*Corr. Author’s Address: PSG College of Technology, Department of Mechanical Engineering, Avinashi road, Coimbatore, India, 1807rm01@psgtech.ac.in 611
Strojniški vestnik - Journal of Mechanical Engineering 67(2021)11, 611-621 Received for review: 2021-08-03
© 2021 Journal of Mechanical Engineering. All rights reserved.  Received revised form: 2021-10-07
DOI:10.5545/sv-jme.2021.7356 Original Scientific Paper Accepted for publication: 2021-11-08
Strojniški vestnik - Journal of Mechanical Engineering 67(2021)11, XXX-4
© 2021 Journal of Mechanical Engineering. All rights reserved.
Original Scientific Paper — DOI: 10.5545/sv-jme.2021.xxxx
Received for review: 2021-08-03
Received revised form: 2021-10-07
Accepted for publication: 2021-11-08
ApplicabilityofMCDMAlgorithmsfortheSelectionofPhase
ChangeMaterialsforThermalEnergyStorageHeatExchangers
PaulGregoryFelix
*
-VelavanRajagopal-KannanKumaresan
PSGCollegeofTechnology,DepartmentofMechanicalEngineering,India
Latentheatthermalenergystorageheatexchangersstoreheatenergybyvirtueofthephasetransitionthatoccursinthethermalstoragemedia. Sincephase
changematerials(PCMs)areutilizedasthemedia,thereisacriticalnecessityfortheappropriateselectionofthePCMutilized. Sincemultiplethermo-physical
propertiesandmultiplePCMsarerequiredtobeevaluatedfortheselection,therearisesaneedformultiplecriteriadecisionmaking(MCDM)algorithmstobe
adoptedfortheselection. Butowingtothedifferentweightestimationtechniquesemployedandthevoluminousquantityofselectionalgorithmsavailable,there
arises a need for a comparative methodology to be adopted. This study was intended to select an optimal PCM for a sustainable steam cooking application
coupled with a thermal energy storage system. In this research study, six PCMs were chosen as the alternatives and five thermo-physical properties were
chosen as the criteria for the evaluation. 11 different algorithms were augmented with 3 different weight estimation techniques and therefore a total of 33
algorithms were employed in this study. All of the algorithms have chosen Erythritol as the optimal PCM for the application. The outcomes of the MCDM
algorithms have been validated through an intricate Pearson’s correlation coefficient study.
Keywords: latent heat, multiple criteria decision making, phase change material, thermal energy storage
Highlights
• A comparative methodology has been proposed to select the optimal PCM for thermal energy storage heat exchangers.
• An optimal PCM for a sustainable steam cooking application has been selected by adopting multiple MCDM algorithms.
• A clear demarcation has been presented between the functionality of all of the algorithm combinations adopted.
• A three case Pearson’s correlation coefficient study has validated the reliability of the ranking outcomes.
0 INTRODUCTION
Phasechangematerials(PCMs)playanimportantrole
in latent heat thermal energy storage (TES) systems.
PCMs act as heat sinks to absorb and store excess
heat energy from then heat source and then release
the stored heat energy as and when required. To
facilitate this process of heat energy storage and
release, TES heat exchangers are employed at the
application site. Several types of heat exchangers
can be adopted for such latent heat systems [1].
On the other hand, the research outcomes based on
renewable sources of energy, more specifically, based
on solar thermal energy has improved over the recent
years, that even steam cooking can be done directly
using steam generated from solar parabolic trough
collectors (PTCs) [2]. But the non-availability of
solar energy throughout the day and night demands
the necessity for a TES system that would store the
excess thermal energy during sunshine hours, and the
stored thermal energy could be retrieved during the
off-sunshine hours. At the application site, steam
generatedfromtheTESheatexchangercanbeutilized
forcookingduringtheoff-sunshinehours,whereasthe
steam generated directly from the solar source (PTCs)
can be utilized for cooking during the sunshine hours.
Taking into consideration the fact that latent heat TES
systems based on PCMs store much more higher heat
than sensible heat systems, it can be asserted that
such TES systems are suitable for this sustainable
steam cooking application. For designing TES heat
exchangersforthisapplication,thefirstimportantstep
hastobetheappropriateselectionofthePCM[3]. This
is because, each PCM has different thermo-physical
propertiesandthechoiceofthePCMexplicitlyaffects
the design. For instance, PCMs having lower latent
heat will increase the size of the heat exchanger.
Hence, the selection of the appropriate PCM suitable
for the application is required to be performed on
scientificevaluationgroundswithmultiplecriteriaand
alternatives(PCMs)considered.
Multiple criteria decision making (MCDM) has
evolved as a mathematical tool to aid designers to
perform subjective evaluations in operation research
[4]. The applications of MCDM algorithms in the
domain of mechanical engineering are multiple. Few
examples include determination of the threshold for
extreme load extrapolation [5], choosing systems for
drying paltry-seeds [6], assessment of energy crops
for producing bio-gas [7], ranking renewable energy
resources [8] and optimal material selection [9].
Concerning PCMs, it has also been observed that
*Corr. Author’s Address: PSG College of Technology, Department of Mechanical Engineering, Avinashi road, Coimbatore, India, 1807rm01@psgtech.ac.in 1

