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Case Studies in Thermal Engineering 39 (2022) 102464
Available online 1 October 2022
2214-157X/© 2022 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/).
The performance of a gamma-type stirling water dispenser with
twin wavy plate heat exchangers
Ammar S. Easa
a
,
b
,
*
, Wael M. El-Maghlany
c
, Mohamed M. Hassan
c
,
Mohamed T. Tolan
a
,
d
a
Mechanical Department, Faculty of Technology and Education, Suez University, Suez, Egypt
b
Department of Mechanical Power Engineering, El-Arish High Institute for Engineering and Technology, El-Arish, North Sinai, Egypt
c
Mechanical Engineering Department, Faculty of Engineering, Alexandria University, Egypt
d
Faculty of Technological Industries, King Salman International University, South Sinai, Egypt
ARTICLE INFO
Keywords:
Water dispenser
Heat pump
Gamma- stirling
Wavy plate heat exchanger
ABSTRACT
Today, households increasingly depend on water dispensers as necessary appliances. In this way,
the demand for water dispensers with environmentally friendly systems is rising around the globe
because there are no eco-friendly alternative water dispensers in the global market as alternatives
to vapor compression refrigeration systems. In the present work, the improved Stirling water
dispensers for cold and hot water are presented as an environmentally friendly alternative. A
gamma-type Stirling water dispenser is improved by integrating twin wavy plate heat exchangers
with varying dimensions. A thermodynamic model is developed to carry Schmitt’s vision of
overcoming the Stirling water dispenser to fruition. The suitable sizes of both heat exchangers are
determined to achieve higher heat removal rates and a higher coefcient of performance (COP).
Due to the heat exchanger’s optimal size, the water cooler generates a cooling load of about 1.4
kW and a heating load of about 4 kW. A suitable and adequate tendency is identied by
comparing the data from the past and the present. The performance of the gamma Stirling water
dispenser was improved by about 22% as a result of using twin wavy plate heat exchangers.
Nomenclature
A Surface area, m
2
f Friction
h Convection coefcient, W/m
2
K
i Net number, pores/inch
k Conductivity, Wm
−1
k
−1
m The mass ow rate, kg/s
N Speed, rpm
NTU Number of transfers of units
P Power, W
p Pressure, Pa
* Corresponding author. Mechanical department, Faculty of Technology and Education, Suez University, Suez, Egypt.
E-mail address: ammar.saad60@suezuniv.edu.eg (A.S. Easa).
Contents lists available at ScienceDirect
Case Studies in Thermal Engineering
journal homepage: www.elsevier.com/locate/csite
https://doi.org/10.1016/j.csite.2022.102464
Received 13 June 2022; Received in revised form 17 September 2022; Accepted 30 September 2022
Case Studies in Thermal Engineering 39 (2022) 102464
2
CL Cooling load, W
HL Heating load, W
R Gas constant, J kg
−1
K
−1
r Crank radius, m
Re Reynold number
S Stroke, m
T Temperature, K
t Time, s
V Volume, m
3
re expansion crank radius
rc compression crank radius
Y Movement
x,y Coordinates, m
Greek letters
ε
Regenerator effectiveness
Φ
C
Compression cylinder bore, m
ɸ
E
Expansion cylinder bore, m
Ɵ
Crank angle, degree
μ
Viscosity, kg m
−1
s
−1
ρ
Density, kg m
−3
Ψ Porosity
Subscripts
C Compression spac
ch Charging
Co Condenser
cw Cooling water
D Displacer
E Expansion space
Ev Evaporator
h Hydraulic
max Maximum
min Minimum
In Inner conditions
Out Outer conditions
p Piston
R Regenerator
Sc Schmidt
sw Swept
t Total
th Thermal
w The wire of the regenerator
1. Introduction
Clean water is vital to human health. Our bodies should have above 50% water to be healthy and t. Drinking pure water is critical.
