Case Studies in Thermal Engineering 25 (2021) 100927
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Case Studies in Thermal Engineering
journal homepage: http://www.elsevier.com/locate/csite
An approximate model of a multilayer wire-on-tube condenser
operating with R134a and R600a: Experimental validation and
parametric analysis
J.M. Belman-Flores a, *, Y. Heredia-Aricapa a, Juan J. García-Pabón b,
A. Gallegos-Muñoz a, J. Serrano-Arellano c, C. Gutiérrez Pérez-Reguera d
a
Department of Mechanical Engineering, Engineering Division, Campus Irapuato-Salamanca, University of Guanajuato, Salamanca-Valle de
Santiago Km 3.5+1.8, CP.36885, Mexico
b
Institute in Mechanical Engineering, Federal University of Itajubá (UNIFEI), Av. BPS, 1303, Itajubá, CEP: 37500903, Brazil
c
Instituto Tecnológico Superior de Huichapan, ITESHU-TecNM, Huichapan Hidalgo, CP.42411, Mexico
d
Mabe TyP, Acceso B#406, Parque Industrial Jurica, Querétaro de Arteaga, CP.76120, Mexico
A R T I C L E I N F O
A B S T R A C T
Keywords:
Domestic refrigerator
Forced convection
Heat transfer
Physical model
Thermal analysis
Wire-on-tube condenser
This study presents the development of a new approximate model for a multilayer wire-on-tube
condenser used in the domestic refrigeration industry. This model is based on physical founda­
tions and empirical correlations, as well as on the ε-NTU thermal analysis methodology. It has
been designed for three zones according to the state of the refrigerant. The input parameters to
the model correspond to typical geometric characteristics of this type of condenser and operating
conditions. As output parameters, the emphasis was placed on the thermal capacity of the
condenser, and the refrigerant side and air-side outlet temperatures. For its validation, tests were
carried out with real refrigerators, one of them operating with R134a and the other with R600a.
The model prediction showed maximum relative errors of ±5% for thermal capacity and ±0.5K
for temperatures. Finally, a parametric study was carried out analyzing the effect of varying the
main geometric parameters such as tube and wire diameters, and wire and tube pitches.
1. Introduction
Domestic refrigerators help preserve the quality of food products longer since keeping these products at low-temperature levels
inhibits the growth of bacteria that help food spoilage [1]. These appliances have become increasingly elaborated in terms of design,
functionality, speed of cooling, aesthetics, storage capacity, among others. Most of these refrigerators are based on vapor compression
technology, which involves high-energy consumption due to various aspects such as type of technology, usage habits, a large number
of units in service, among others, Belman-Flores et al. [2]. Thus, different strategies have been implemented over the years to make
these systems more efficient, including the design, analysis, and optimization of main components.
One of the areas of great interest in the domestic refrigeration industry is the development of more compact heat exchangers. Wireon-tube type heat exchangers are the most widely used equipment as condensers. These heat exchangers consist of a tube bent in the
form of a coil, through which the refrigerant circulates, and of wires welded externally to the tube on both sides. Thus, heat transfer
* Corresponding author.
E-mail address: jfbelman@ugto.mx (J.M. Belman-Flores).
https://doi.org/10.1016/j.csite.2021.100927
Received 22 January 2021; Received in revised form 24 February 2021; Accepted 3 March 2021
Available online 9 March 2021
2214-157X/© 2021 The Author(s).
Published by Elsevier Ltd.
This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/).
Case Studies in Thermal Engineering 25 (2021) 100927
J.M. Belman-Flores et al.
