity has much more impact when the natural convection is neglected through comparing the curves of a = 120° and a = 120° (adiabatic). The melting time would increase to 1200 min when the heat conduction through the tube wall is neglected. So, the conductivity of outer tube has a great impact on the melting process of the 3 full-scale fins LTES unit, even if the natural convection is neglected.

0.6

5. Conclusions

0.6

0.4 W=1.0 mm W=1.5 mm W=2.0 mm W=2.5 mm

0.2

0.0 0

50

100

150

200

250

Time (min) Fig. 11. The liquid fraction at different fin thickness in the full-scale sleeve-tube unit with a = 120°.

Liquid fraction

1.0

α =30o

0.4

α =60o α =90o

0.2

α =120o α =120o (adiabatic)

0.0 0

200

400

600

800

1000

1200

Time (min) Fig. 12. The liquid fraction with 3 full-scale fins when natural convection neglected.

The heat transfer enhancement (HTE) between group 1 and 2 is calculated as:

HTE ¼

The melting process of PCM in sleeve-tube unit was numerically investigated in this study. The effects of the fin-ratio, fins included angle and outer tube conductivity on PCM melting process were studied numerically with 2D assumption. The numerical model was investigated by the published data, and the experimental and numerical results showed a good agreement, which indicates the proposed numerical model procedures are acceptable and the following conclusions can be drawn: (1) The heat transfer can be enhanced by adding half-scale fins in the sleeve-tube LTES unit and the fin-ratio has effect to shorten melting time of PCM, but the effect of reducing fin-ratio to speed melting process is not remarkable.

completely melting time of group 1  completely melting time of group 2  100% completely melting time of group 1

P. Wang et al. / Energy Conversion and Management 110 (2016) 428–435

(2) Considering the combined effects of the conductivity of the outer tube and the angle between neighboring fins on melting process, the melting time of PCM can be reduced by 49.1% and the optimal a value is between 60° and 90° for the three full-scale fins units; the fin thickness has little impact on melting process in the full-scale fins unit with a = 120°. (3) The natural convection has great effect on melting process. The most effective angle between neighboring fins is 60–90° when natural convection is considered. Besides, the outer tube conductivity has much more impact on the melting process. In the designing of sleeve-tube LTES unit, the outer tube should be made of high conductivity material when the fins connect with the outer tube. Acknowledgments The authors gratefully acknowledge financial supports from the China 973 Research Program (2015CB251301), the National Natural Science Foundation of China (61274015), Beijing Natural Science Foundation, China (3151001), and Jiangsu Research and Development Project, China (BE2015199). References [1] Aghbalou F, Badia F, Illa J. Exergetic optimization of solar collector and thermal energy storage system. Int J Heat Mass Transf 2006;49:1255–63. [2] Koca A, Oztop HF, Koyun T, Varol Y. Energy and exergy analysis of a latent heat storage system with phase change material for a solar collector. Renewable Energy 2008;33:567–74. [3] Ahmad M, Bontemps A, Sallée H, Quenard D. Thermal testing and numerical simulation of a prototype cell using light wallboards coupling vacuum isolation panels and phase change material. Energy Build 2006;38:673–81. [4] Gómez MA, Álvarez Feijoo MA, Comesaña R, Eguía P, Míguez JL, Porteiro J. CFD Simulation of a concrete cubicle to analyze the thermal effect of phase change materials in buildings. Energies 2012;5:2093–111. [5] Agyenim F, Hewitt N. The development of a finned phase change material (PCM) storage system to take advantage of off-peak electricity tariff for improvement in cost of heat pump operation. Energy Build 2010;42:1552–60. [6] Wang X-Q, Mujumdar AS, Yap C. Effect of orientation for phase change material (PCM)-based heat sinks for transient thermal management of electric components. Int Commun Heat Mass Transfer 2007;34:801–8. [7] Farid MM et al. A review on phase change energy storage: materials and applications. Energy Convers Manage 2004;45:1597–615.

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