Results in Engineering 16 (2022) 100627
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Results in Engineering
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A novel experimental case study on optimization of Peltier air cooler using
Taguchi method
Zuhair R. Abdulghani
Department of Mechanical Engineering Technology, Yanbu Industrial College, Yanbu Al-Sinaiyah City, 41912, Saudi Arabia
A R T I C L E I N F O
A B S T R A C T
Keywords:
Cost rate
Thermoelectric
Peltier
Optimization
Taguchi
Nowadays, the commercial application of Thermoelectric Peltier cooler has widely increased including portable
air/water refrigerator, electronic cooling process, thermal management systems in medical science, water
distillation process and so on. Many studies have proved that the thermal/exergetic/economic performance of
Peltier cooler significantly depends on fluid flow conditions on both sides of the module, input power and
number of Peltier modules. Hence, in this research, attempts are made to provide an experimental-based opti­
mization process for Peltier air cooler using well-known Taguchi method. Thermal fluid conditions, input power
and number of modules (in the same total input power) are varied to optimize the cooler from COP (coefficient of
performance), exergetic efficiency and cost per unit of cooling viewpoints. Number of modules are changed from
1 to 2, 3 and then 4 modules. The air flow rate and input power are varied between 30 and 78 m3/h and 22–60 W
respectively for each tested mode. The results indicate that, the greater number of modules provides higher COP
(in the same total input power). Optimum number of modules minimizes the cost per unit of cooling of the Peltier
cooler. Increment of air flow on the cold side, increases and then decreases the COP of the cooler which is
meaningful. Number of modules was found as the most effective factor while input power and thermal fluid
conditions are as the second and the third effective parameters. Interestingly, Taguchi method can identify the
impact level of each factor (number of modules, input power and air flow) on desired parameters (COP, cooling
cost and exergy efficiency) as reported and discussed in this paper.
1. Introduction
Thermoelectric Peltier cooler application is increased day by day
including medical science [1], air cooler [2,3], portable refrigeration
systems [4], water cooling process [5], electronic cooling [6] and so on.
Portable picnic and automobile Peltier based refrigerators are now
widespread available in the market [7]. Optimum working condition
from all thermal, economic and exergetic aspects is crucial in such ap­
plications in which low power consumption means longer availability of
the battery power.
Many parameters such as capital cost of the thermoelectric materials
(ceramic, n-type and p-type electrode), maintenance cost, power cost,
exergy cost and operation costs are effective factors in economic
consideration of thermoelectric cooler. That is why different techniques
such as Exergy Economic Approach, Thermo-economic Functional
Analysis, Specific Exergy Cost and so on have been presented by the
experts for economic analysis of engineering systems. According to the
attitude of the current study, the recent progress on optimization process
of thermoelectric coolers and thermoelectric generator are summarized
in the following.
Yin and He [8] worked on optimization of thermoelectric cooler with
temperature dependent materials using analytical method. They indi­
cated that the multi-parameter optimization can enhance the efficiency
of the cooler by 30%. Lundgarad and Sigmund [9] designed a Peltier
cooler using topology optimization by Numerical simulation. Lamba
et al. [10] worked on efficiency optimization of a Peltier cooler from leg
geometry viewpoint meaning trapezoidal leg shape. They employed
genetic algorithm as their methodology. Provensi et al. [11] studied a
counter current flow multi-stage thermoelectric air cooler and tried to
determine the optimum number of modules as a function of thermal
load. They concluded that the optimum number of modules is enhanced
with cooling capacity. Gong et al. [12] numerically optimized a compact
Peltier cooler from current, leg geometry and contact layers viewpoints.
Based on their findings, smaller leg has stronger cooling efficiency while
larger cross section results in higher operation reliability. Cai et al. [13]
numerically optimized a Peltier cooling system as a CPU cooling device.
