Analytical optimization of interior PCM for energy storage in a lightweight passive solar room

Applied Energy 86 (2009) 2013–2018

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Analytical optimization of interior PCM for energy storage in a lightweight passive solar room Wei Xiao, Xin Wang *, Yinping Zhang Department of Building Science, School of Architecture, Tsinghua University, Beijing 100084, PR China

a r t i c l e

i n f o

Article history: Received 25 July 2008 Received in revised form 27 November 2008 Accepted 9 December 2008 Available online 31 January 2009 Keywords: Energy storage Analytical Optimization PCM Lightweight envelope Passive solar room

a b s t r a c t Lightweight envelopes are widely used in modern buildings but they lack sufficient thermal capacity for passive solar utilization. An attractive solution to increase the building thermal capacity is to incorporate phase change material (PCM) into the building envelope. In this paper, a simplified theoretical model is established to optimize an interior PCM for energy storage in a lightweight passive solar room. Analytical equations are presented to calculate the optimal phase change temperature and the total amount of latent heat capacity and to estimate the benefit of the interior PCM for energy storage. Further, as an example, the analytical optimization is applied to the interior PCM panels in a direct-gain room with realistic outdoor climatic conditions of Beijing. The analytical results agree well with the numerical results. The analytical results show that: (1) the optimal phase change temperature depends on the average indoor air temperature and the radiation absorbed by the PCM panels; (2) the interior PCM has little effect on average indoor air temperature; and (3) the amplitude of the indoor air temperature fluctuation depends on the product of surface heat transfer coefficient hin and area A of the PCM panels in a lightweight passive solar room. Ó 2008 Elsevier Ltd. All rights reserved.

1. Introduction Solar energy has an enormous potential for space heating of buildings in winter. However, solar radiation is a time-dependent energy source with an intermittent and variable character with the peak solar radiation occurring near noon. Thermal energy storage can provide a reservoir of storage to adapt the fluctuation of solar energy [1]. For a direct-gain house with lightweight envelope, solar utilization is difficult due to the small building thermal capacity. A solution to increase the thermal capacity is to incorporate phase change material into the lightweight envelope, which is of large energy storage density and nearly isothermal nature during the phase change process compared with the sensible heat storage. For a passive solar house design, the solar energy can be stored in the PCM panels which undergo phase change process from solid to liquid during daytime and are later released passively to the room air when the PCM changes from liquid to solid. This mechanism can not only utilize variable solar energy efficiently, but can also lower the indoor air temperature fluctuation [2,3]. Over the past decade, many researchers have investigated the thermal performance of PCM wall (or floor and ceiling) by experiments and simulations for energy-saving in passive solar buildings and money-saving in off-peak heating buildings. Athienitis * Corresponding author. Tel.: +86 10 62796113; fax: +86 10 62773461. E-mail address: [email protected] (X. Wang). 0306-2619/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2008.12.011

performed an experimental investigation of gypsum board impregnated with a phase change material in a direct-gain outdoor testroom. The results showed that the utilization of PCM-gypsum board in a passive solar building may reduce the maximum room temperature by about 4 °C during the daytime and can reduce the heating load at night [4]. Ahmad et al.’s study also showed that the impact of PCM was remarkable with a reduction of the indoor air temperature amplitude of approximately 20 °C in the lightweight test-cell [5]. Stovall and Tomlinson analyzed the PCM wallboard for load management and to enhance comfort. Their results showed that the wallboard was ineffective in modifying the comfort level but did provide significant load management relief [6]. Using TRNSYS, Ibanez et al. [7] evaluated the influences of walls/ ceiling/floor with PCM in the whole energy balance of a building. Most of the PCM composites are prepared by immersion of wallboard or by direct incorporation at the mixing stage of wallboard production. However, as Schossig et al. [8] pointed out, leakage may be a problem over a period of many years for this method. Micro-encapsulation makes it possible to integrate PCM into conventional building materials. The micro-encapsulated PCM material has the advantages of easy application, good heat transfer and no need for protection against destruction. In recent years, a kind of novel PCM, the shape-stabilized PCM (SSPCM), has been researched as energy storage components in buildings. The enthalpy model was widely used to optimize SSPCM, because it is simpler in phase change calculation as it takes enthalpy as the only variable