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612 Paul Gregory Felix – Velavan Rajagopal – Kannan Kumaresan
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researchers have applied MCDM algorithms to select
the appropriate PCM for low-temperature applications
[10], ground source heat pump application [11] and
even for domestic water heating [12]. While selecting
a suitable material, it is necessary to estimate strategic
weights for each evaluative criterion such that the
decision becomes subjective. But the choice of
the algorithms applied for a particular case depends
on the decision of the heat exchanger designer. It
has been observed from peer literature that many
research studies have limited their study designs to
a very few algorithms with a limited choice of
weight estimation techniques. Concerning the weight
estimation techniques, it has been learned that using
either only subjective or only objective weighting
scheme in the study can be considered as a deficiency
[11]. Hence, heat exchanger designers are required
to refer to multiple literature sources to understand
the functional mechanism of several algorithms and
will need to perform an intricate study on various
weight estimation and MCDM techniques to arrive at
a conclusion to select which MCDM algorithm would
be appropriate. But, in this study, a methodology
incorporating a comparative study design has been
proposed.
This current study presents a novel comparative
approach than several previous works such that an
intricate comparative selection can be made. This
research study, through its proposed methodology,
asserts that, for a PCM selection involving multiple
alternatives, a comparative study involving multiple
MCDM algorithms can provide a reliable solution to
the selection process. This is asserted because, the
methodology does not rely only on one algorithm,
but instead has adopted multiple combination of
algorithms for the selection. Hence, the PCM selected
through this methodology will be a reliable choice for
the heat exchanger.
1 METHODS
1.1 StudyDesign
This current study was performed in three parts.
The first part of this study was to select the
alternative PCMs and criteria through a pre-screening
and then estimating the desired weights through
entropy weight method (EWM), criteria importance
throughinter-criteriacorrelation(CRITIC)methodand
analytic hierarchy process (AHP) method. The second
part was to apply the derived weights to select the
suitable PCM through 11 selected algorithms. The
third part of the research was to perform a Pearson’s
correlation coefficient study to correlate the outcomes
of various algorithms and validate the concurrence of
the outcomes. The study design adopted is presented
in Fig. 1.
Since steam is required to be generated (from the
heat exchanger) at the application site at a minimum
temperature of 100
◦
C, PCMs were desired to have
a melting temperature around 120
◦
C. Hence from an
initialscreening,sixPCMswereselected. Theselected
PCMs along with their thermo-physical properties
(criteria) are presented in Table 1. In Table 1, it
can be observed that a mix of both laboratory grade
PCMs and commercial PCMs have been considered.
But however, all of the PCMs were selected such that
they share a close melting temperature to 120
◦
C. But,
out of the alternatives, one PCM is required to be
selectedbasedontheotherthermo-physicalproperties.
There has been no specific preference among the
mix of laboratory grade and commercial grade PCMs
in this analysis. The research methodology has
been oriented such that there exists no bias between
selecting laboratory and commercial grade materials
and hence this methodology can be envisaged to
select any kind of PCM that would be technically
appropriate for the particular application in study.
Among the listed criteria, specific heat alone was
categorized as a non-beneficial criterion. This is
because, for the steam cooking application, higher
magnitudes of melting temperature, heat of fusion,
density, thermal conductivity was preferred. Hence,
the aforementioned four parameters were considered
as beneficial criteria. Whereas, for the application,
lower specific heat magnitude is preferred, as a higher
specificheatwillincreasethemeltingtimeofthePCM.
Since this steam cooking application is intended to
be integrated with solar energy, faster melting and
charging of the PCM was preferred as the entire
charging process will have to be completed within
the sunshine hours. Hence specific heat alone was
considered as a non-benefit criterion.
1.2 Estimationofthecriteriaweights
1.2.1 EWM
In this method, the decision matrix X was normalized
using the sum method (Eq. (1)), and the weights w
j
were estimated through calculating the entropy value
E
j
[12], as presented in Eq. (2). The decision matrix
X is an array of the considered m alternatives and n
criteria. In the equation, p
ij
indicates the normalized
value of the decision matrixX.
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613 Applicability of MCDM Algorithms for the Selection of Phase Change Materials for Thermal Energy Storage Heat Exchangers
Strojniški vestnik - Journal of Mechanical Engineering 67(2021)11, XXX-4
Pre-screeningofPCMs
Selectionofcriteriaandalternatives
CRITICmethod EWM AHPmethod
WSM WPM SAW COPRAS ARAS WASPAS MOORA TOPSIS GRA VIKOR PROMETHEE
Comparisonoftheoutcomes
SelectionofthebestPCM
ValidationoftheoutcomesthroughaPearson’scoefficientstudy
Fig. 1. Study design adopted
Table 1. Considered alternatives and criteria
PCM no. Name Melting temperature Heat of fusion Density Thermal conductivity Specific heat Reference
[
◦
C] [kJkg
−1
][ kgm
−3
][ Wm
−1
K
−1
][ kJkg
−1
K
−1
]
1 Erythritol 120 331 1480 0.733 1.35 [14]
2 MgCl
2
.6H
2
O 117.5 200 1569 0.704 2.25 [15]
3 PlusICE A118 118 195 900 0.22 2.2 [16]
4 PlusICE H120 120 120 2220 0.506 1.51 [17]
5 PlusICE S117 117 125 1450 0.7 2.61 [16]
6 PlusICE X120 120 180 1245 0.36 1.5 [17]
p
ij
=
x
ij
n
∑
j=1
x
ij
, (1)
E
j
=−
m
∑
i=1
p
ij
.ln p
ij
ln n
and w
j
=
1−E
j
m
∑
i=1
(1−E
j
)
. (2)
1.2.2 CRITICMethod
In this method, the decision matrix elements x
ij
were
normalized using Eq. (3) and the weights were
estimated using C
j
as presented in Eq. (4) [13]. In
the equation, r
jj
n represents the relative correlation
coefficient between the j
th
and j
n th
criteria and σ
j
represents the standard deviation of the normalized
matrix.
Applicability of MCDM Algorithms for the Selection of Phase Change Materials for Thermal Energy Storage Heat Exchangers 3