Duan et al. [14] and Tian et al. [15] worked on material optimization of
thermoelectric cooler for building cooling application. They showed that
if the figure of merit is optimized to 3, the COP of the Peltier air cooler is
E-mail address: abdulghaniz@rcyci.edu.sa.
https://doi.org/10.1016/j.rineng.2022.100627
Received 10 July 2022; Received in revised form 14 August 2022; Accepted 1 September 2022
Available online 6 September 2022
2590-1230/© 2022 The Author. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Z.R. Abdulghani
Results in Engineering 16 (2022) 100627
optimizations have been performed for cooling application of thermo­
electric module. Particularly, the mentioned optimization should be
carried out from all economic, thermal and exergetic viewpoints
simultaneously. The impact level (intensity of being effective either
positive or negative) of input power, number of modules and fluid flow
conditions (most important parameters for Peltier module as an air
cooler) on COP, cooling cost and exergetic efficiency have not been
investigated yet. Hence, in this research, attempts are made to provide
an experimental-based optimization process for Peltier air cooler using
well-known Taguchi method which is able to clarify the contribution of
each parameter (impact level) in addition to their optimum value (both
quantitative and qualitative). To reach the aim of this research, thermal
fluid conditions, input power and number of modules (in the same total
input power) are varied to optimize the cooler from COP (coefficient of
performance), exergetic efficiency and cost per unit of cooling
viewpoints.
Nomenclature
Ċ
COP
e
E
k
ṁ
n
P
Q
R
S/N
T
V
y
Z
Ż
ε
U
w
Cost rate ($/s)
Coefficient of performance
Mass-related specific exergy (J/kg)
Exergy, (W)
Thermal conductivity, (Wm− 1 K− 1 )
Mass flow rate (kg/s)
Number of tests
Power, (W)
Heating/cooling capacity, (W)
Electrical resistance, (Ω)
Signal to noise ratio
Temperature, (K)
Electrical voltage, (V)
Response factor
Capital investment cost ($)
Capital investment cost rate ($/s)
Effectiveness
Uncertainty
Power or work, W
2. Problem definition and process strategy
Thermoelectric cooler is recently used in commercial scale for
different purposes such as portable refrigerators, water cooling process,
local air-cooling process and so on. Previous studies indicate that the
main characteristics of thermoelectric cooling i.e., COP, exergetic effi­
ciency and cost of cooling significantly depend on thermal fluid condi­
tions on both sides of the module, input power into the thermoelectric
and number of employed Peltier modules for a given input power. Not
only the impact of these parameters can be positive or negative, their
level of impact (percentage of contribution) is different from each other.
Hence, decision making process requires an optimization process to
identify their impacts in terms of both quantitative and qualitative as­
pects. Hence, in this research, Taguchi optimization method is employed
to address the mentioned problem for a thermoelectric air-cooling unit
in which the water fluid passes through the hot side while the air fluid
passes through the cold side. The required information was gathered
through a set of experiments as are described step by step in the
following.
increased to 1.42–7.44. Moria et al. [16] experimentally investigated the
exergoeconomic characteristics of a Peltier air cooler. They found out
that, a greater number of modules can provide higher COP. However,
capital cost and other economic factors limits the number of modules.
Higher input power reduces the COP while its effect on cooling cost
depends on the electricity price of the region. Pohls and Mozharivskyj
[17]
tried
to
optimize
thermoelectric
material
using
scattering-dependent model. Miao et al. [18] optimized a thermoelectric
generator for an industrial application. They concluded that the mini­
mum cost of power generation process by TEG in industrial scale is 1.76
$/W. Demeke et al. [19] utilized genetic optimization technique to
optimize the segmented thermoelectric power generator to find an
efficient design for thermoelectric generator. In another investigation,
Ge et al. [20] tried to optimize the thermoelectric generator with vari­
able cross-section leg from geometric viewpoint for solar energy appli­
cation using finite element method. According to their results, internal
resistance of optimized TEG is more than that of common rectangular
TEG. Chen et al. [21] compared a segmented thermoelectric generator
with convectional structure of TEG using a mathematical model to find
the optimized converting angle. Zaher et al. [22] performed an opti­
mization study for annular thermoelectric generator applicable for heat
recovery process. Yan et al. [23] tried to determine the most efficient
channel cross-section shape applicable in thermoelectric power gener­
ators mounted on hot/cold surface. Based on their results, rectangular
cross-section can provide the highest output power and thermal effi­
ciency. Tian et al. [24] proposed annular segmented thermoelectric
generator and tried to identify the impact of all geometric characteristic
on thermoelectric generator performance. Cao et al. [25] proposed a
thin film solar thermoelectric generator. They found out that the effect
of leg thickness in this specific application is much more important than
the effect of leg length and other geometric aspects. Co-axial ring-shape
leg was introduced by Tian et al. [26] and Li et al. [27] and investigated
from economic, mechanical and energetic aspects. Kishore et la [28].
optimized the segmented thermoelectric generator using Taguchi
method. The impact of all design parameters such as height of seg­
mentation, hot/cold side temperature and load resistance were investi­
gated. They believe that limited required number of experiments (25
tests rather than 3125 test-run) is a potential feature of Taguchi
technique.