Water dispensers are handy for cold and hot water. These days, it is almost impossible to live without a water dispenser. Water dis-
pensers utilize vapor compression refrigeration (VCR), which uses refrigerants that are harmful to the environment and use a lot of
energy [1–5]. A convention was ratied in the United Kingdom in 1987 to avoid additional ozone layer destruction due to CFC
emissions. According to the Montreal Protocol, the CFC group of refrigerants was the primary cause of ozone layer depletion and
should be outlawed by 2010 [6]. In addition to improving VCR, two signicant issues (global warming owing to HCFC uid usage and
increased refrigeration demand worldwide) have motivated engineers to explore alternatives to vapor-compression refrigeration. In
contrast, using ecologically friendly uids and enhanced energy efciency leads to novel refrigerants and technologies like Stirling
refrigerators [7]. Robert Stirling came up with the Stirling machine, a heat engine with an external heat source. As a result, Stirling
machines were eco-friendly devices [8–11]. Closed regenerative thermodynamic cycles were the most common, such as the Stirling
refrigeration cycle [12]. Stirling machines were perfect for refrigerators due to their high performance, low power consumption, low
starting power, rapid cooling, and compact size [13–16]. There were different Stirling machines: gamma, alpha, and beta. The
thermodynamic cycles of any arrangement were the same, regardless of the mechanical design. The alpha type features a twin-cylinder
A.S. Easa et al.
Case Studies in Thermal Engineering 39 (2022) 102464
3
layout with a single piston in each cylinder [17]. In comparison, the displacer and a piston of beta-type were situated in a twin cylinder.
The gamma-type Stirling machine consists of a piston and a displacer, each in its cylinder [18]. The beta machines were smaller than
the gamma and alpha types [19]. Stirling machines were affected by the properties of the working uid. Working uids such as ni-
trogen, Helium, and hydrogen were typically utilized, hydrogen providing the best performance. Nonetheless, Helium was less harmful
than nitrogen [20]. Furthermore, Helium has high specic heat and conductivity [21].
Multi-objective optimization of a gamma Stirling refrigerator based on analytical and experimental data for air, Helium, or carbon
dioxide as a working uid was examined [22]. The working uid of Helium or air produced the best COP results. The cooling load and
COP employing air and helium rise as the charge pressure increases, and as the speed of the refrigerator rises, so does the cooling load.
A numerical assessment of a beta-type refrigerator employing a tube-shaped heat exchanger tted with twisted tapes has been
investigated [23]. The ndings revealed that increasing the number of twisted tapes improves the performance. The refrigerator
powered by a solar heat engine produced around 0.00028 TR/CC and COP =0.529 at 800 rpm. An alpha Stirling refrigerator was
numerically investigated with various operating uids in FORTRAN [24]. Using hydrogen as a working uid improves the re-
frigerator’s performance because of its high specic heat and low-pressure losses. At 800 rpm, the refrigerator generates a cooling
power of 477 W at a COP of 2.77. Control volume analysis was used to investigate the thermodynamics of an alpha-type Stirling
refrigerator [25]. The operating uid was air. It is found that the refrigerator’s heat transfer surface area increases its efciency.
Meanwhile, the design was suitable for Stirling refrigerators based on the ndings of the control volume study. An experimental
examination of a beta Stirling cooler using air as a working gas was investigated [26]. The regenerator’s thermal losses were included
in the study. The maximum cooling load was obtained at a regenerator porosity of roughly 85%. A solar duplex Stirling refrigerator was
studied analytically using numerical thermodynamics [27]. Thermal conduction differences between the solar Stirling refrigerator’s
heat reservoirs and working uid were investigated. At COP =0.5307, the refrigerator produced around 2480 W. A beta-type Stirling
cooler’s performance was studied experimentally and analytically using Helium as a working uid [28]. Increasing the charging
pressure and operation speed results in lower operating temperatures. A numerical analysis of the Stirling refrigerator’s performance
as a dual unit was conducted [29]. Helium, air, nitrogen, or hydrogen are all suitable working uids. The results show that Helium is
the most effective operating uid for the refrigerator. An elliptical tube heat exchanger and a cylinder with various bores were used to
study the Beta Stirling refrigerator’s performance [30]. Evaporator and condenser tubes were 33% more efcient using elliptical
cross-section tubes. At a 0.2 elliptical ratio, using oval tubes in the condenser and evaporator increases the cooling load by around 24%.