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614 Paul Gregory Felix – Velavan Rajagopal – Kannan Kumaresan
Strojniški vestnik - Journal of Mechanical Engineering 67(2021)11, XXX-4
p
ij
=
x
ij
−min
j
(x
ij
)
max
j
(x
ij
)−min
j
(x
ij
)
, (3)
w
j
=
C
j
n
∑
j
n
=1
C
j
=

σ
j
n
∑
j
n
=1
(1−r
jj
n)

n
∑
j
n
=1

σ
j
n
∑
j
n
=1
(1−r
jj
n)
. (4)
1.2.3 AHPmethod
In this method, a relative importance decision matrix
with elements a
jj
n was constructed using the Saaty’s
scale[10]andtheweightswereestimatedbyusingEq.
(5). The relative matrix is a matrix representing the
importance of one criterion over another.
w
j
=
a
jj
n

n
∑
j
n
=1
a
jj
n

n
. (5)
1.3 EstimationoftheOptimalPCM
1.3.1 WeightedSumMethod(WSM)
In this method, the decision matrix was normalized
using the square root method. The alternatives were
ranked based on the weighted sums S
WSM
i
estimated
using Eq. (6).
S
WSM
i
=
n
∑
j=1
w
j
×
x
ij
p
ij
=
n
∑
j=1
w
j
×
x
ij

n
∑
j=1
x
2
ij
. (6)
1.3.2 WeightedProductMethod(WPM)
In this method, the weighted product for each
alternative was estimated by raising the normalized
decision matrix elements to the power of the weights,
aspresentedinEq. (7)andthealternativeswereranked
based onP
WPM
i
.
P
WPM
i
=
n
∏
j=1

x
ij
p
ij

w
j
=
n
∏
j=1

x
ij

∑
n
j=1
x
2
ij

w
j
. (7)
1.3.3 SimpleAdditiveWeighting(SAW)method
This method is similar to WSM, except to the fact
that the normalization of the decisive matrix with
elements x
ij
was performed separately for both the
benefit criteria elements and the non-benefit criterion
elements. The normalization was performed using Eq.
(8). The preference indexV
i
was then estimated using
Eq. (6) and the alternatives were ranked.
p
ij
=