Based on literature review, extremely few experimental-based
3. Taguchi optimization process (step-by-step)
Taguchi method [29,30] is one of the popular and practical optimi­
zation tools to determine the optimum working conditions through a
limited number of experiments. Taguchi method not only reduces the
effects of uncontrollable factors but also decreases the required time and
costs associated with the optimization process. Taguchi technique can
identify the impact of any effective parameters while the rest of the
parameters are constant. This process is repeated for all desired pa­
rameters. To consider the impact of all parameters, a matrix of all pa­
rameters with enough number of variations in appropriate range is
required. The range and number of required testes are not arbitrary and
should be selected based on specific criterion behind this strategy. The
required steps to optimize a system via this technique is briefly sum­
marized in the following.
3.1. Identification of the objectives
Step 1. is identification of the objective. The objective of the current
optimization process is finding the optimum values of design and
working conditions of a given Peltier air cooler, the impact level of the
effective parameter (positive or negative) and their percentage
contribution.
3.2. To identify the desired characteristics and their evaluation
Step 2. is identification of the desired characteristics of the system.
Desired important characteristics of any thermoelectric air cooler are
2
Z.R. Abdulghani
Results in Engineering 16 (2022) 100627
mainly coefficient of performance (COP) which is indicator of thermal
behavior of the cooler, cost per unit of cooling ($/kWh of cooling) which
is an indicator of economic aspect of the cooler and exergetic efficiency
which is the performance of the cooler from the Second Law of Ther­
modynamic viewpoint.
Table 2
Taguchi L16 OA array.
Experiment No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
3.3. Selection of variable factors and their level
Step 3. is Selection of variable factors and their level. For a thermo­
electric air cooler, the main effective variable parameters are air flow
rate, total input power into the system and number of Peltier modules. It
is noted that, for a given total input power, different number of jointed
thermoelectric modules will result in different thermal, exergetic and
economic characteristics [31–33]. More number of modules increases
the COP. However, there will be a critical number after which the
cooling cost may increase. The selected various factors in this research
are “number of modules”, “input power” and “air flow rate”; and each
factor is considered through four levels as provided in Table 1.
Step 4. is selection of an orthogonal array which is an important step
in Taguchi method. In this research there are three factors (number of
modules, air flow rate and input power) and each of them has four levels.
Hence, based on the strategy of the Taguchi system, an orthogonal array
of L16 is used as shown in Table 2. It should be noted that, the
arrangement of the matrix is not arbitrary and should be based on the
theory behind the Taguchi method to appropriately consider the impacts
of all factors on desired parameters [31] (Minitab software was
employed for this aim). As can be seen in Tables 2, 16 set of experiments
are required. The values of COP, Exergy efficiency and cost per unit of
cooling should be evaluated for each tested condition using the data
extracted from the experiments.
In order to perform the required experiments shown in Table 2, the
following test rig was designed (see Fig. 1). Generally, four thermo­
electric modules are placed in the line and 1, 2, 3 or all of them are
connected into the input electrical power based on Table 5. Popular fin
pin heat-sink is attached to the cold/hot side (air/water fluid). Water
passes through the hot side as a common temperature adjustment
technique for hot side. Air flow was adjusted and recorded using a
professional digital air flow meter (SMC PFMB7501-04-F). Elaborate
tiny grooves are created on the heat-sinks to measure the thermoelectric
surface temperatures (required in evaluation of COP) using thin wire Ktype thermocouples. Inlet/outlet/surface temperatures are recorded by
12-channel BTM-4208SD data logger. Popular TEC1-12706 commercial
thermoelectric is used in this study. As described above, COP, exergetic
efficiency and cost per unit of cooling are the derided factors. All these
factors are evaluated using measured experimental data for each row
shown in Table 2. The evaluation process of COP and exergetic effi­
ciency are graphically illustrated in Fig. 2.