Nomenclature
A
a, b
C
Cp
Cr
COP
D
FP, FC
G
Gr
H
h
k
L
Ltp
Lwp
ṁ
n
NTU
Pr
Q
RA
Re
S
T
U
y
area [m2]
Kays and London correlation constant [-]
thermal capacitance [W/K]
specific heat [J/kg K]
heat capacity ratio [-]
coefficient of performance
diameter [m]
correction factor in cross flow [-]
gravity [m/s2]
Grashof number [-]
height [m]
heat transfer coefficient [W/m2 K]
thermal conductivity [W/m K]
length [m]
characteristic tube length
characteristic wire length
mass flow rate [kg/s]
Zukauskas correlation constant [-]
number of transfer units [-]
Prandtl number [-]
heat transfer rate [W]
area ratio [-]
Reynolds number [-]
pitch [m]
temperature [K]
overall heat transfer coefficient [W/m2 K]
depth [m]
Greek symbol
effectiveness [-]
efficiency [-]
thermal emittance [-]
Stefan-Boltzmann constant [W/K4 m2]
dynamic viscosity [kg/m s]
density [kg m-3]
ε
η
εapp
σ
μ
ρ
Subscripts
air
cond
conv
dsh
ext
f
g
i
in
min
o
r
rad
s
sub
t
w
air
condensation
convection
desuperheating
external
saturated liquid
saturated vapor
inlet
internal
minimum
outlet
refrigerant
radiation
surface
subcooling
tube
wire, wall
takes place on the external surfaces of the tube and wires, either by natural or forced convection. One of the designs of this type of
exchanger is mounted on the back of the plate-shaped refrigerator, where the heat transfer mechanisms present are natural convection
and radiation. Another important design is the spiral condensers or jelly roll, which is more compact, and its dominant heat transfer
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J.M. Belman-Flores et al.
mechanism is forced convection.
Most of the research of this type of heat exchangers is oriented to the study of correlations for heat transfer. For example, Tagliafico
and Tanda [3] evaluated the heat transfer by radiation and natural air side convection of a wire-on-tube heat exchanger. The authors
identified the main geometric parameters that affect heat transfer. Melo and Hermes [4] developed an experimental π-type correlation
for the combination of heat transfer by natural convection and radiation, this correlation was used to analyze geometric aspects such as
tube diameter, tube rows, and wires on heat transfer. Espíndola et al. [5] also researched the natural-draft wire-on-tube condensers by
proposing an improved semi-empirical heat transfer correlation.
In the literature there are also works focused on analyzing forced-draft wire-on-tube condensers. Barbosa and Sigwalt [6] analyzed
heat transfer and pressure drop in prototypes of spiral wire-on-tube condenser. They evaluated the influence of geometric parameters,
where the wire spacing was the one that most contributed to the performance of the heat exchanger. Gönül et al. [7] experimentally
and numerically studied the thermal behavior of wire-on-tube heat exchangers exposed to forced convection. The authors evaluated
the heat transfer under the variation of the geometric parameters of the exchanger, as well as different airspeeds, with wire diameter
being the most important parameter in heat transfer. Saleh [8] evaluated the global heat transfer coefficient in a wire-on-tube through
an experimental and numerical study. The research was based on the temperature distribution and the heat transfer coefficient along
the length of the condenser; for this purpose, three zones were analyzed according to the state of the refrigerant.
Literature shows other studies based on the modeling of the wire-on-tube condenser. For instance, Bansal and Chin [9] developed a
model for a wire-on-tube in a real refrigerator by using finite element and incorporating thermodynamic fundamentals. This model was
proposed as a tool for the design and optimization of this type of heat exchanger. The authors analyzed the influence of geometric
parameters such as wire and tube pitches, and diameters on the thermal capacity of the condenser. Another model like the one cited
above for a wire-on-tube was proposed by Ameen et al. [10]; the authors contributed with the adequate dimensioning of the number of
tubes to achieve a complete condensation of the refrigerant under different operating conditions. Dos Santos et al. [11] proposed a
numerical model based on finite volume to characterize the thermal–hydraulic behavior of a typical wire-on-tube condenser. They
analyzed the influence of void fraction correlations considering a homogeneous two-phase flow model. Azzouzi et al. [12] studied the
effect of subcooling and analytically analyzed the condenser additive surface of the wire-on-tube condenser on the performance of a
domestic refrigerator operating with refrigerants R12, R134a, and R600a. The authors concluded that R600a had a higher coefficient
of performance, COP, and a lower additive surface compared to R134a. Jeon et al. [13] modeled a refrigeration cycle where the
wire-on-tube was characterized using a tube-by-tube method to analyze an in-line-array tube bundle condenser.
