effect of multiple phase change materials (pcms) slab configurations on thermal energy storage

Energy Conversion and Management 47 (2006) 2103–2117

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Effect of multiple phase change materials (PCMs) slabconfigurations on thermal energy storage

Shadab Shaikh a,*, Khalid Lafdi a,b

a Department of Mechanical Engineering, University of Dayton, 300 College Park, Dayton, OH 45469, USAb AFRL/MLBC, WPAFB, OH 45433, USA

Received 5 July 2005; accepted 12 December 2005Available online 13 February 2006

Abstract

The present work involves the use of a two dimensional control volume based numerical method to conduct a study of acombined convection–diffusion phase change heat transfer process in varied configurations of composite PCM slabs. Sim-ulations were conducted to investigate the impact of using different configurations of multiple PCM slabs arrangementswith different melting temperatures, thermophysical properties and varied sets of boundary conditions on the total energystored as compared to using a single PCM slab. The degree of enhancement of the energy storage has been shown in termsof the total energy stored rate. The numerical results from the parametric study indicated that the total energy charged ratecan be significantly enhanced by using composite PCMs as compared to the single PCM. This enhancement in the energystorage can be of great importance to improve the thermal performance of latent thermal storage systems.� 2006 Elsevier Ltd. All rights reserved.

Keywords: Phase change material; Energy storage; Melting

1. Introduction

The use of PCMs (phase change material) for thermal energy storage (TES) has gained considerable impor-tance in recent years. Latent heat thermal storage has proved to be an effective means for solar energy utili-zation and industrial waste heat recovery due to its high storage capacity and small temperature variationfrom storage to retrieval. Traditional TES systems commonly use PCMs with a single phase change temper-ature. During the past decade, the use of multiple PCMs for TES systems has acquired great significancebecause of their potential for superior thermal performance.

Farid and Kanzawa [1,2] proposed a heat storage module consisting of a number of cylindrical capsulesfilled with phase change materials with air flowing across them. They observed a significant improvement in

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doi:10.1016/j.enconman.2005.12.012

* Corresponding author. Tel.: +1 937 229 4363; fax: +1 937 229 3433.E-mail address: [email protected] (S. Shaikh).

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Nomenclature

Cp specific heat, J/kg Kf liquid fractionf n liquid fraction previous iterationf n+1 liquid fraction current iterationg acceleration due to gravity, m/s2

K thermal conductivity, W/m KL dimension of side of PCM slab, mQ energy charged, Jt time, stm melting time, sDt time stepT temperature, Ku x component of velocityv y component of velocityDV solid volume, m3

x horizontal coordinatey vertical coordinate

Greek symbols

a thermal diffusivity, m2/sb volumetric thermal expansion coefficient, 1/Kk latent heat of fusion, J/kgl absolute viscosity, kg/msm kinematic viscosity, m2/sq density, kg/m3

s dimensionless, mtL2

Superscript

n nth time step

Subscripts

l liquids solidm meltingM maximumw wall

2104 S. Shaikh, K. Lafdi / Energy Conversion and Management 47 (2006) 2103–2117

the rate of heat transfer during energy charge and discharge when phase change materials with differentmelting temperatures were used. Gong et al. [3] first analyzed cyclic energy storage systems using multiplePCM slabs. They developed a 1-D numerical model and found that the instantaneous heat flux on the heattransfer surface could be enhanced using a composite PCM slab arrangement when energy is charged anddischarged from the same side of the slab. Gong and Mujumdar [4,5] then investigated the charge anddischarge kinetics of TES in composite PCM slabs. Gong and Mujumdar further presented a 1-D finite ele-ment conduction based model to analyze the energy charge and discharge rates using multiple slabs of dif-ferent PCMs. They concluded that the magnitude of enhancement depends upon the arrangement of PCMsand their thermophysical properties. Lim et al. [6] performed a second law analysis for the use of multiplePCMs placed in series and melted by the same stream of hot fluid. They pointed out that the use of multiplePCMs could reduce the exergy loss of the system and derived the optimal condition for a system composed