Uncertainty analysis is carried out using the same technique
described by Moffat [34]. In this method, the uncertainty value of any
parameter is evaluated using the uncertainty value of its independent
effective parameters. For example, the uncertainty of coefficient of
performance (COP) depends on the uncertainty of cooling capacity and
uncertainty of input power because COP = QP. Hence, its uncertainty can
be calculated by Eq. (7) in which UCOP in uncertainty of COP, UQ is
Level 1
Level 2
Level 3
Level 4
1
30
22
2
40
35
3
55
49
4
78
60
Air flow rate (m3/h)
Input power (W)
1
1
1
1
2
2
2
2
3
3
3
3
4
4
4
4
30
40
55
78
30
40
55
78
30
40
55
78
30
40
55
78
22
35
49
60
35
22
60
49
49
60
22
35
60
49
35
22
Cost per unit of cooling (economic indicator) is evaluate using Spe­
cific Exergy Costing theory as explained in detail by Refs. [15,16]. It
should be noted that, cost per unit of cooling depends on material,
electricity, investment/capital/maintenance costs as well as exergy
transfer cost and is evaluated using Eq. (8).
∑
∑
Ċp,k + Żk +
(Ċi )k = Ċq,k +
(Ċe )k
(8)
i
e
where Ċp,k is exergy stream of power or work, Żk is capital/operating/
maintenance costs and Ċi is cost rate associated with entering exergy
stream of mass transfer [15,16]. Ċq,k is exergy stream of heat transfer
and Ċe is exiting exergy stream of mass transfer. Exergy stream of power
and heat can be written in the form of Eqs. (4) and (5) in Fig. 2) in which
cp and cq are the average cost per unit of exergy ($/kWh). Ėq is the same
as ĖQC or ĖQh as provided in Fig. 2. Eq. (8) should be applied for hot side
ceramic, cold side ceramic and thermocouples (as three main compo­
nents of the thermoelectric) and are solved as a system of equations.
In-detail explanations on the value of any mentioned factors have been
provided before by Refs. [15,16] and the same values are employed in
this research. The required investment costs in evaluation process are
summarized in Table 4 [15,16].
3.5. Signal to noise ratio (S/N)
Evaluation the signal to noise ratio (S/N), using Eq. (9), in which “n”
is the number of tests and “y” is the response factor) which provides the
desirable signal value and undesirable noise value respectively. Signal to
noise ratio is the optimization criterion in Taguchi method. Three stra­
tegies are possible in Taguchi method to evaluate the SN ratio including
“the higher the better”, “the lower the better”, and “the nominal is
better”. For cooling characteristics or exergetic efficiency that is “the
higher the better” while for the cooling cost it will be “the lower the
better”. To analyze the obtained results using Taguchi method, Minitab
Table 1
The factors, their level, and values through the optimization process.
Number of Peltier modules
Air flow rate (m3/h)
Input power (W)
Number of modules
uncertainty of cooling capacity and UP is uncertainty of input power. It is
noted that, these uncertainties should also be evaluated using the same
formula with their own parameters. This process is continued till reach
the basic parameters i.e., temperature, flow rate and so on which are
directly measured by the instruments. The uncertainty of the basic pa­
rameters is the same as the accuracy/resolution of the measuring in­
strument and operator errors. The maximum uncertainty of the basic
and other parameters is summarized in Table 3.
√̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
(
)2 (
)2
∂COP
∂COP
UCOP . = .
(7)
UQ +
UP
∂Q
∂P
3.4. Selection of an orthogonal array and required experiments
Factors
Parameters
3
Z.R. Abdulghani
Results in Engineering 16 (2022) 100627
Fig. 1. General view of the experimental set-up.
Fig. 2. Calculation process of thermal and exergetic factors.
4
Z.R. Abdulghani
Results in Engineering 16 (2022) 100627
Table 3
Maximum uncertainty of parameters.
Parameters
Uncertainty
Measuring of temperature
Measuring of air flow
Measuring of water flow
COP
Exergy efficiency
Cost per unit of cooling
±0.1 ◦ C
±2%
±2%
7.3%
3.1%
6.2%
Table 4
Investment costs of the materials.
Investment cost
Number of
investment cost of
modules
ceramic
1
3.2 $
2
6.4 $
3
9.6 $
4
12.8 $
Cost of electricity ($/s)
investment cost of
thermocouples
2.5 $
5.12 $
7.6 $
10.24 $
Fig. 3. Comparison of COP between current study and Tian et al. [3].