Based on the above, it can be said that the literature is fundamentally limited in characterizing this type of heat exchangers. Among
the results, it is observed that there is an interest in analyzing the effect of some geometric parameters on the performance of the heat
Fig. 1. Schematic representation and geometry of the wire-on-tube condenser under study.
3
Case Studies in Thermal Engineering 25 (2021) 100927
J.M. Belman-Flores et al.
exchanger. This way, a model of the wire-on-tube condenser can be used for a better understanding of its geometric parameters and it
can be applied for improving the design. Therefore, this work focuses on the development and validation of an approximate physical
model of a wire-on-tube condenser that allows characterizing the thermal behavior using geometric input parameters.
The present study aims to show the development of a new approximate model based on physical foundations and empirical cor­
relations for a multilayer wire-on-tube condenser, so this study aims to expand knowledge in the analysis of this design. The model has
been validated with experimental results from two real refrigerators. One of the test refrigerators works with R134a and the other with
R600a. A description of the experimental facility and procedure, and the instrumentation used in data collection are presented in the
development of this work. Then, the model developed for the evaluation of the condenser is presented, in which the thermal capacity of
the condenser and the temperatures at the outlet of the air and the refrigerant are evaluated. Besides, there is a simulation of condenser
performance based on the variation of geometric parameters. Finally, the proposed model can be used as a tool in the design and
prediction of multilayer wire-on-tube condensers.
2. Experimental facility and procedure
2.1. The multilayer wire-on-tube condenser
The heat exchanger considered in this work is a multilayer wire-on-tube like the one shown in Fig. 1a, which is composed of a tube
whose arrangement provides the shape of the layers, and wires symmetrically welded on both sides of the tube. The structure of the
heat exchanger represents a cube of height, H, width, Lw, and depth, y. The tube and wires are made of carbon steel and painted black
on its outer surface. In Fig. 1b the most representative geometric parameters of this type of heat exchangers are indicated, the external
diameters, Dw and Dt of the wires and tube, and the tube pitch, St, and the wire pitch, Sw. The geometric dimensions of the condenser are
specified in Table 1.
2.2. Experimental refrigerator
The experimental bench comprises two identical MABE refrigerators in their volumetric capacity, one works with refrigerant
R134a, model RMT1951X with a refrigerant charge of 120 g, and the other with R600a model RMS510IBBRX0 with a refrigerant
charge of 45 g, both are of the no-frost type (automatic defrost). Each refrigerator has a volumetric capacity of 0.51 m3 and its external
dimensions are 1.80 m x 0.75 m x 0.80 m (height x width x length). Each one has two compartments: a fresh food compartment and a
freezer, where heat transfer is conducted through forced convection by a fan located inside the evaporator space. The refrigerators are
also equipped with a hermetic reciprocating compressor model CBE122L2KK for R134a and model MKH113L2 for R600a, these with
different cooling capacities. Finally, there is a multilayer wire-on-tube type condenser for forced convection with identical charac­
teristics in both refrigerators (see Table 1).
In Fig. 2, it can see the experimental bench, as well as the instrumentation used, measurement equipment, a data acquisition
system, and a portable PC for storing and handling information.
2.3. Instrumentations and measurements
The refrigerators were instrumented to conduct the characterization of the multilayer wire-on-tube condenser. Three thermo­
couples were attached to the pipe wall with 3 M dielectric adhesive tape and thermal paste, thus, temperatures were measured at the
inlet, at the middle, and at the outlet of its length, thereby defining the thermal condition of the refrigerant in the condenser. While for
the airside, five thermocouples located on opposite faces of the condenser were used, thus defining the entry and exit of air in the
condenser. Six other thermocouples were located inside the refrigerator compartments, three in the freezer, and three in the fresh food
compartment, to observe the stabilization period of the refrigerator. All thermocouples used are K-type with an uncertainty of
±0.03 ◦ C.