x
ij
max
j
x
ij
, for benefit criteria.
min
j
x
ij
x
ij
, for non-benefit criterion.
(8)
1.3.4 ComplexProportionalAssessment(COPRAS)Method
In this method, the decision matrix was normalized
using the sum method. Then, the maximizing index
S
+i
forthebenefitcriteriawasestimatedasarow-wise
sum of the weighted normalized matrix for the benefit
criteria values, and the minimizing index S
−i
was
estimatedinthesamewayforthenon-benefitcriterion
[18]. Utilizing the estimated values, the relative
weight Q
c,i
was computed using Eq. (9). Then the
performance index U
i
was estimated using Eq. (10)
and the alternatives were then ranked based onU
i
.
Q
c,i
=S
+i
+
min
i
S
−i
m
∑
i=1
S
−i
S
−i
m
∑
i=1
min
i
S
−i
S
−i
, (9)
U
i
=
Q
c,i
Q
c,max
×100. (10)
1.3.5 AdditiveRatioAssessment(ARAS)Method
In this method, for each criterion, the optimal value
was determined based on whether the criterion was
a benefit or a non-benefit attribute and the decision
matrix augmenting the optimal value was then weight
normalized using the sum method. Then, the
optimality function S
i
and the utility degree K
i
was
estimated using Eq. (11) [19]. The alternatives were
then ranked based onK
i
.
K
i
=
S
i
S
opt
=
n
∑
j=1
p
aug
ij
w
j
S
opt
. (11)
1.3.6 Weighted Aggregated Sum Product Assessment
(WASPAS)Method
This method is a combination of WSM and WPM.
In this method, the normalized decision matrix was
estimated by segregating the beneficial criteria and
non-beneficial criterion using the maximum-minimum
method as presented in Eq. (8). Then the total
relative importanceQ
i
was estimated through Eq. (12)
[20]. The alternatives were ranked based on the total
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615 Applicability of MCDM Algorithms for the Selection of Phase Change Materials for Thermal Energy Storage Heat Exchangers
Strojniški vestnik - Journal of Mechanical Engineering 67(2021)11, XXX-4
relative importance. In the equation, λ represents a
transformation constant. In this case, a λ of 0.5 was
adopted.
Q
i
=λ
n
∑
j=1
p
ij
w
j
+(1−λ)
n
∏
j=1
p
w
j
ij
. (12)
1.3.7 Multi-Objective Optimization on the Basis of Ratio
Analysis(MOORA)Method
In this method, the decision matrix was normalized
using the square root method as in WSM and WPM
[21]. Then the normalized assessment sumS
i
for each
alternative was estimated by subtracting the weighted
sum of the non-benefit attributes from the weighted
sum of the benefit attributes, as presented in Eq.
(13). Then the alternatives were ranked based on the
assessment sum.
S
i
=
n
∑
j=1
p
ij
×w
j
  
Weighted sum of
non-benefit attributes
−
n
∑
j=1
p
ij
×w
j
  
Weighted sum of
benefit attributes
. (13)
1.3.8 Technique for Order Preference by Similarity to Ideal
Solution(TOPSIS)
In this method, the decision matrix was normalized
using the square root method as in Eq. (6). Then the
relativeclosenesstotheidealsolutionP
i
wasestimated
by Eq. (14) [12]. In the equation, A
∗
j
represents the
best criterion value of the weighted normalized matrix
(positive ideal) and A
−
j
represents the worst criterion
value (negative ideal). The alternatives were then
ranked based on the relative closeness.
P
i
=

n
∑
j=1
(p
ij
.w
j
−A
−
j
)

n
∑
j=1
(p
ij
.w
j
−A
∗
j
)+

n
∑
j=1
(p
ij
.w
j
−A
−
j
)
. (14)
1.3.9 GreyRelationalAnalysis(GRA)method
In this method, the alternatives were ranked based
on the grey relational degree b
i
[22]. The deviation
Δ
0i
was estimated as a difference between the
referenceseries(largestvalueseries)andtheindividual
alternativeseries[22]. ByestimatingΔ
0i
,thevaluesof
b
i
were calculated as presented in Eq. (15).
b
i
=
n
∑
j=1
w
j
min
i
min
j
Δ
0i
(j)+δmin
i
min
j
Δ
0i
(j)
Δ
0j
(j)+δmin
i
min
j
Δ
0i
(j)
. (15)
1.3.10 VIKORmethod
VIKOR is an abbreviation for its Serbian expansion
‘Vise kriterijumska optimizacija i kompromisno
resenje’ which means Multi-criteria compromise
ranking. In this method, the normalized decision
matrix was obtained using the square root method as
in Eq. (6). From the normalized matrix, the maximum
criterionvalue p
∗
j
andtheminimumcriterionvalue p
−
j
were estimated and were applied to Eqs. (16) to (18)
toestimatetheaggregatefunctionU
V
i
(alsoreferredas
VIKOR index) for each alternative. In the equations,
the superscripts ‘
∗
’ and ‘
−
’ represents the maximum
andminimumvaluerespectively. Thealternativeswere
then ranked in the increasing order ofU
V
i
[23].
U
V
i
=v

S
i
−S
∗
S
−
−S
∗

  
I
+(1−v)