Ċp = 10− 8 × Pin
software was employed.
)
(
n
S
1∑
1
= − 10 log
N
n i=1 y2i
(9)
4. Results and discussions
First, the evaluated COP, cost of cooling and exergetic efficiency for
each set of experiment (see Table 2) are tabulated as Table 5; and then
the optimization process by Taguchi method is reported and discussed.
As described in the literature review, Tian et al. [3] has worked on a
single thermoelectric air cooler (the same type of thermoelectric i.e.,
TEC1-12706). Although they tested different values of inlet air flow,
their results of COP can be compared with the presents results as a
sample comparison/validation process (see Fig. 3). The difference be­
tween the results can be related to the different values of the inlet air
flows in these studies. They have used water fluid for the hot side (the
same as current study). They did not provide any optimization process
and they did not change the number of modules which are covered in
this research.
Fig. 4. SN ratio graphs for COP of the cooler at different levels of con­
trol factors.
The obtained results for the optimization process of COP are pro­
vided in Fig. 4 for number of modules, air flow rate and input power. The
maximum SN ratio is the optimum condition of each factor. As can be
seen in Fig. 4, a greater number of modules provides higher COP (for a
given total input power) and optimum number in the tested range, is 4
number of thermoelectric with signal to noise ratio of around 4.
More number of modules (in the same total input power) provides
higher COP. Based on the intrinsic feature of any individual Peltier
Table 5
The obtained results from the experiments.
Experiment
No.
Parameters
Results
Number
of
modules
Air
flow
rate
(m3/
h)
Input
power
COP
Exergy
efficiency
%
Cost per
unit of
cooling
($/kWh)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
1
1
1
1
2
2
2
2
3
3
3
3
4
4
4
4
30
40
55
78
30
40
55
78
30
40
55
78
30
40
55
78
22
35
49
60
35
22
60
49
49
60
22
35
60
49
35
22
0.42
0.38
0.28
0.25
0.864
1.19
0.640
0.822
1.06
0.95
3.15
1.51
1.19
1.17
1.88
2.6
7.3
5.21
4.32
3.81
8.12
9.16
5.78
6.43
9.16
8.24
10.95
9.09
9.52
9.94
10.48
11
0.72
1.4
3.83
5.37
0.832
0.731
3.10
1.70
0.674
0.865
0.563
0.76
0.66
0.64
0.64
0.67
Fig. 5. COP variation of a single module with input voltage.
5
Z.R. Abdulghani
Results in Engineering 16 (2022) 100627
module, higher input DC voltage (input power) provides more cooling
capacity but lower COP. This can be seen in Fig. 5 which shows the
variation of COP with input voltage for a single TEC12706 module
published by the manufacture.
As explained, if two, three or four modules are jointed to each other
and the same total input power of a single module is applied to the
system, each module will work with lower DC voltage (total power is
distributed between them) and provides higher COP. Hence, the total
COP of the system will be higher. However, it should be noted that,
based on Fig. 4, the slope of the SN ratio is reduced with increment of the
number of modules. It means that, the intensity of the COP improvement
is reduced step by step; and for a given total input power there will be a
critical number of modules after which the COP may not be increased
(internal resistance of more number is accumulated as a negative
feature).
As can be seen in Fig. 4, for the air flow optimization from COP
viewpoint, SN ratio is increases first and then is reduced. The maximum
SN ratio belongs to the air flow rate of 55 m3/h. This curve is important
as it shows a peak point in the mentioned value. When air flow is zero,
the cold side of the module goes to the minimum value (for a given input
power). With increment of air flow, the temperature of the colds side
starts to become warmer as a portion of the generated cooling is trans­
ferred to the air. However, if the air flow is further increased to higher
than 55 m3/h, no further cooling is transferred to the air and the COP
may reduce as the maximum cooling has already been transferred to the
air fluid. Based on Fig. 4, higher total input power reduces the SN ratio
which means lower value of COP. The optimum input power takes place
in the minimum input power. The reason of COP reduction because of
higher input power was explained before above.
Fig. 6 illustrates the optimization process for cost per unit of cooling
with variation of three parameters including number of modules, air
flow rate and input power.
SN ratio for cost per unit of cooling, is increased with increment of
number of modules and optimum value is shown for 4-modlue case.