S. Shaikh, K. Lafdi / Energy Conversion and Management 47 (2006) 2103–2117 2105

of two PCMs. Adebiyi et al. [7] reported that the efficiency of a packed bed TES using five PCMs exceededthat of a unit using a single PCM as much as 13–26%. Watanbe et al. [8] used water as the heat transferfluid in their analysis and found that there was an enhancement of the energy charge–discharge rates in asystem using three PCMs. Gong and Mujumdar [9] proposed a solar receiver store consisting of multiplePCMs and found that the fluctuation of the outlet temperature of the heat transfer fluid can be greatlydamped using multiple PCMs compared with a single PCM. Bellecci and Conti [10–12] set up a numericalmodel to simulate the cyclic thermal process in solar receiver units composed of a single PCM and devel-oped criteria for optimal design of these units. Wang et al. [13,14] presented a theoretical investigation andnumerical analysis for multiple PCM slabs to enhance the charge and discharge rates of the TES systems.They noted that the phase change time of composite PCMs with optimum linear phase change temperaturedistributions can be decreased by as much as 25–40%. Wang et al. [15] further conducted an experimentalstudy of a heat storage capsule employing three different PCMs and showed that the charging rate of thecapsule can be enhanced using multiple PCMs instead of a single PCM. Cui et al. [16] recently proposed anumerical model for a solar receiver thermal storage module using three PCMs. They pointed out that themultiple PCM system can be advantageous to enhance the energy and reduce the fluctuation of the gas exittemperature of the receiver device.

The objective of the present work is to investigate numerically the phase change process of a heat storagesystem using multiple rectangular slabs of different PCMs considering combined convection and diffusion.Numerical experiments are conducted for different configurations of composite slabs arranged in distinct geo-metric patterns. Each of these composite slab PCM systems are simulated to investigate the influence of thesevaried arrangements of PCMs with different melting points, thermophysical properties and different bound-ary conditions on the transient phase change heat transfer process. The numerical computations are used toconduct a comparative study of the above multiple PCM arrangements relative to a single PCM slab. Thesearch of the literature revealed that the work of Gong and Mujumdar [5] is the most related investigationto the present work. There are, however, several new features in the present study. The combination of con-vection phenomena with the diffusion process adds the buoyancy induced motion in the liquid, which plays avery important role in the propagation of the melt interface. In addition to this, different composite slabdesigns are analyzed through this study, and a detailed parametric study is conducted for each design.The aim of the entire analysis is to improve the thermal performance of TES systems by improving theirenergy storage capacity.

2. Mathematical formulation

The physical system consists of a thin square slab of ‘i’ PCMs. The ‘i’ PCMs are arranged in different pat-terns as shown in Fig. 1. The case of composite slabs of PCMs arranged in parallel is shown in Fig. 1a, whileFig. 1b gives the case for a series arrangement and Fig. 1c gives the arrangement of PCMs combined in amatrix form. The multiple PCMs in each case are arranged in two ways based on their melting temperatures.For the parallel and series cases, the PCMs are arranged in increasing or decreasing order of their meltingpoints from top to bottom and from left to right, respectively. For the matrix slab case, one type consistsof PCMs along the left diagonal with higher melting point and the other type with PCMs along the right diag-onal with higher melting point. All these composite slab arrangements shown below, together with a singlePCM slab, are analyzed during the melting process due to an isothermal heat source on the left wall whileall the other three walls are kept insulated.

For a mathematical description of the thermal process, the following assumptions are made:

1. Each PCM is isotropic and homogeneous.2. The thermophysical properties for all PCMs are constant in each phase except its mass density (Boussinesq

approximation).3. Laminar, incompressible and 2-D convection in the melt.4. The thermal resistance at the interface between any two PCMs is neglected.5. The velocities along the X and Y direction at the interface between any two PCMs is neglected to inhibit the

mixing of the melted liquid from the two PCMs due to convection motion.

1

2

.

.

i

1 2 . . i

1 2

2 1

(a) (b)

(c)

wmT wmT

wmT

Fig. 1. Different configurations of composite PCM slabs arrangements. (a) Parallel arrangement, (b) series arrangement, (c) matrixarrangement.