R
i
−R
∗
R
−
−R
∗

  
II
, (16)
I=

n
∑
j=1
w
j

p
∗
j
−p
ij
p
∗
j
−p
−
j

−

n
∑
j=1
w
j

p
∗
j
−p
ij
p
∗
j
−p
−
j

∗

n
∑
j=1
w
j

p
∗
j
−p
ij
p
∗
j
−p
−
j

−
−

n
∑
j=1
w
j

p
∗
j
−p
ij
p
∗
j
−p
−
j

∗
, (17)
II=

max
i
w
j

p
∗
j
−p
ij
p
∗
j
−p
−
j

−

max
i
w
j

p
∗
j
−p
ij
p
∗
j
−p
−
j

∗

max
i
w
j

p
∗
j
−p
ij
p
∗
j
−p
−
j

−
−

max
i
w
j

p
∗
j
−p
ij
p
∗
j
−p
−
j

∗
. (18)
1.3.11 Preference Ranking Organization Method for
EnrichmentValuation(PROMETHEE)
Inthismethod,thedecisionmatrixwasnormalizedand
the overall global preference index P
j
was estimated
by estimating the difference in the values of one
alternative criterion with another (preference matrix).
Using the preference matrix, the positive preference
flow φ
+
(i) and negative preference flow φ
−
(i) (for
non-benefitcriterion)wasestimated. Thenthenetflow
φ(i) was ultimately estimated using Eq. (19) [24].
Thenthealternativeswererankedbasedonthenetflow
(PROMETHEE II).
φ(i)=
1
m−1
∑
x∈X
n
∑
j=1
w
j
P
j
(i,x)
  
φ
+
(i)
−
1
m−1
∑
x∈X
n
∑
j=1
w
j
P
j
(x,i)
  
φ
−
(i)
.
(19)
Applicability of MCDM Algorithms for the Selection of Phase Change Materials for Thermal Energy Storage Heat Exchangers 5

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616 Paul Gregory Felix – Velavan Rajagopal – Kannan Kumaresan
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Table2. Estimated evaluating parameters through the employed algorithms
Algorithm Algorithm Evaluating parameter Phase change material
index name Parameter Symbol 1 2 3 4 5 6
1 WSM-EWM Weighted sum S
WSM
i
0.5064 0.4511 0.2896 0.3581 0.4097 0.3107
2 WSM-CRITIC Weighted sum S
WSM
i
0.4662 0.4413 0.3189 0.3811 0.4166 0.3320
3 WSM-AHP Weighted sum S
WSM
i
0.5350 0.4385 0.3282 0.3284 0.3780 0.3277
4 WPM-EWM Weighted product S
WPM
i
0.4868 0.4489 0.2641 0.3407 0.3910 0.3076
5 WPM-CRITIC Weighted product S
WPM
i
0.4491 0.4394 0.2944 0.3651 0.4027 0.3275
6 WPM-AHP Weighted product S
WPM
i
0.5140 0.4363 0.3037 0.3082 0.3574 0.3240
7 SAW-EWM Preference index V
i
0.9407 0.5017 0.8331 0.8166 0.1956 0.3776
8 SAW-CRITIC Preference index V
i
0.9402 0.6142 0.8684 0.8425 0.1014 0.1942
9 SAW-AHP Preference index V
i
0.9752 0.5584 0.7802 0.8887 0.1086 0.2075
10 COPRAS-EWM Performance index U
i
, % 100 78.6542 49.3705 69.8570 67.6893 61.4469
11 COPRAS-CRITIC Performance index U
i
, % 100 82.0728 58.1734 79.7784 73.2509 70.3310
12 COPRAS-AHP Performance index U
i
, % 100 73.1212 54.0881 59.7485 59.4716 61.2537
13 ARAS-EWM Utility degree K
i
0.9403 0.7420 0.4625 0.6609 0.6408 0.5787
14 ARAS-CRITIC Utility degree K
i
0.9358 0.7710 0.5473 0.7517 0.6908 0.6621