However, from three modules to the four modules, the slope of SN ratio
is reduced. This is because of higher capital cost when the number of
modules is increased. In other words, a greater number of modules is
good from cooling viewpoint which is positive from economic view­
point. However, simultaneously, a greater number of modules causes
higher capital/operation cost. As long as the increment rate of negative
feature is lower than the increment rate of positive feature, the economic
factor is increased. Nonetheless, if the number of modules is increased
more and more, the SN ratio of the cooling cost may start to reduce.
Hence, for a given input power, there will be a critical number of
modules that should be considered in real applications. According to
Fig. 6, increment of air flow and input power, reduces their related SN
ratio. Thus, optimum value of these parameters from economic
Fig. 7. SN ratio graphs for Exergetic effectiveness at different levels of con­
trol factors.
viewpoint are their minimum value. Higher input power not only re­
duces the COP, but also it causes higher electricity price. The increment
of cooling capacity due to higher input power (positive aspect of higher
input power) is not able to overcome its negative aspects (lower COP and
higher electricity price). That is why, it reduces the cost per unit of
cooling.
Fig. 7 illustrates the optimization process for Exergetic effectiveness
with variation of three parameters including number of modules, air
flow rate and input power.
As can be seen in Fig. 7, the general curve behavior of SN ratio of the
number of modules, air flow rate and input power for optimization of
exergetic efficiency is similar to the cost per unit of cooling (however the
slope of the curves are different). This shows how the economic factor
and exergetic factor are dependent on each other and that is why many
expressions such as Exergoeconomic have been emerged in recent de­
cades. The optimum values (maximum SN ratio) for number of module,
air flow rate and input power are 4, 30 m3/h and 22 W respectively. The
optimum conditions of all tested parameters are summarized in Table 6.
As described before, one of the interesting features of Taguchi
method is the identification of the contribution percentage of each factor
on desired parameters [33]. It helps to determine the most effective
factor on the value of desired parameters. The contribution of each
factor on Cost per unit of cooling, COP and exergetic effectiveness is
represented in Fig. 8. The number of modules plays a key role in thermal,
economic and exergetic characteristics of the Peltier based air cooler.
The second effective factor is input power and the third one in air flow
rate. The contribution of air flow rate on COP is only 8% while its
contribution on economic factor and exergy factor are around 25% and
15% respectively. Briefly, Number of modules play a key role (roughly
50%) in all factors. The contribution of air flow is small in all factors, and
it is around 8% in COP. The impact of input power on cooling cost, COP
and exergy efficiency are 33, 30 and 20% respectively.
5. Conclusion
This paper shows how Taguchi method can be employed for
Table 6
Optimum condition for Cost per unit of cooling, COP and Exergetic
Effectiveness.
Factors
Number of Peltier modules
Air flow rate (m3/h)
Input power (W)
Fig. 6. SN ratio graphs for cost per unit of cooling at different levels of con­
trol factors.
6
Cost per unit of
cooling
COP
Exergetic
Effectiveness
Level
Value
Level
Value
Level
Value
4
1
1
4
30
22
4
3
1
4
55
22
4
1
1
4
30
22
Z.R. Abdulghani
Results in Engineering 16 (2022) 100627
Fig. 8. Contribution of each factor on Cost per unit of cooling, COP and Exergetic effectiveness.
optimization process of a Peltier air cooler from energy, economic and
exergetic viewpoints. Number of modules, air flow rate and input power
are considered as the variant parameters. The results showed that,
higher number of modules increases the COP, reduces the cost and in­
creases the exergetic efficiency. However, there will be a critical value
for number of modules as capital and other marginal costs may over­
come to its positive feature. A peak point was observed for COP versus
air flow rate. For all factors, the optimum value of “number of modules”
and “input power” were observed at level 4, level 1, respectively. The
optimum value of COP for air flow rate took place in Level 3. The
contribution of each factor can be determined in Taguchi method as
well. Number of modules play a key role (roughly 50%) in all factors.
The contribution of air flow is small in all factors, and it is around 8% in
COP. The impact of input power on cooling cost, COP and exergy effi­
ciency are 33, 30 and 20% respectively.
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Author contribution section
R. Abdulghani. Writing - Original Draft, Data curation, Methodology,
Conceptualization, Supervision.
Declaration of competing interest
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influence
the work reported in this paper.
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