6. Each PCM melts at a well defined phase change temperature. Initially, all the PCMs are at a uniform tem-perature, which is less than their phase change temperatures.

Based on the above assumptions, the governing equations for the heat transfer melting process are asfollows:

Continuity:

ouoxþ ov

oy¼ 0. ð1Þ

Momentum:

X-direction

oðquÞotþ oðquuÞ

oxþ oðquvÞ

oy¼ o

oxl

ouoy

� �þ o

oyl

ouoy

� �� oP

oxþ ASu. ð2Þ

Y-direction

oðqvÞotþ oðquvÞ

oxþ oðqvvÞ

oy¼ o

oxl

ovox

� �þ o

oyl

ovoy

� �� oP

oy� qgbðT � T mÞ þ ASv. ð3Þ

Energy:

oðqT Þotþ oðquT Þ

oxþ oðqvT Þ

oy¼ o

oxKCp

oTox

� �þ o

oyKCp

oToy

� �� q

Cpkofot

. ð4Þ

The condition that all the velocities in the solid regions are zero is provided in the enthalpy-porosityapproach by appropriately defining a parameter AS in the momentum equations [17]. The basic principle isto reduce gradually the velocities from a finite value in the liquid to zero in the solid over the computationalcell that undergoes phase change. This can be achieved by assuming that such cells behave as porous mediawith porosity equal to the liquid fraction. In order to achieve this behavior, an appropriate definition of AS is

AS ¼ �Cð1� f Þ2

f 3 þ b

" #; ð5Þ


where C is a constant for the mushy region morphology and b is a small number to avoid division by zero. Incalculating the source terms of the momentum equations, the values of C and b are taken as 1.6 · 106 kg/m3 sand 10�3, respectively.

3. Numerical method

The governing differential equations are solved using a control volume based finite difference methodemploying a staggered grid. The standard SIMPLE algorithm is used to solve the coupled continuity andmomentum equations. The formulation is fully implicit in time, and the convection–diffusion terms were trea-ted by the hybrid scheme [18]. A line by line solver based on the TDMA (tri-diagonal matrix algorithm) is usedto solve iteratively the algebraic discretized equations. An under relaxation factor of 0.5 is used in solving theu-momentum and v-momentum equations, and a factor of 0.3 is used in solving the pressure correctionequations.

The general form of the discretized equation for any variable / is given by

ap ¼X

n¼W ;E;S;N

an/n þ a0p/

0p þ S; ð6Þ

where S is the source term and

a0p ¼

qDVDt

. ð7Þ

In each iteration, the solid–liquid interface has to be determined. In this work, the solid–liquid interface wasdetermined based on the value of the liquid fraction. The liquid fraction is updated using the equation,

f nþ1 ¼ f n þ apcðT � T mÞ; ð8Þ
where ‘c’ is a constant given by
c ¼ CpDtqkDV

. ð9Þ

Fig. 2. Effect of grid density on liquid formation.


To prevent the liquid fraction having unrealistic values, the liquid fraction values should be restricted to liebetween zero and one.

TableMelt t

Time (

1060120

f n ¼ 1 if f nþ1 > 1;

0 if f nþ1 < 0.

�ð10Þ

The above mentioned numerical method was implemented in a MATLAB program. Before implementing theprogram for the final runs, a number of numerical experiments were conducted for melting of gallium for thegrid sensitivity analysis. The effect of grid density on the rate of liquid formation is shown in Fig. 2. Based onthese results, a 30 · 30 uniform square grid was employed for the final computations. The convergence criteriawas to reduce the maximum mass residual of the grid control volumes below 10�5, and the residuals in all thedependent variables, namely temperature and the velocities to be less than 10�6.

4. Results and discussion

4.1. Validation of numerical method

As a first step, the code was validated by comparing the results for the present numerical method with 1-Danalytical, 2-D numerical and experimental results available in the literature. Table 1 compares the melt thick-ness of gallium in a 1-D conduction melting obtained from the present method with the analytical solution [19]for different grid densities at different times. The numbers in parentheses indicate the percentage error. It isclear from the table that as the mesh size is refined, the numerical results approach the analytical solution.