15 ARAS-AHP Utility degree K
i
0.9752 0.7164 0.5273 0.5888 0.5858 0.6
16 WASPAS-EWM Relative importance Q
i
0.9356 0.7423 0.4453 0.6525 0.6339 0.5758
17 WASPAS-CRITIC Relative importance Q
i
0.9350 0.7785 0.5435 0.7523 0.6940 0.6699
18 WASPAS-AHP Relative importance Q
i
0.9728 0.7217 0.5144 0.5891 0.5852 0.6031
19 MOORA-EWM Assessment sum S
i
0.4205 0.3080 0.1497 0.2620 0.2437 0.2153
20 MOORA-CRITIC Assessment sum S
i
0.3750 0.2877 0.1687 0.2779 0.2383 0.2296
21 MOORA-AHP Assessment sum S
i
0.4555 0.3061 0.1986 0.2315 0.2243 0.2393
22 TOPSIS-EWM Relative closeness P
i
0.8452 0.6029 0.2191 0.4195 0.4786 0.3134
23 TOPSIS-CRITIC Relative closeness P
i
0.7929 0.5895 0.2070 0.4866 0.4722 0.3467
24 TOPSIS-AHP Relative closeness P
i
0.9369 0.4902 0.3004 0.2579 0.3232 0.3080
25 GRA-EWM Grey Relational degree b
j
0.1510 0.1024 0.0632 0.099 0.0929 0.0782
26 GRA-CRITIC Grey Relational degree b
j
0.1509 0.0917 0.0648 0.1190 0.0827 0.0989
27 GRA-AHP Grey Relational degree b
j
0.1601 0.0933 0.0666 0.0909 0.0818 0.0843
28 VIKOR-EWM VIKOR index U
V
i
0 0.1744 0.5 0.3973 0.3833 0.3116
29 VIKOR-CRITIC VIKOR index U
V
i
0 0.2273 0.5 0.3362 0.3394 0.2726
30 VIKOR-AHP VIKOR index U
V
i
0 0.2912 0.3043 0.5 0.4870 0.3434
31 PROMETHEE-EWM Net flow φ(i) 0.4902 0.0918 -0.3992 0.0254 -0.0867 -0.1214
32 PROMETHEE-CRITIC Net flow φ(i) 0.4635 -0.0482 -0.3844 0.1832 -0.2380 0.0238
33 PROMETHEE-AHP Net flow φ(i) 0.5879 0.0347 -0.2866 -0.0674 -0.2162 -0.0524
1.4 ValidationoftheOutcomes
Tovalidatethereliabilityoftheoutcomes,acorrelation
of outcomes method adopted by Villacreses et al.
[25] was adopted in this current study. The ranking
outcomes acheived through all of the 33 algorithms
were correlated with each other. Three cases of
correlations were performed and Pearson’s correlation
coefficient was estimated for all of the cases. In
the first case, the outcomes were correlated by
considering all of the PCMs. In the second case,
a rank-wise frequency estimation was performed and
the alternatives witnessing highest first, second and
third rank frequencies alone were considered for the
correlation. In the third case, adopting the similar
procedure, the alternatives witnessing highest first and
secondrankfrequenciesalonewereconsidered. Based
ontheresultsofthethreecases, the concurrenceofthe
outcomes were validated. The Pearson’s coefficients
r
kl
were estimated using Eq. (20). In the validation
process, all 33 algorithms were correlated with each
other and hence a total of 1089 Pearson’s coefficients
were estimated for a single case.
r
kl
=
m
∑
i=1
(k
i
−
¯
k)(l
i
−
¯
l)