A 25% increase in cooling load may be achieved using compression to expansion bore ratio. A Stirling/Pulse tube hybrid refrigeration
model and its verication were examined [4]. The results of an experiment support the theoretical hypothesis. They agree on both
stages’ temperature-cooling capability and acoustic power and pressure. The theoretical model explains a phase change in the allo-
cation of inter-stage cooling capacity. It may also be used to explicitly examine the thermodynamic features of Stirling/pulse tube
hybrid refrigerators theoretically. A thermoacoustic-Stirling refrigeration system for recovering low to medium-grade waste heat has
been studied numerically by Ref. [15]. The thermoacoustic properties of the system were thoroughly investigated to comprehend its
operation and cooling performance. This system was also tested for the effects of temperature and pressure on its thermodynamic
performance. At a refrigeration temperature of 10 ◦C, a 2 kW-class compressor for air-conditioning refrigeration may achieve a COP of
more than 0.62 under ambient temperature conditions of 50 ◦C. An ideal second-order thermal model with loss effects was used [31].
The Stirling refrigerator’s working gas temperature and overall performance were studied concerning the shuttle heat loss in the
differential equations. A Study of operating parameters (temperature, pressure, and frequency) on refrigeration machine performance
has also been carried out via parametric means. According to the data, using a lower frequency or more signicant pressure might
boost performance. Stirling/pulse tube hybrid refrigeration has been researched numerically and experimentally [32]. The system can
achieve cooling capacities of 8.8 W at 80 K and 0.81 W at 30 K with an input electric power of 245 W. A study of the free-piston Stirling
heat pump’s temperature adaptability was conducted by Ref. [33]. SAGE software is used to analyze the performance of an electrically
driven free-piston Stirling heat pump. The numerical simulation results show that 1 kW of electricity, 40 ◦C of heating temperature,
and 20 ◦C of ambient temperature can be used to generate 2409 W of heating capacity. Multi-stage heat-driven piston-coupled
thermoacoustic Stirling cooler modeled numerically by Ref. [34]. The piston design method was explained based on the principle
of acoustic impedance matching. Optimized systems were used to run a variety of simulations. Thermal-to-cooling Carnot efciency
was 23% at 873 K, and 130 K. Improve efciency and cooling capacity by more than 60% and 80%, respectively, over the previous
model.
Due to restricted manufacturing volume and operating conditions (high temperature and pressure), Stirling cycle devices are costly
to build. Stirling machines, notable refrigerators, have been studied for almost a century. The ndings demonstrate performance gains,
and further applications are examined. Domestic or commercial refrigeration seldom uses Stirling cycle cooling at moderate/ambient
temperatures. Stirling refrigerators with average temperatures, where high operating temperature and pressure are not needed, have
lower mass manufacturing costs than Stirling engines. Most recently, the Sterling cycle has been proposed as a water dispenser to use
the waste heat generated by the hot heat exchanger. Numerical analysis of alpha-type dispensers was investigated by Ref. [36]. The
effectiveness of the dispenser is evaluated using a mathematical model based on Schmidt analysis. The researchers obtained a tem-
perature of 95◦Celsius for their water using Stirling water dispensers instead of electric heaters. Also, Stirling water dispenser per-
formance was studied experimentally to reduce energy consumption and improve efciency by utilizing the waste heat of both pistons’
friction [37]. Water jackets can use the waste heat produced by piston friction to enhance the efciency of the Stirling water dispenser.