1hickness in 1-D conduction melting of gallium

min) Grid density

0.1 0.05 0.03 0.01 Analytical

0.0053 (78.6%) 0.011 (55.6%) 0.0181 (27.02%) 0.0241 (2.8%) 0.02480.0364 (40.2%) 0.0575 (5.5%) 0.0591 (2.9%) 0.0607 (0.3%) 0.06090.0745 (13.4%) 0.0827 (3.9%) 0.0843 (2.09%) 0.0860 (0.12%) 0.0861

Fig. 3. Comparison of melt interface with experimental result for melting of gallium.

Fig. 4. Comparison with numerical result for the effect of natural convection on liquid formation for melting of gallium.


Further comparison is made in Fig. 3 where the melt interface location is compared for the convection–diffusion melting of gallium in a rectangular enclosure with top and bottom walls insulated and the otherboundary conditions similar to those employed by Gau and Viskanta [20] in their experimental investigation.The interface is shown for three different times, t = 3,6, and 10 min from the onset of melting.

The last comparison with the literature is given in Fig. 4. In this figure, the percentage of liquid formation iscompared for the melting of gallium with isothermal boundary conditions from four sides as employed byGhasemi and Molki [21]. The rate of liquid formation is shown for two different values of Rayleigh numbers,Ra = 104 and Ra = 106. The good agreement between the results is supportive of the present numerical approach.

4.2. Parametric study

In order to investigate the effects of various parameters on the total energy charged during the convection–diffusion phase change, the various configurations shown in Fig. 1 were simulated. For comparison with thethermal performance of the different composite slabs arrangements, a single PCM slab was simulated.

Initially, all the slabs were assumed to be at a uniform temperature of 303 K. The left side of the slab wassubjected to a constant temperature of Tw, which is above the fusion temperature of the PCMs, while the othersides of the slab were kept insulated. Numerical experiments were conducted for the following four cases:

(a) PCM melting points(b) Thermal conductivity ratio between solid and liquid(c) Boundary wall temperature(d) Latent heat of fusion

4.2.1. PCM melting points

To start the analysis procedure, a single PCM slab was simulated first. The parameters selected for thePCM used for simulation of the single slab are as listed in Table 2. The PCM is chosen such that its thermo-physical properties resemble that of paraffin wax. The simulation process, which involves the transient phase

Table 2Properties of PCM for single slab

Cpl 1000 J/kg K Tm 333 KCps 1000 J/kg K

Kl 0.8 W/mK Tw 363 KKs 0.8 W/mK

ql 775 kg/m3 l 2.65 · 10�3 kg/m sqs 825 kg/m3

k 100,000 J/kg L 0.05 m

Fig. 5. Progress of liquid–solid interface for single PCM slab.


change heat transfer due to combined convection–diffusion, was performed until approximately 85% of thesingle slab was melted. The total phase change time for this melting period was about 1200 s. Fig. 5 showsthe progress of the melt interface after every 200 s for the case of the single PCM slab.

At time t = 200 s, the melt interface is fairly proportionate along its length except for a slight motion at thetop, suggesting the dominance of the conduction mode of heat transfer. As the melting process continues, thefluid near the isothermal surface rises to the top, replacing the colder fluid. As time progresses, this buoyancyinduced motion of the fluid due to the temperature gradient causes the melt volume at the top to move at afaster rate compared to the fluid at the bottom. This is evident from the melt interfaces for time t = 400–1200 s, which are curved due to the effect of the natural convection process, thus augmenting the overall melt-ing process.