m
∑
i=1
(k
i
−
¯
k)
2

m
∑
i=1
(l
i
−
¯
l)
2
. (20)
2 RESULTS AND DISCUSSION
2.1 SelectionoftheOptimalPCMthroughMCDMAlgorithms
In this study, a total of 33 solution combinations
were tested. The weights were obtained, and further
the obtained weights were employed to estimate the
evaluating parameters. The evaluating parameter
for each algorithm was estimated and the alternative
PCMs were ranked based on the magnitude of the
6 Paul Gregory Felix - Velavan Rajagopal - Kannan Kumaresan

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617 Applicability of MCDM Algorithms for the Selection of Phase Change Materials for Thermal Energy Storage Heat Exchangers
Strojniški vestnik - Journal of Mechanical Engineering 67(2021)11, XXX-4
Table 3. Estimatedweightsthroughtheemployedmethods
Criteria EWM CRITIC AHP
Melting temperature 0.0003 0.2030 0.0676
Heat of fusion 0.3077 0.2021 0.4531
Density 0.1778 0.1794 0.0743
Thermal conductivity 0.3615 0.2515 0.2636
Specific heat 0.1528 0.1640 0.1414
evaluating parameters. The estimated evaluating
parameters are presented in Table 2 and the graphical
form of the ranking outcomes is presented in Fig. 2.
The weights obtained for each case is presented in
Table 3. From the table, it can be observed that the
weights obtained through the objective and subjective
methods differ from each other. Since the weights
differ, the functional priority for each criterion is
changed. This will have implications on the outcomes
as well. The objective method EWM has prioritized
thermalconductivityovertheothers,andhasestimated
melting temperature to be the least prioritized criteria.
ButinthecaseoftheCRITICmethod,thoughthermal
conductivity has been prioritized over the others, all
other criteria have been estimated to have similar
weights. Further, observing the weights obtained
through the subjective AHP method, heat of fusion
has been estimated to have the highest priority and
melting temperature has been estimated to have the
least priority. This was expected because EWM and
CRITIC are objective methods, wherein the outcomes
were purely based on mathematical outcomes and
AHP is a subjective approach wherein the outcomes
were based on the preferences from the designer.
Since in the EWM and CRITIC methods, thermal
conductivity has been estimated to have the highest
priority, the outcomes employing those weight will
prefer materials with higher thermal conductivity. On
the contrary, AHP has estimated the highest priority
for latent heat of fusion. Hence the method will prefer
corresponding outcomes. The results are reliable as
thereisacleardemarcationbetweenthesubjectiveand
objective weighting scheme outcomes. But since this
current study is intended to select a PCM through a
comparative approach, this variation will be helpful
to select the optimal PCM from a holistic approach.
The necessity for such a holistic approach arises as
this research study addresses the research gap due to
the deficiency of utilizing limited weight estimation
schemes.
From the figure, it can observed that the first
alternative PCM Erythritol has been ranked as the
best alternative in all of the algorithms. Also, it
can be observed that the PCM MgCl
2
.6H
2
O (MCHH)
has been ranked as the second best PCM in most
algorithms. On a comparative note, it can be further
observed that the solutions derived through applying
EWM weights and CRITIC weights are similar in
most cases. But comparing the efforts required
for each method, it was observed that COPRAS,
GRA, PROMETHEE methods required more level of
mathematicalcomputationsthantheothermethods.
2.2 Pearson’s Coefficient Study
To validate the reliability of the outcomes, a three
case Pearson’s coefficient study was performed. The
results of the study are presented in Fig. 3. In the
first case of the Pearson’s study, it was observed that
most of the correlation coefficients were above 0.5,
but yet there was a significant quantity of coefficients
below 0.5. This indicates that all six ranks of the
33 algorithms did not concur each other. But, the
objective of this study was to select the optimal PCM
for the TES heat exchanger. If one would accentuate
the objective, it is necessary that the first ranked PCM
and the second ranked PCM is similar in most cases.
This approach to study the concurrence of the first
ranked and the second ranked PCM was employed
to validate the reliability of this comparative study
and as it could be noted from Table 3, PCMs were
ranked purely based on their evaluating parameters.
Even when there is a very small difference between
the evaluating parameters, the PCMs will still be
rankedbasedonthe differences. Further, theapproach
does not rely upon a single combinational algorithm,
but depends on the comparative conclusion derived
through employing 33 combinational algorithms. In
thisstudy,allofthealgorithmshadrankedErythritolas
thesuitablePCM,irrespectiveofthetypeofalgorithm
and the weight estimation scheme employed. Further,
most of the algorithms have ranked MCHH as the
secondbestsuitedPCM.Hence,therankingschemeis
reliable. To verify the reliability of the outcomes, two
more cases were performed. A frequency study was
performed to proceed further. A rank wise frequency
was recorded. The rank wise data is presented in Fig.
3. It has been observed that Erythritol was the best
rankedPCM(Rank1)inallofthealgorithms. Further,
MCHH has been estimated as the second best PCM
in 28 of 33 algorithms. Similarly for all other ranks,
the frequencies were recorded. From the frequency
study, it was observed that Erythritol, MCHH, and
PlusICE H120 were the first three prioritized PCMs
frommajorityofthealgorithms. Hence,forthesecond
caseofPearson’sstudy,onlythethreewereconsidered
ApplicabilityofMCDMAlgorithmsfortheSelectionofPhaseChangeMaterialsforThermalEnergyStorageHeatExchangers 7