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Nomenclature Ai Ao ACH cp EPCM G hin H Hm k L P PCM m Qr Qcov Qr,in

area of interior PCM panel (m2) total area of exterior envelops (m2) air change per hour (h1) specific heat (J kg1 °C1) total amount of latent heat capacity (kJ) ventilation flow rate (m3 s1) heat transfer coefficient of interior surface (W m2 °C1) enthalpy (kJ kg1) heat of fusion (kJ kg1) thermal conductivity (W m1 °C1) thickness (mm) periods (s) phase change material mass (kg) transmitted solar radiation on the interior surfaces (W) convection heat transfer rate from the indoor heat sources (W) radiation heat transfer rate from indoor heat sources (W)

instead of temperature and specific heat capacity [9–12]. All of these studies show a lot of potential for building envelope containing PCMs. For the optimization of PCM panels utilization in buildings, a few of empirical guidelines are available. Drake found the optimal phase change temperature of PCM wallboard to be proportional to the absorbed solar energy [13]. Peippo et al.’s analysis of a PCM wall in a passive solar house indicated that the optimal diurnal heat storage occurred with a phase change temperature 1–3 °C above the average room temperature based on the simulation results [14]. Zhang and Xu studied the thermal performance of SSPCM floor used in passive solar buildings and found that the suitable phase change temperature was roughly equal to the average indoor air temperature of sunny winter days [15,16]. However, these aforementioned optimization was made for a given building and given weather conditions. Few analytical studies of the building with PCM panels have been conducted. Neeper conducted an analytical study of the interior PCM wallboard through a simplified model and concluded the maximum diurnal energy storage occurred when the PCM phase change temperature equaled the average room temperature [17]. However, his work did not consider the radiation absorbed by the PCM wallboard and lacked the analytical method to get the average room temperature and to estimate the benefit of the PCM panels. The aim of this paper is to present an analytical methodology to optimize an interior PCM for energy storage in a lightweight passive solar room. Firstly, an idealized model of an interior PCM panel which is subjected to a periodic boundary condition is put forward to obtain a general rule for the optimal phase change temperature. And the optimum is defined as the heat balance between the energy stored and released in a cycle. Next, a simplified model is established to theoretically optimize an interior PCM for energy storage in a lightweight passive solar room. Analytical equations are presented to calculate the optimal phase change temperature and total amount of latent heat capacity and to estimate the benefit of the interior PCM for energy storage. From the analytical equations, it is easy to understand the key influence factors of interior PCM for energy storage, and to calculate the optimal phase change temperature and total amount of latent heat capacity in a lightweight passive solar room. Finally, the analytical methodology is applied to optimize the interior PCM for energy storage in a direct-gain room with realistic outdoor climatic condition of Bei-

Ta T a DTa To T o

DTo U V

indoor air temperature (°C) average indoor air temperature (°C) amplitude of indoor air temperature fluctuation (°C) outdoor air temperature(°C) average outdoor air temperature (°C) amplitude of outdoor air temperature fluctuation (°C) overall heat transfer coefficient (W m2 °C1) volume of the room (m3)

Greek letters density (kg m3) time (s)

q s

Subscripts i serial number of interior PCM panels in indoor o outdoor r radiation

jing. The analytical optimization agrees well with the conclusions from detailed simulations based on a verified numerical enthalpy model. 2. Analytical optimization principle A schematic of a direct-gain passive solar room is shown in Fig. 1. The PCM panels attached to the interior surfaces (partition walls, floor and ceiling) serve as the transmitted solar energy and internal heat gains storage panels. The PCM absorbs energy at daytime while PCM changes from solid to liquid, and releases the energy and freezes back to solid when the room temperature falls in the evening. In order to simplify the analysis, an idealized lightweight passive solar room with interior PCM for energy storage subjected to a periodical climatic condition and indoor heat sources is considered here. The following assumptions are made: (1) the sensible thermal capacity of lightweight envelope is neglected; (2) a single coefficient, hin, represents the combined radiative and convective heat transfer between wall surfaces and surroundings; (3) the idealized PCM panels have sufficient latent heat capacity at a single phase change temperature, Tm; (4) as the thermal resistance (1/ hin) at the surface is large enough compared to the internal thermal conduction resistance of thin PCM panel, the internal temperature distribution is assumed uniform; (5) the PCM panel surface away from the room is assumed to be insulated, approximately be the case of interior building envelope [17].

b

a

PCM

A

window

Fig. 1. Schematic of the direct-gain passive solar room: (a) location of room A in the building; (b) profile of room A with PCM panels.