Following the computation for the single PCM slab, computations were performed for the differentarrangements of the 2-PCM, 3-PCM and 2-PCM-matrix composite slabs. The boundary wall temperatureTw and the size of the slab, as well as the thermophysical properties, are all the same for the different compositeslab arrangements except for the melting temperatures of the PCMs. The melting temperatures are assigned tothe composite slabs such that their average equals the melting temperature of the single slab. Also, for thecomposite slabs, depending on whether the PCMs are arranged in series or parallel, the length of eachPCM along the partition is L1 = L2 = L/2 for the 2-PCM slab and L1 = L2 = L/3 for the 3-PCM slab. For

Table 3Comparison of energy charged for 2-PCM composite slab

Case Slab type Melting temp. [K] Qt [J] Qt/QM Enhancement compared to single slab [%]

1. Single 333 1.875e+5 0.5859 –

2. Multiple series (2-PCM) L = 338 1.7406e+5 0.5439 0R = 328

3. Multiple series (2-PCM) L = 328 2.1261e+5 0.6644 13.39R = 338

4. Multiple parallel (2-PCM) T = 338 2.0876e+5 0.6524 11.34B = 328








L: Left PCM; R: right PCM; T: top PCM; B: bottom PCM.


the PCM matrix arrangement, the slab was divided into four equal partitions with each PCM occupying 1/4 ofthe total size of the slab. The matrix slab basically consisted of two different PCMs, with the same PCMs(either PCM-1 or PCM-2) arranged along the right and left diagonals as shown in Fig. 1c.

All the composite slabs arrangements were simulated for a melting time of tm = 1200 s to compare theenergy charged with that for the single slab.

From Table 3, it can be seen that different enhancements of the cumulative energy charged were observedfor different configurations of the 2-PCM composite slabs, consisting of different arrangements of PCMs withrespect to their melting points. As noted from Table 3, the highest enhancement in the energy charged for the2-PCM series arrangement is found for case 7 (16.42%). This corresponds to the case of the PCMs arranged inincreasing order of their melting points from left to right, with the PCM with the lowest melting point near theisothermal wall. For the 2-PCM parallel arrangement, the highest enhancement is found for case 8 (15.14%)with the PCMs arranged in increasing order of melting points from the bottom to the top. For both cases 7and 8, the melting temperatures of the PCMs are equally decreased with respect to the boundary walltemperature.

From Table 4, the same observations were obtained as those from Table 3. From the comparison betweenthe composite slab arrangements of 2-PCM and 3-PCM slabs, the important point to be noted is that thecumulative energy charged for both the series and parallel arrangements is greater for the 3-PCM slab as com-pared with the 2-PCM slab. For the 3-PCM slab, enhancements of 21.89% (case 7) and 17.38% (case 8) areobtained for the series and parallel arrangements, respectively.

Figs. 6 and 7 give the movement of the melt interface at every 200 s for the 3-PCM slab series (case 7) andparallel (case 8) arrangements, respectively. From Fig. 6, it can be seen that the melt interface is augmented bythe buoyancy driven natural convection, and the leftmost PCM with the lower melting point melts at a fasterrate as compared to the single PCM slab in Fig. 5 at time t = 200 s. Further, for case 7 in Table 4, which cor-responds to an equal distribution of the melting points of the PCMs with the boundary, it was found that the

Table 4Comparison of energy charged for 3-PCM composite slab


1. Single 333 1.875e+5 0.5859 –

2. Multiple series (3-PCM) L = 343 1.8145e+5 0.5670 0M = 333R = 323

3. Multiple series (3-PCM) L = 323 2.2457e+5 0.7018 19.78M = 333R = 343

4. Multiple parallel (3-PCM) T = 343 2.1899e+5 0.6843 16.80M = 333B = 323










L: Left PCM; M: middle PCM; R: right PCM; T: top PCM; B: bottom PCM.


time lag between the completion of melting of the left PCM slab and the start of melting of the middle PCMslab, and later, the time lag between the completion of melting of the middle PCM slab and the start of meltingof the right PCM slab was an optimum to give the maximum energy charged for case 7 compared to the other3-PCM and 2-PCM series arrangements.

From Fig. 7, it can be seen that the low melting point PCM at the bottom starts melting first, and the effectof buoyancy boosts the melting of the middle PCM, and later, the top PCM. Once again, the arrangement ofPCMs in case 8 of Table 4, which corresponds to an equal distribution of melting temperatures with theboundary, proves to be the best compared to the other 3-PCM and 2-PCM parallel arrangements, thus result-ing in the highest energy charged among all the parallel arrangements. The point worth noting is that by

Fig. 6. Progress of liquid–solid interface for 3-PCM slab series arrangement.