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)11, 611-621
618 Paul Gregory Felix – Velavan Rajagopal – Kannan Kumaresan
Strojniški vestnik - Journal of Mechanical Engineering 67(2021)11, XXX-4
1 2 3 4 5 6
1
2
3
4
5
6
PCMs
Rank
EWM
CRITIC
AHP
(a)WSM
1 2 3 4 5 6
1
2
3
4
5
6
PCMs
Rank
EWM
CRITIC
AHP
(b) WPM
1 2 3 4 5 6
1
2
3
4
5
6
PCMs
Rank
EWM
CRITIC
AHP
(c)SAW
1 2 3 4 5 6
1
2
3
4
5
6
PCMs
Rank
EWM
CRITIC
AHP
(d) COPRAS
1 2 3 4 5 6
1
2
3
4
5
6
PCMs
Rank
EWM
CRITIC
AHP
(e)ARAS
1 2 3 4 5 6
1
2
3
4
5
6
PCMs
Rank
EWM
CRITIC
AHP
(f) WASPAS
1 2 3 4 5 6
1
2
3
4
5
6
PCMs
Rank
EWM
CRITIC
AHP
(g)MOORA
1 2 3 4 5 6
1
2
3
4
5
6
PCMs
Rank
EWM
CRITIC
AHP
(h) TOPSIS
1 2 3 4 5 6
1
2
3
4
5
6
PCMs
Rank
EWM
CRITIC
AHP
(i) GRA
1 2 3 4 5 6
1
2
3
4
5
6
PCMs
Rank
EWM
CRITIC
AHP
(j) VIKOR
1 2 3 4 5 6
1
2
3
4
5
6
PCMs
Rank
EWM
CRITIC
AHP
(k)PROMETHEE
Fig. 2. Comparisonofthe various ranking outcomes
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Strojniški vestnik - Journal of Mechanical Engineering 67(2021)11, 611-621
619 Applicability of MCDM Algorithms for the Selection of Phase Change Materials for Thermal Energy Storage Heat Exchangers
Strojniški vestnik - Journal of Mechanical Engineering 67(2021)11, XXX-4
Fig. 3. Panels (a)-(c) present the variation of the Pearson’s correlation coefficients for different cases and panels (d)-(i) presents the ranking outcome
frequencies of the PCM alternatives
Applicability of MCDM Algorithms for the Selection of Phase Change Materials for Thermal Energy Storage Heat Exchangers 9

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)11, 611-621
620 Paul Gregory Felix – Velavan Rajagopal – Kannan Kumaresan
Strojniški vestnik - Journal of Mechanical Engineering 67(2021)11, XXX-4
for correlation and for the third case of the Pearson’s
study, only Erythritol and MCHH were considered.
The second case correlations indicates that there is
comparatively stronger correlation than the first case.
Further, the third case indicates that there is very
strong correlation compared to other cases. All of the
thirdcasecorrelationshaverenderedacoefficientof1.
Hence from this three case analysis, the reliability of
theresultshavebeenvalidated.
2.3 DiscussionfromHeatExchangerPerspective
Byapplyingtheaforementionedalgorithms,Erythritol
has been selected as the optimal PCM for the steam
cooking application. If one would intricately observe
the functionality of the various weight estimation
techniques, it can be observed that the objective
techniquesEWMandCRITIChaveprioritizedthermal
conductivity whereas subjective AHP has prioritized
latent heat of fusion. This can be ascribed to the
Saaty’s scale weights provided by the the authors. But
despite this observation, all algorithms have selected
Erythritol. Erythritol has the highest latent heat of
fusion(331kJkg
−1
)amongthealternatives,andhence
less quantity of the PCM is required. Since, less
quantity of PCM is required, the heat exchanger size
will be comparatively smaller than when other PCMs
are used. Further, Erythritol chosen has the highest
thermalconductivityandandhencethemeltingtimeof
the PCM will also be comparatively lower. The lower
specific heat of Erythritol also is an added benefit.
Further, if one would consider the highest density,
PlusICE H120 has the highest density, but since latent
heat and thermal conductivity were prioritized over
density, the algorithms have preferred Erythritol over
PlusICE H120 PCM. Hence, from a heat exchanger
design perspective, it can be inferred that the chosen
PCM can be strongly envisaged to be suitable for the
sustainablesteamcookingapplication.
From this study, a clear demarcation has been
asserted between the functionality of all of the
considered algorithms. From the study, by combining
the weights and the main algorithms, it was observed
that TOPSIS, GRA, VIKOR and PROMETHEE
algorithms have significantly distinguished the
outcomes based on each weight estimation scheme.
Furtherinsteadofrelyingononesinglealgorithm,this
methodhasmadeareliableselectionoutofthevarious
combinational algorithms proposed. Hence, this novel
method integrating MCDM and Pearson’s coefficient
studyishighlyrecommendedforindustrialpractice.
3 CONCLUSIONS
Renewable energy based steam cooking paves the
way for a sustainable steam cooking process when
integrated with PCM based TES heat exchangers.
However the optimal selection of the PCM plays a
crucial role in the heat exchanger design. Hence,
this research work has performed a comparative
study for the selection of the appropriate PCM for
the application. This study has tested 11 MCDM
algorithms with 3 weight estimation techniques and
through all of the algorithms, Erythritol has been
chosen as the appropriate PCM. Erythritol has
satisfactory thermo-physical properties to be used
in the TES heat exchanger for the application.
The ranking outcomes from various algorithms were
validated through a three case Pearson’s correlation
coefficientstudy. ThePearson’scorrelationcoefficient
studyhasvalidatedthatallofthealgorithmshavevery
strong correlation in selecting the first and the second
bestPCMs.
4 ACKNOWLEDGEMENTS
The authors would like to thank the Department of
Science and Technology (DST), Government of India
andPSGCollegeofTechnology,Coimbatore,Indiafor
theirfinancialsupport.
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