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2.1. Optimization of phase change temperature

For a periodically climatic condition, the outdoor air temperature can be written as

One of the most important parameters for the operation of a PCM panel is the phase change temperature. If the phase change temperature is too high, the amount of energy stored by the PCM will be too low in the daytime; if the phase change temperature is too low, it will be difficult to maintain the indoor air temperature at a comfortable level during the night. According to the aforementioned assumptions, the energy conservation equation for a single PCM panel is written as

mi

dHi ¼ hin  Ai  ðT a  T m;i Þ þ Q r;i þ Q r;in;i ds

ð1Þ

where the subindex ‘‘i” refers to a PCM panel with the index ‘‘i”. With a periodic climatic condition and indoor heat sources, the PCM panels store and release energy periodically. For an optimal phase change temperature, the energy stored and released by the PCM panel should be equal in a cycle. The enthalpy of the PCM panel does not change after a cycle. After integration on both sides of the Eq. (1), the optimal phase change temperature can be obtained

T m;i

¼ T a þ

R P

ðQ r;i þ Q r;in;i Þds hin  P  Ai

ð2Þ

Eq. (2) indicates that the optimal phase change temperature relates not only to the average room temperature but also to the absorbed radiation. If the absorbed radiation is zero, the optimal phase temperature equals the average room temperature. This is consistent with Neeper’s conclusion [17]. 2.2. Estimation of average indoor air temperature Average indoor air temperature is necessary to calculate the optimal phase change temperature according to Eq. (2). Assume the transmitted solar radiation through the window and the radiation from the indoor heat sources are distributed uniformly over the interior surfaces. The optimal phase change temperature for all the PCM panels can be written as the same equation

T m ¼ T a þ

R P

ðQ r þ Q r;in Þds hin  P  A

P

ð3Þ P

P

where Q r ¼ i Q r;i ; Q r;in ¼ i Q r;in;i ; A ¼ i Ai . For a lightweight exterior envelopes, the thermal capacity is neglected. The heat balance equation of indoor air is

Q cov þ U  Ao  ðT o  T a Þ þ hin  A  ðT m  T a Þ þ G  qair  cP;a  ðT o  T a Þ ¼ qair  cP;a  V a 

dT a ds

ð4Þ

where U denotes mean heat transfer coefficient of exterior envelopes, including exterior walls, windows, and so on. Substituting Eq. (3) into (4) and after some rearrangements, Eq. (5) is as follows:

dT a þ BT a ¼ C ds

ð5Þ

where

UAo þ Gqair cP;a þ hin A B¼ qair cP;a V a ðUAo þ Gqair cP;a ÞT o þ hin AT a þ qc þ 1P CðsÞ ¼ qair cP;a V a Z

CðsÞeBs ds þ C 0 

where C0 is an integration constant.

ð7Þ

where w = 2p/P. Substituting Eq. (7) into (6), the indoor air temperature can be written as

UAo þ Gqair cP;a T a ¼ T o þ T q þ qair cP;a V a R

where T q ¼

P

Z

f ðwsÞ  eBs ds þ C 0 eBs

ð8Þ

ðQ r þQ r;in þQ cov Þds

ðUAo þGqair cP;a ÞP

.

After a sufficient long time, the solution approaches a periodic function as

UAo þ Gqair cP;a T a ¼ T o þ T q þ qair cP;a V a

Z

f ðwsÞ  eBs ds

ð9Þ

For the right part of the equation, the first term is the average outdoor air temperature and the second term is the steady-state indoor air temperature rise due to the transmitted solar energy and indoor heat sources. From Eq. (9), the average indoor air temperature is as follows:

T a ¼ T o þ T q

ð10Þ

Eq. (10) indicates that the interior latent heat storage does not change the average indoor air temperature for given U and G. For a given lightweight room and given boundary conditions, the optimal phase change temperature of the interior PCM panels can be derived from Eqs. (3) and (10). 2.3. Estimation of indoor air temperature fluctuation The outdoor air temperature can be expressed by Fourier series as the sum of sinusoidal components of periods 24, 12, 8 h and so on. Only the fundamental component of 24 h is considered as follows:

T o ¼ T o þ DT 0 sinðws þ bÞ

ð11Þ

After integrating, the indoor air temperature Eq. (9) can be written as

T a ¼ T o þ T q þ

ðUAo þ Gqair cP;a Þ  DT o pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sinðws þ b  uÞ qair cP;a V a B2 þ w2

ð12Þ

w ffi and cos u ¼ where the phase shift u ¼ arctan wB, with sin u ¼ pffiffiffiffiffiffiffiffiffiffi B2 þw2 B pffiffiffiffiffiffiffiffiffiffi ffi. 2 B þw2

For a 24-h cycle, w = 2.2722  105 radians s1. Numerical calculation shows that, normally w  B. For example, B = 3.4963  103 s1 for the model room described in Section 3.1 is much less than above w. So the phase shift approximately equals zero. Substituting the expression of B into (12) and after some rearrangements, we have

ðUAo þ Gqair cP;a Þ  DT o ffi T a ¼ T o þ T q þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðUAo þ Gqair cP;a þ hin AÞ2 þ ðqair cP;a V a wÞ2 R P

 sinðws þ bÞ

ðQ r þ Q r;in Þds

The general solution of the differential Eq. (5) is

T a ¼ eBs ½

T o ¼ T o þ f ðwsÞ

ð6Þ

ð13Þ

The last term is the periodic fluctuating component, whose amplitude DTa depends on the amplitude of the outdoor air temperature fluctuation DTo and the product of the surface heat transfer coefficient hin and area A of PCM panels. The amplitude of indoor air temperature fluctuation decreases with increasing hinA, and approaches zero as hinA of PCM panels approaches to infinity.

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2.4. Optimization of the total amount of latent heat capacity

Erelease

According to the aforementioned assumption of sufficient latent heat capacity, the PCM panels can absorb all of radiation energy and can always absorb energy when the room temperature exceeds Tm. Part or all of the stored energy may be withdrawn from the PCM panels during an interval when Ta is less than Tm. The energy stored in a cycle is

ðT a  T m Þþ ds þ

P

Z

ðQ r þ Q r;in Þds T a > T m

Erelease ¼ hin A

Z

ðQ r þ Q r;in Þds

ð20Þ

P

ð14Þ

P

3. Application of the analytical optimization

ðT m  T a Þþ ds T m > T a

ð15Þ

P

For the optimal phase change temperature as shown in Eq. (3), the enthalpy of the PCM panels does not change after a cycle, so the energy stored and released in a cycle should be equal. The optimal amount of latent heat capacity to perform the cycle can be written as

EPCM ¼ Estorage ¼ Erelease

ð16Þ

For sinusoidal outdoor air temperature, the indoor air temperature can be derived from Eq. (13). Fig. 2 shows a schematic diagram of sinusoidal indoor air temperature based on Eq. (13). According to Eq. (16), the optimal amount of latent heat capacity can be derived by calculating any one of the two expressions, Estorage and Erelease. Here Erelease is chosen to be studied in detail. Contributions to the integral (15) occur between the times s1 and s2, indicated by the shaded region in Fig. 2. The times s1 and s2 are given by

(

If X < 1.0, the optimal phase change temperature is above the maximum indoor air temperature. The optimal amount of latent heat capacity of PCM panels to perform the cycle can be easily derived as

Erelease ¼

The energy released in a cycle is

Z

ð19Þ

T a þ DT a  sinðp  ws1  bÞ ¼ T m

ð17Þ

ðws1 þ bÞ þ ðws2 þ bÞ ¼ 3p

Substituting Eqs. (3) and (13) into (17), s1 and s2 can be solved as

8 p  arcsin X  b > > < s1 ¼ w > > s ¼ 2p þ arcsin X  b : 2 R w

ð18Þ

ðQ r þQ r;in Þds

where X ¼ Ph APDT a . If X < 1.0, the optimal phase change in temperature is within the indoor air temperature range. After integration, Eq. (15) becomes