In addition, the low and high pressures (condenser input) were measured using pressure transducers with a measurement range of
0–25 bar and uncertainty of ±1%. The mass flow rate was measured by Coriolis-effect flowmeter with uncertainty ±0.22%. The signals
generated by the measurement devices were stored in a PC-based compact RIO data acquisition system using LabView software. Data
Table 1
Geometry of the wire-on-tube condenser.
Tube inner diameter, Di
Tube outer diameter, Dt
Wire diameter, Dw
Wire length (width), Lw
Height, H
Wire pitch, Sw
Tube pitch, St
Characteristic tube length, Ltp
Characteristic wire length, Lwp
Total tube length, Lt
Number of layers
3.34 mm
4.75 mm
1.37 mm
165.1 mm
161.0 mm
4.06 mm
25.4 mm
4.06 mm
25.4 mm
8.5 m
7
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Case Studies in Thermal Engineering 25 (2021) 100927
J.M. Belman-Flores et al.
Fig. 2. Test bench showing refrigerator that works with R600a on the left, the PC and data acquisition system in the middle, and the refrigerator
that works with R134a on the right.
recording was established at 2-s intervals throughout the measurement process. The tests conducted without a thermal load had an
approximate duration of 12 h and 20 h for tests with a thermal load. Also, a speed regulator dimmer was used to control the speed of the
fan attached to the condenser, and an anemometer was used to measure the airspeed with an uncertainty of ±3% of reading.
2.4. Test procedure
Different steady-state tests were carried out to better map the thermal behavior of the condenser and validate the model proposed
in this study. Both refrigerators were evaluated simultaneously in a room chamber with a temperature of 25 ◦ C ± 1 ◦ C and relative
humidity of 60 ± 5% (based on both factory evaluations and the Mexican norm NOM-015-ENER-2012). To simulate a range of
operating conditions in both refrigerators, in this work the following parameters were varied: the damper position (control element),
the thermal load (food, which was simulated with containers full of water) in the compartments, and the airspeed in the condenser. The
airspeed was varied by regulating the voltage using a dimmer model SCR2000 with a voltage input of 220/110 V and voltage output
range between 50-220 V. Table 2 defines the values for which the different tests were carried out, considering that these parameters
can alter the thermal behavior of the refrigerator. The position of the damper and the thermal load are parameters directly associated
with the usage habits, while the speed of the air is associated with some mechanical failure of the fan attached to the condenser. Note
that the tests were obtained with the combination of these parameters.
The tests were carried out without opening the doors, starting from a transient behavior (compressor start-up) until reaching
thermal stability in both compartments of the refrigerator, this occurred around 6 h without thermal load and around 12 h with the
thermal load. This was observed with the thermocouples located within the compartments, which presented a maximum temperature
variation of ±2 ◦ C during the ON-OFF cycle. Each steady-state condition, that is, each point used in the validation, was determined by
averaging the temperature in the last 20 min of an ON period. Note that in this period the condenser works, that is, the conditions of the
air inlet and outlet temperature in the condenser are known since the fan works. Also, the stable thermal behavior of the refrigerator is
featured.
Table 2
Variation of test parameters.
Parameters
Damper position
Low
Medium
High
Thermal load [liters]
Airspeed [m/s]
Freezer compartment
Fresh food compartment
2
4
6
8
5
9
13
17
5
2
3
4
5
Case Studies in Thermal Engineering 25 (2021) 100927
J.M. Belman-Flores et al.