Using the waste heat of both pistons at 1200 rpm increases the heating and cooling loads of the current water dispenser by about 2952
W and 834 W, respectively.
Wavy ns dominate straight ns in terms of heat transmission. However, most research on Stirling machines now in existence
focuses on shell and tube or tubular heat exchangers. It is unknown how well the Stirling machine, which may be used in the heat
A.S. Easa et al.
Case Studies in Thermal Engineering 39 (2022) 102464
4
recovery process, performs while utilizing wavy plate heat exchangers. Numerically parametric research on large-size wavy plate heat
exchangers is studied by Ref. [38] to ll the gap in the comprehensive design knowledge for large-size wavy plate heat exchangers with
improved efciency. The gamma-type Stirling water dispenser performance using twin wavy plate heat exchangers has not yet been
studied from previous publications and the author’s knowledge. This work uses twin wavy plate heat exchangers at various dimensions
Fig. 1. The schematic drawing for the proposed system.
Fig. 2. Heat exchangers with wavy plates.
A.S. Easa et al.
Case Studies in Thermal Engineering 39 (2022) 102464
5
to enhance the gamma-type Stirling water dispenser performance.
2. Water dispenser analysis
Reversible Stirling cycles are used to construct the suggested water dispenser, which provides the highest potential performance.
The current work illustrates that the proposed water dispenser utilizes a Gamma-type Stirling water dispenser with a typical crank
mechanism. Three heat exchangers are included in the proposed refrigerator, a twin-cylinder design made of power and displacer
pistons with a 90-degree phase angle, as seen in Fig. 1. The offered water dispenser uses twin wavy plate heat exchangers. The
dimension of the wavy plate heat exchangers is illustrated in Fig. 2. It is planned to utilize a wire mesh as a regenerator. Helium has
been chosen as the working uid. When performing a Schmidt analysis of the proposed refrigerator, it is essential to consider the
pressure drops via the heat exchangers and their linked sections.
2.1. Thermodynamic model
An original crank mechanism is used to open and close the Gamma Stirling water dispenser. The actual movement of the two
pistons is based on the direction of the rst piston [39] and can be considered, respectively, as follows:
YD=r×1−cos(θ) + 1
re1−
1− (re2×sin2θ
(1)
YC=r×1−cosθ−
π
/
2
+1
rc1−
1− (rc2×sin2θ−
π
/
2
(2)
Both the expansion and compression spaces have different volumes, which are itemized below:
VE=VE,sw
2×1−cos(θ) + 1
re1−
1− (re2×sin2θ
(3)
VC=VE,sw
2×1−cos(θ) + 1
re1−
1− (re2×sin2θ
+VC,sw
2×1−cosθ−
π
/
2
+1
rc1−
1− (rc2×sin2θ−
π
/
2
(4)
The total water dispenser volume is as follows:
VT=VE++VEv +VR+VCo +VC(5)
The regenerator temperature is as follows according to Schmid’s model [1]:
TR=TC−TE
ln TC
TE
(6)
The total mass of the working gas is:
mT=p(VE+VEv)
R TE
+VR
R TR
+(Vc+VCo)
R TC=pchVmax
RTch
(7)
Thus, the instantaneous pressure [8] is:
p=mT
(VE+VEv)
RTE+VR
RTR+(VC+VCo)
RTC(8)
Reynolds numbers for the proposed water dispenser were calculated, and the conservation of mass equation was applied to the
workspaces of the dispense as follows [40]:
ReEv =4m.
π
dh
μ
Ev
(9)
ReR=16 m.(1−
ψ
)
π
dw
μ ψ
R
(10)
ReCo =4m.
π
dh
μ
Co
(11)
The cooling and heating rates are calculated as follows:
CL =NpEdVE=UCoACo (LMTD) = m.
CoCpCo (Ti−To) = m.