Fig. 7. Progress of liquid–solid interface for 3-PCM slab parallel arrangement.


having the bottom PCM in the parallel arrangement with the lowest melting point compared to the middle andtop PCMs, or in other words by arranging the PCMs in decreasing order of their melting points from top tobottom, the maximum advantage of the buoyancy effect was utilized.

The different enhancements for the energy charged corresponding to the different configurations of the2-PCM matrix slab are given in Table 5. For the matrix slab, the trend observed for energy enhancement wasdifferent than that found with the series and parallel composite slab arrangements. The highest enhancement

Table 5Comparison of energy charged for 2-PCM composite slab matrix


1. Single 333 1.875e+5 0.5859 –

2. Matrix-1 (2-PCM) LD = 338 2.0621e+5 0.6444 9.98RD = 328

3. Matrix-2 (2-PCM) LD = 328 1.9685e+5 0.6152 4.99RD = 338

4. Matrix-1 (2-PCM) LD = 343 1.9362e+5 0.6051 3.26RD = 323

5. Matrix-2 (2-PCM) LD = 323 1.8815e+5 0.5880 0.35RD = 343

6. Matrix-1 (2-PCM) LD = 348 1.8228e+5 0.5696 0RD = 318

7. Matrix-2 (2-PCM) LD = 318 1.7194e+5 0.5373 0RD = 348

LD: Left diagonal; RD: right diagonal.


was obtained for case 2 (9.98%), which corresponds to the arrangement with the minimum difference of meltingpoints between the two PCMs. However, similar to the observation found in the parallel arrangement shown inFig. 7, for case 2 in Table 5, the PCM at the bottom and near the isothermal boundary was the one with lowermelting point. Thus, the maximum effect of buoyancy driven convection was observed in case 2 , causing aug-mentation of the melt interface and resulting in the highest enhancement of energy charged compared to the othermatrix slab arrangements. The movement of the melt interface after every 200 s for the 2-PCM matrix slab cor-responding to case 2 in Table 5 is shown in Fig. 8.

The overall highest enhancement for all the composite slab arrangements as compared to the single slab wasfound for case 7 of Table 4, corresponding to the 3-PCM series slab arrangement. The best configurationamong the series, parallel and matrix slab arrangements, namely case 7 of Table 4, case 8 of Table 4 and case2 of Table 5, respectively, were selected for further parametric study at the next step.

Fig. 8. Progress of liquid–solid interface for 2-PCM slab matrix arrangement.

Table 6Effect of change in thermal conductivity ratio

Case Kl/Ks tm [s] Qt [J] Qt/QM Enhancement [%]

1. Single 1 1200 1.875e+5 0.58593-PCM (series) 2.2855e+5 0.7142 21.893-PCM (parallel) 2.2008e+5 0.6877 17.38Matrix-1 2.0621e+5 0.6444 9.98

2. Single 0.8 1350 1.930e+5 0.60313-PCM (series) 2.3211e+5 0.7253 20.263-PCM (parallel) 2.2609e+5 0.7065 17.14Matrix-1 2.1406e+5 0.6690 10.90





4.2.2. Thermal conductivity ratio

For this study, all the parameters, including the boundary conditions, were kept fixed for the selected com-posite slab arrangements as used before and only the ratio of thermal conductivity Kl/Ks was changed. Table 6gives the comparison of the total energy charged for the three selected composite slab arrangements as com-pared to the single PCM slab. The melting time tm shown corresponds to the 85% melting time of the singleslab for each case in Table 6. The same melting time corresponding to the respective case was used for thethree composite slab arrangements. From Table 6, it can be seen that decreasing the value of Kl/Ks in the range1–0.6, decreases the enhancement in the energy charge rate by a small amount for the 3-PCM series and par-allel cases. A further decrease in the value of Kl/Ks results in a bigger reduction in the percentage enhancement.On the other hand, for the case of the matrix slab, a decrease in the value of Kl/Ks results in an increase in theenhancement of energy charged. For Kl/Ks = 0.2, the enhancement in the energy charged for the matrix slab ishighest, namely 14.74% and more than the enhancements for the series and parallel cases. This difference in theenhancement trend found for the matrix slab can be due to the pattern of arrangement of the PCMs inthe matrix form.