3.1. Description of the lightweight passive solar room as an example A typical lightweight south-facing middle room in a multi-layer building in Beijing, China, is considered in a typical day of January. This room has only one exterior wall-the south wall, and the others are all interior envelope (room A shown in Fig. 1). The dimension of the room is taken as 4.0 m(length)  5.0 m(width)  2.8 m(height). The south wall is made of 60-mm-thick expanded polystyrene (EPS) board. There is a 7 m2 double-glazed window in the south wall, whose average transmittance is 0.58. PCM panels are attached to the surfaces of interior walls, floor and ceiling. The ACH is assumed to be 0.5 h1. The total indoor heat generation rate by the equipment, light and occupants etc. is assumed to be 76 W. Approximately 30% of the internal heat is absorbed by the building envelope through radiation [18]. Table 1 lists the main parameters of the room studied. The Chinese typical day weather [19] of January in Beijing is chosen as the outdoor climate data. The hourly variation of outdoor air temperature and solar radiation on the south wall is shown in Fig. 3. The average outdoor air temperature is 2.9 °C. The amount of solar radiation on a vertical south-facing surface is about 12.07 MJ/m2.

Table 1 Main parameters of the lightweight south-facing room. U-value for south wall (W m2 °C1)

South wall area (m2)

U-value for windows (W m2 °C1)

Southfacing glazing (m2)

Ventilation flow rate (m3 s1)

0.54

7.0

2.68

7.0

7.78  103

10

1000

Tm

o

outdoor temperature ( C)

o

temperature ( C)

Beijing Typical day weather of January

ΔTa

Ta

900 800

5

outdoor temperature solar radiation

700 600 500

0

400 300 -5 200 100 0

-10

τ1

time (s)

τ2

Fig. 2. Schematic diagram of sinusoidal cycle of room temperature with relation to optimal phase change temperature.

0

4

8

12

16

solar radiation on the south wall (Wm-2)

Estorage ¼ hin A

Z

pffiffiffiffiffiffiffiffiffiffiffiffiffiffi   Z 1 arcsin X 2 1  X 2  hin A  DT a ¼ Þ  ðQ r þ Q r;in ds þ þ 2 p w P

20

time (hour) Fig. 3. Hourly variation of outdoor air temperature and solar radiation on the south wall.

W. Xiao et al. / Applied Energy 86 (2009) 2013–2018

(20). The thickness of the panel is assumed to be 20 mm. The optimal heat fusion of the PCM panels based on the given parameters (q = 900 kg m3) is about 35 kJ kg1.

o

indoor temperature ( C)

28 -1 o

o

26

T m=18 C

24

T m=20 C

-1

k=0.2W m C -1 Hm=100kJ kg

o

2017

o

T m=22 C

22

3.3. Comparison between the analytical and simulated optimization

20 18 16 14 12 0

4

8

12

16

20

time (hour) Fig. 4. Simulated hourly indoor air temperature versus phase change temperature.

3.2. Analytical optimization process and results For periodical outdoor conditions, the average indoor air temperature of the room can be expressed as Eq. (10). According to the parameters of Table 1, the average indoor air temperature is 17.2 °C. The transmitted solar radiation through the window and the radiation heat from the indoor heat sources are assumed to be distributed over the room interior surfaces uniformly. The optimal phase change temperature of the PCM panels can be expressed as Eq. (3). Using a value of 2.7 W m2 °C1 for the surface heat transfer coefficient hin [6], the optimal phase change temperature is 19.9 °C, which is about 2.7 °C above the average indoor air temperature. In order to estimate the indoor air temperature fluctuation by Eq. (13), the outdoor air temperature is expressed by Fourier series as the sum of sinusoidal components. Only the fundamental component of 24 h is considered here.

T o ¼ 2:9 þ 3:48 sinðws þ 3:68Þ

ð21Þ

Substituting Eq. (21) into (13), the indoor air temperature depending on time is obtained.

T a ¼ 17:2 þ 0:47 sinðws þ 3:68Þ

ð22Þ

Because the optimal phase change temperature is above the maximum indoor air temperature, the optimal amount of latent heat capacity of about 630 kJ m2 can be easily calculated by Eq.