CwCpCw (Ti−To)(12)
HL =NpCdVC=UEvAEv (LMTD) = m.
EvCpEv (Ti−To) = m.
CwCpCw (Ti−To)(13)
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6
The working uid’s heat transfer coefcient and friction factor were determined using the following relationships [38]:
Nu =Nu0∗EA∗EPp ∗EPt ∗EPh ∗EPL ∗ELw (14)
Nu0=−212.7273 ∗Re−0.212 +70.66.1Pr
1
/
3
for turbulent flow (15)
NU0=0.1201 ∗Re0.5915 +7.0691Pr
1
/
3
for laminar flow (16)
EA=0.9556 ∗e0.00415∗A
Lref +0.001863 ∗e0.484∗A
Lref for turbulent flow (17)
EA=0.7252 ∗e0.06254∗A
Lref (18)
EPp =4.416 ∗Pp
Lref −0.5747
−0.3751 (19)
EPt =0.05957 ∗Pt
Lref 1.412
+0.9399 (20)
EPh =0.03096 ∗e−0.008399∗Ph
Lref +0.9953 ∗e−5.439∗10−6∗Ph
Lref (21)
EPL =0.4277 ∗e−0.003036∗PL
Lref +1.003 ∗e−2.346∗10−5∗PL
Lref (22)
ELw =120.5∗Lw
Lref −1.264
+0.6543 for laminar flow (23)
ELw =280.1∗Lw
Lref −1.756
+0.9309 for turbulent flow (24)
The heat exchangers pressure drops through can be determined as follows:
f=ɸIn
l
2Δp
ρ
v2(25)
f=f0∗EA∗EPp ∗EPt ∗EPh ∗EPL ∗EPW (26)
f0=1.852 ∗Re−0.554 for laminar flow (27)
f0=2.993 ∗Re−0.582 for turbulent flow (28)
EPp =591.7∗Pp
Lref −3.184
+0.03583 (29)
EPt =0.2424 ∗PPt
Lref 1.705
+0.7576 (30)
EPh =8.11 ∗Ph
Lref −0.9604
+0.9499 (31)
EPL =0.001159 ∗PL
Lref 0.9786
(32)
ELw =1.165 ∗106∗Lw
Lref −3.353
+0.6695 (33)
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Case Studies in Thermal Engineering 39 (2022) 102464
7
EA=0.5001 ∗e0.13492∗A
Lref +9.552 ∗10−5∗e0.9422∗A
Lref (34)
The pressure drop through the regenerator as a consequence of variable ow was considered using the following equation [23]:
log(fR) = 1.73 −0.93 log(ReR)if 0<ReR≤60 (35)
log(fR) = 0.714 −0.365 log(ReR),if 60 <ReR≤1000 (36)
log(fR) = 0.015 −0.125 log(ReR),if ReR>1000 (37)
ψ
=1−1000i
25.4×
π
4dw(38)
ΔpR=fRlR(1−
ψ
)(
ψ
dw)
ρ
Rv2
R2(39)
The regenerator effectiveness is dened as follows:
ε
=NTUR/(1+NTUR)(40)
NTUR=2StR×lRdh,R(41)
StR=0.595 Re0.4
R.PrR(42)
NTUR=2×0.595
Re0.4
R.PrRlRdh,R(43)
The following are the coefcients of performance for refrigerators and heat pumps of the proposed Gamma water dispenser:
COPref =CLW(44)
COPhp =HLW(45)
2.2. Computer program
Spreadsheet-based computer software was created to analyze the numerical performance of the current water dispenser throughout
one cycle at a 1.0-degree crank-angle step, with all parameters computed immediately as the crank-angle was increased. The
refrigerated space temperature is maintained at 4 ◦C. In comparison, the cooling water temperature is maintained at 25 ◦C, and the
temperature of the heated space is maintained at 95 ◦C. The effectiveness of the wire net regenerator remained at or above 97%
throughout the test. The operational parameters and refrigerator COP were adjusted until the optimal dimensions were found, which
resulted in better refrigerator COP, heat pump COP, cooling load, and heating load.