4.2.3. Boundary wall temperature

In this analysis also, all the three selected configurations were analyzed. Again, all the parameters for thethree selected composite slab arrangements were kept fixed except the boundary wall temperature and thePCM melting points. The melting points distribution for the 3-PCM series and parallel configurations wasmade in a similar way as in the cases 7 and 8 of Table 4, respectively. For the matrix slab, the melting pointsdistribution was similar to that of case 2 of Table 5. The details of the boundary temperature and PCM melt-ing points are shown in Table 7, which gives the enhancement of total energy charged. Once again, the melt-ing time tm used for each case corresponds to the 85% melting time of the single slab for the respective case inTable 7. As seen from Table 7, the enhancement of the energy charged for the 3-PCM series and parallelslabs decreases with the increase in the difference of the boundary wall temperature and the PCM meltingtemperatures. This result has a potential for TES applications involving low temperatures. On the otherhand, for the matrix slab, once again, the trend is different with a small increase in the enhancement ofenergy charged.

Table 7Effect of change in isothermal boundary

Case [K] tm [s] Qt [J] Qt/QM Enhancement [%]

1. Single Tw = 333, Tm = 323 3200 1.5817e+5 0.60833-PCM (series) Tw = 333, Tm1 = 318 1.9981e+5 0.7685 26.323-PCM (parallel) Tm2 = 323, Tm3 = 328 1.9092e+5 0.7343 20.69Matrix-1 Tw = 333, Tm1 = 318, Tm2 = 328 1.6936e+5 0.6514 7.08




Table 8Effect of change in latent heat

Case k [J/kg] tm [s] Qt [J] Qt/QM Enhancement [%]

1. Single 100,000 1200 1.875e+5 0.58593-PCM (series) 2.2855e+5 0.7142 21.893-PCM (parallel) 2.2008e+5 0.6877 17.38Matrix-1 2.0621e+5 0.6444 9.98





4.2.4. Latent heat of fusion

For this study, again, all the parameters including the boundary conditions were kept fixed for the selectedcomposite slab arrangements as used before and only the latent heat of the PCMs was changed. Table 7 showsthe comparison of the total energy charged for the three selected composite slab arrangements as compared tothe single PCM slab. The melting time tm shown corresponds to the 85% melting of the single slab for eachcase in Table 8. The same melting time corresponding to the respective case was used for the three compositeslab arrangements. From Table 8, it can be observed that by increasing the latent heat of fusion of the PCMs,the enhancement of the energy charged increases for all three selected composite slabs configurations.

5. Conclusions

A numerical investigation was conducted to study a combined convection–diffusion phase change heattransfer in varied configurations of composite slabs consisting of several PCMs. Simulations were performed


for melting of a single PCM slab and composite PCM slabs arrangements. A detailed parametric study involv-ing the different arrangements of melting temperatures of the PCMs, their thermal properties and differentboundary conditions was conducted for the various arrangements of composite PCM slabs, namely 2-PCMseries and parallel, 3-PCM series and parallel and 2-PCM matrix slab. The effect of this parametric analysison the total energy stored was investigated by comparison with the single PCM slab. It was found from thenumerical experiments that for the same set of thermophysical properties, the total energy charged by themelting of the composite slab arrangements can be significantly enhanced compared to that of a singlePCM slab by using composite PCMs with different melting temperatures. Also, the effects of buoyancy drivennatural convection play a vital role in the amount of enhancement produced by the different composite slabconfigurations. In addition to this, the magnitude of enhancement depends on the different types of compositeslab arrangements itself, their thermophysical properties, like the changes in latent heat and liquid–solidthermal conductivity ratio, and also on the variations in the boundary conditions.

Acknowledgements

The authors are thankful to Dr. A. Elgafy and Dr. O. Mesalhy for their suggestions and excitingdiscussions.

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effect of multiple phase change materials (pcms) slab configurations on thermal energy storage

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