A verified enthalpy model extended from floor to walls and ceiling is applied to simulate the lightweight south-facing middle room mentioned in Section 3.1. The model was validated with the experimental data in a cabin in Beijing without an auxiliary heating supply [9]. In numerical simulations the properties of hypothetical PCM panels based on SSPCM wallboard are set as q = 900 kg m3, cP = 1.05 kJ kg1 °C1, and k = 0.2 W m1 °C1 [10]. The temperature range of phase change transition zone is assumed to be 0.5 °C. In total amount of latent heat capacity analysis, only the heat of fusion is changed while the thickness is kept constant of 20 mm. In principle, the equivalent heat of fusion could be changed when PCM is dispersed in building construction. These property values of PCM panel used in the simulation are not intended to represent a particular material. Fig. 4 shows the simulated results for typical day weather of January in Beijing. The average indoor air temperatures for different phase change temperatures are equal, which are the same as the analytical result 17.2 °C from Eq. (10) that is somewhat low for comfort. The optimal value of Tm is about 20.0 °C, which keeps higher minimum night temperature and better reduces indoor air temperature swing than other phase change points. The optimal phase change temperature from simulation is approximately equal to the analytical result from Eq. (3), which is 19.9 °C. The amplitude of indoor air temperature fluctuation from the analytical method is 0.47 °C, which is much less than the simulation result 0.76 °C due to the realistic outdoor air temperature, thermal resistance of PCM panels, and phase transition temperature range. But the curvilinear trends of the indoor air temperatures are similar to each other. Both the indoor air temperature fluctuations are very small. Fig. 5 shows the simulated hourly indoor air temperature with different heat of fusion and the average temperature is somewhat low for comfort. It indicates that when the heat of fusion is higher than 30 kJ kg1, the minimum indoor air temperature at night is almost not affected, while the indoor air temperature has no sharp increase at daytime. The optimal heat fusion of PCM panels based on simulation is about 14% smaller than the analytical result 35 kJ kg1 because the sensible heat capacity of the room is neglected in the analytical optimization.

4. Conclusions o

Hm=20

Tm=20 C

Hm=30

L

=20mm

PCM

Hm=40 Hm=50

o

indoor temperature ( C)

20

18

Hm=100

16

14 0

4

8

12

16

20

time (hour) Fig. 5. Simulated hourly indoor air temperature for various heat fusion of PCM (Hm, kJ kg1).

In this paper an analytical approach is put forward to optimize the phase change temperature and the total amount of interior latent heat capacity in a lightweight passive solar room. The optimization is applied to a typical passive solar room in Beijing with interior PCM panels as energy storage components. The analytical average indoor air temperature, optimal phase change temperature, and the amount of interior latent heat capacity agree well with the simulated results, and the modeling program was validated with experimental data. The following conclusions can be made from the analytical study: (1) the equation of the optimal phase change temperature of interior PCM in a lightweight passive solar room is obtained. The optimal phase change temperature depends on the average indoor air temperature and increases with the increase of the radiation absorbed by the PCM panels; (2) the equation of the average indoor air temperature of the lightweight room is obtained. From the equation we can see that interior PCM for energy storage has little effect on average indoor air

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temperature; (3) the equation of the amplitude of the indoor air temperature fluctuation is obtained. The amplitude decreases with the increase of the product of surface heat transfer coefficient hin and surface area A of the PCM panels. This is because the large surface area increases the heat charge/discharge rate of PCM panels. The presented analysis is expected to be helpful for the design and application of interior PCM for energy storage in passive solar buildings. Acknowledgements This work was supported by the National 11th Five-Year Plan of Dept. of Science, China (Nos. 2006BAA04B02, 2006BAJ02A09). References [1] Zalba B, Marin JM, Cabeza LF, Mehling H. Review on thermal energy storage with phase change: materials, heat transfer analysis and applications. Appl Therm Eng 2003;23(3):251–83. [2] Khudhair MA, Farid MM. A review on energy conservation in building applications with thermal storage by latent heat using phase change materials. Energ Convers Manage 2004;45:263–75. [3] Zhang YP, Zhou GB, Lin KP, Zhang QL, Di HF. Application of latent heat thermal energy storage in buildings: state-of-the-art and outlook. Build Environ 2007;42(6):2197–209. [4] Athienitis AK, Liu C, Hawes D, Banu D, Feldman D. Investigation of the thermal performance of a passive solar test-room with wall latent heat storage. Build Environ 1997;32(5):405–10. [5] Ahmad M, Bontemps A, Sallee 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(6):673–81.

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