3. Results and discussion
In order to enhance the performance of the Stirling water dispenser, twin wavy plate heat exchangers were investigated as hot and
Fig. 3. COP and heating/cooling loads of the water dispenser versus wavy amplitude of the heat exchangers.
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Case Studies in Thermal Engineering 39 (2022) 102464
8
cold heat exchangers. The heating and cooling loads and the heat pump/refrigeration COP of the Stirling water dispenser were
investigated concerning the wavy amplitude, plate pitch, wavelength, length, height, thickness, charged pressure, and rotating speed
of the plates.
3.1. Inuence of the heat exchanger wavy amplitude on the water dispenser performance
The inuence of the wavy amplitude of the heat exchanger on the ref/HP COPs and the heating/cooling loads of the water dispenser
at a different wavy amplitude is shown in Fig. 3. A wavy plate heat exchanger with an amplitude of 0.0 m (the straight plate) is used as
a reference line. The wavy amplitude of twin heat exchangers is studied from 0 m to 0.02 m. The increased wavy amplitude improves
the heating/cooling loads due to the increase of heat transfer coefcient of both heat exchangers. Specically, for the wavy amplitudes
of 0.02 m, heating/cooling loads by 21.16% and 22.63%. On the other hand, the refrigerator COP and heat pump COP has also
increased as wavy amplitude increases by about 89% and 119%, respectively, due to the increase in heat transfer coefcients.
3.2. Effect of plate pitch of the heat exchangers on the water dispenser performance
Fig. 4 displays the effect of varying the plate pitch of the heat exchanger on the ref/HP COPs and the heating/cooling loads of the
water dispenser. Twin heat exchangers are analyzed, focusing on the plate pitch between 0.002 and 0.022 m. Plate pitch discoveries
have a signicant impact on the performance of the water dispenser. Heating/cooling loads are reduced by 17.84 and 16.12%,
respectively, when plate pitch is 0.022 m. Conversely, as plate pitch rises, the COP of a refrigerator decreases by about 54%, and the
COP of a heat pump decreases by about 47%. Because of a higher Reynolds number, narrower plate pitch has a combined effect that
increases the heat transfer coefcient. One can say that the faster air moves, the more efciently heat are transferred through con-
vection. The air velocity rises as the plate pitch decreases because the shorter hydraulic radius of the two heat exchangers causes an
increase in air velocity.
3.3. Inuence of heat exchanger plate thickness on the water dispenser performance
The impact of the plate thickness of both heat exchangers on the COPs and the heating/cooling loads of the water dispenser at a
different plate thickness is exposed in Fig. 5. A wavy plate heat exchanger with an plate thickness of 0.2 mm (the thin plate) is used as a
reference line. The plate thickness of twin heat exchangers is studied from 0.2 to 2.2 mm. The increased plate thickness improves the
Fig. 4. COP and heating/cooling loads of the water dispenser versus plate pitch of the heat exchangers.
Fig. 5. COP and heating/cooling loads of the water dispenser versus Plate thickness of the heat exchangers.
A.S. Easa et al.
Case Studies in Thermal Engineering 39 (2022) 102464
9
heating/cooling loads due to the heat transfer coefcient of both heat exchangers. Specically, for the plate thickness of 2.2 mm,
heating/cooling loads by 22.20% and 15.42%. On the other hand, the refrigerator COP and heat pump COP have also improved as
plate thickness increased by about 119% and 109%, respectively, because of the heat transfer coefcient increase. Furthermore, the
laminar and turbulent regimes demonstrate that plate thickness enhances efciency; however, in the laminar regime, plate thickness
increases effectiveness more slowly than it does in the turbulent regime [38]. Higher convection heat transfer is achieved due to the
increased velocity inside the greater plate thickness [41], resulting in a reduction in the temperature of the hot Helium released from
the plate due to its increased thickness.
3.4. Effect of plate height of the heat exchangers on the water dispenser performance
Fig. 6 displays the effect of varying the plate height of the heat exchanger on the ref/HP COPs and the heating/cooling loads of the
water dispenser. Twin heat exchangers are analyzed, focusing on the plate height between 0.005 and 0.055 m. Plate height discoveries
have an essential impact on the performance of the water dispenser. Heating/cooling loads are increased by 28.51 and 14.32%,
respectively, when plate height is 0.055 m. On the other hand, cooling and heating loads have also improved as plate height increased
by about 19% and 22%, respectively. Due to an increase in channel cross-sectional area, the volumetric airow rate signicantly rises
when plate height is raised. This implies that the rate of heat transmission will likewise rise considerably.
3.5. Effect of heat exchanger plate length on the water dispenser performance
Fig. 7 illustrates how the heat exchanger plate length affects the Stirling water dispenser’s performance at various values of the
plate length. Compared to 0.15 m plate length, the refrigeration COP is improved by roughly 116.9% at 0.05 m plate length. Addi-
tionally, it raises the heat pump’s COP by approximately 89.83%. On the other hand, for shorter plate lengths, cooling and heating
loads have also increased by almost 23% and 19%, respectively. The longer the plate length, the air has more time to remain in contact
Fig. 6. COP and heating/cooling loads of the water dispenser versus Plate height of the heat exchangers.
Fig. 7. COP and heating/cooling loads of the water dispenser versus Plate length of the heat exchangers.
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Case Studies in Thermal Engineering 39 (2022) 102464
10
with the plate wall. Additionally, when the plat length grows, the water dispenser’s dead volume rises, pressure losses via the heat
exchanger increase, and energy consumption rises.
3.6. Effect of the wavelength of the heat exchangers on the water dispenser performance
Fig. 8 shows the impact of the heat exchanger’s wavelength on the ref/HP COPs and heating/cooling loads of the water dispenser at
various wavelengths. The reference line is a wavy plate heat exchanger with a shorter wavelength of 0.02 m. Twin heat exchangers’
wavelengths between 0.02 and 0.07 m are investigated. Because the longer wavelength improves both heat exchangers’ heat transfer
coefcients, the heating and cooling loads are improved. Heating and cooling demands are 23% and 19% for wavelengths of 0.07 m.
On the other hand, when wavelength grows, the COP of a refrigerator and a heat pump has also increased by around 131.44% and
94.91%, respectively.
Fig. 8. COP and heating/cooling loads of the water dispenser versus wavelength of the heat exchangers.
Fig. 9. COP and cooling load of the water dispenser versus charging pressures at different frequencies.
Fig. 10. Heating load and COP of the water dispenser versus charging pressures at different frequencies.
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Case Studies in Thermal Engineering 39 (2022) 102464
11
3.7. Effect of charging pressure on the water dispenser performance
Fig. 9 depicts the cooling power and ref COP of the present water dispenser at various frequencies as a function of charging
pressure; the more signicant rise in setting pressure, the greater the cooling capacity and the lower the ref COP. The mass of the
operating uid rises because of an increase in charge pressure. However, pressure losses rise as the charged mass increases, requiring
more power to operate the water dispenser. Fig. 10 shows how the charging pressure change impact both heating load and HP COP,
with higher charging pressures resulting in a higher heating load and lower HP COP. Helium range has an ideal speed range of 800
revolutions per minute. As long as leaks are avoided, the water dispenser may generate 1400 W of cooling power and about 4000 W of
heating power.
3.8. Comparison between the current work with the previous studies
Table 1 compares the present work to those of the past. Comparing present ndings to prior ones demonstrates an acceptable
pattern. Contrasts show that the recommended water dispenser detects a 22% increase in heating load and a 19% increase in cooling
load.
4. Conclusions
This paper has studied the performance of a Stirling water dispenser with an evaporator and a condenser made of twin wavy plate
heat exchangers. The water dispenser’s primary dimensions for improved ref/HP COP and more signicant cooling/heating load were
discovered. The following are the most important ndings:
Table 1
Evaluation of current and previous work.
Frequency, rpm 100 200 300 400 500 600 700 800 1000 1200
Cooling load, present work 0.38 0.59 0.88 1.19 1.35 1.50 1.77 1.99 2.17 2.63
Heating load, present work 0.59 0.92 1.46 1.86 2.73 3.10 3.92 4.49 5.00 5.56
Cooling load [36], 2019. 0.11 0.20 0.29 0.38 0.47 0.56 0.66 – – –
Heating load [36], 2019. 0.16 0.33 0.51 0.67 0.85 1.02 1.17 – – –
Cooling load [1], 2021. 0.30 0.59 0.85 1.10 1.32 1.53 1.71 1.88 2.17 2.38
Heating load [1], 2021. 0.36 0.74 1.14 1.54 1.96 2.38 2.82 3.28 4.22 5.21
Cooling load [23], 2019. 0.14 0.28 – 0.6 0.84 0.94 0.92 0.72
Table 2
The proposed water dispenser Dimensions.
Description Dimensions
Piston cylinder diameter 0.1 m
Displacer cylinder diameter 0.1 m
Stroke 0.1 m
Phase angle 90◦
The cold heat exchanger (wavy plate)
Amplitudes of the double wavy pattern 0.02 m
Plate height 0.055 m
The thickness of the plate 0.0025 m
Wavelength 0.07 m
Plate pitch 0.025 m
Plate length 0.05 m
Regenerator (wire net)
Regenerator Length 0.035 m
Wire net 200 pores per inch
The hot heat exchanger (wavy plate)
Amplitudes of the double wavy pattern 0.02 m
Plate height 0.055 m
The thickness of the plate 0.0025 m
Wavelength 0.07 m
Plate pitch 0.025 m
Plate length 0.05 m
Operating condition
Charged pressure 5 bars
Rotational speed 800 rpm
Working uid Helium
A.S. Easa et al.
Case Studies in Thermal Engineering 39 (2022) 102464
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•The suitable dimensions of both heat exchangers are listed in Table 2 to achieve higher heat removal rates and a higher coefcient
of performance (COP).
•The proposed water dispenser develops 1.4 kW of cooling load and 4 kW of the heating load.
•The water dispenser can be produced to test its efcacy in a virtual environment utilizing the calculated dimensions.
•A suitable and adequate tendency is identied by comparing the data from the past and the present.
•The COP of the gamma Stirling water dispenser was improved by about 22% due to using twin wavy plate heat exchangers.
•The use of twin wavy plate heat exchangers improves the Heating load of the Stirling water dispenser by about 37% compared to
using shell and tube heat exchangers.
•The use of twin wavy plate heat exchangers improves the cooling load of the Stirling water dispenser by about 19% compared to
tubular heat exchangers having inserted twisted tapes.
•The Stirling water dispensers have a higher cooling/heating load and a suitable COP. It is suggested to be manufactured and
presented in the market as an environmentally friendly alternative
CRediT authorship contribution statement
Ammar S. Easa: Conceptualization, Writing – original draft, Resources, Methodology, Formal analysis, Investigation, numerical
approach, Writing – review & editing. Wael M. El-Maghlany: Conceptualization, Resources, Methodology, Formal analysis, Inves-
tigation, Writing – review & editing. Mohamed M. Hassan: Conceptualization, Formal analysis, Investigation, Writing – review &
editing. Mohamed T. Tolan: Methodology, Writing – review & editing, Formal analysis.
Declaration of competing interest
The authors declare that they have no known competing nancial interests or personal relationships that could have appeared to
inuence the work reported in this paper.
Data availability
No data was used for the research described in the article.
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