3. Model description
The model presented in this work for a multilayer wire-on-tube condenser is based on physical foundations together with the
incorporation of empirical correlations. Note that in this study we do not consider a hydraulic model, our interest is focused on thermal
analysis. The input parameters of the model are represented by the geometric structure of the condenser such as the external diameters
of the wires and tube, the tube and wire pitch. Other input parameters are the pressure and temperature of the refrigerant at the
condenser inlet, as well as the mass flow of the refrigerant and the air temperature at the condenser inlet.
The output parameters are those that provide knowledge about the thermal behavior of the equipment and with which the pro­
posed model will be validated according to the experimental part. In this study, the refrigerant outlet temperature, the air temperature
at the condenser outlet, and the thermal capacity of the equipment have been considered as parameters to be validated. The math­
ematical expressions developed during the characterization of the condenser were programmed in the Engineering Equation Solver
software, EES, Klein [14].
3.1. Thermal analysis
The thermal analysis of the wire-on-tube condenser is based on the ε-NTU method, and on the characterization defined by three
zones according to the condition of the refrigerant: desuperheating, condensation, and subcooling zone. In each zone, an energy
balance has been applied between both fluids (refrigerant and air), expressed in a general way by the following equations:
)
)
(
(
ṁr · hr,i zone − hr,o zone = Cair,zone · Xzone · Tair,ozone − Tair,izone
(1)
)
)
(
(
ṁr · hr,i zone − hr,o zone = εzone · Cmin,zone · Tr,ozone − Tair,izone
(2)
From Eq. (1), Cair,zone represents the air-side thermal capacitance for each zone. To define the air cooling more closely, in the multilayer wire-on-tube condenser by forced convection, the model considers the coil arrangement. In this case, the air stream is split into all
three zones, the air mass flow is proportional to the area of each heat transfer zone concerning the total area of the heat exchanger.
Therefore, the fractions of the mass flow for each zone change and that in turn affects the thermal capacitance depending on the
following proportion, Martins Costa and Parise [15]:
Xzone =
Azone
Atotal
(3)
On the other hand, in Eq. (2) the effectiveness, εzone, in each zone of the wire-on-tube condenser is indicated, this parameter de­
pends on the flow arrangement. For the desuperheating and subcooling zone, Eq. (4) is used, while for the condensation zone Eq. (5),
Incropera et al. [16].
)
(
1
·{1 − exp[ − Cr zone · (1 − exp( − NTUzone ))]}
εzone =
(4)
Cr zone
(5)
εzone = 1 − exp( − NTUzone )
The NTUzone represents the number of heat transfer units in each zone. The global heat transfer coefficient, U, is largely defined by
the system. It is determined as a function of the radiation heat transfer in the tube wall, and by the thermal resistance by convection of
both fluids (air and refrigerant). This coefficient is based on the total external area (external area of the tube and total area of the
wires), as shown in Eq. (6). In this sense, the thermal contact resistance between the tube and the wire is not considered because the
wires are welded to the surface of the tube.
U=R
1
A
hi
t ext /Dt in )
+ RA · Dt in · 2ln(D
+ ho 1· η
· kt
(6)
s
RA indicates the ratio between the total outer area of the wire-on-tube condenser and the inner area of the tube; whereas ηs rep­
resents the global surface efficiency which can be estimated using Eq. (7).
ηs = 1 − (1 − ηw )
Aw
Atotal
(7)
ηw indicates the efficiency of the wires and represents one of the factors that affect the thermal performance of the wire-on-tube
condenser. This value is obtained considering an adiabatic boundary condition through Eq. (8), Incropera et al. [16]. AW and Atotal
indicate the total area of the wires and the total area of the outer surface, respectively.
ηw =
tanh(mL)
mL
(8)
where,
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Case Studies in Thermal Engineering 25 (2021) 100927
J.M. Belman-Flores et al.
√̅̅̅̅̅̅̅̅̅̅
4ho
m=
kt Dw
L=
(9)
St
2
(10)
3.2. External heat transfer coefficient
The side-air heat transfer coefficient (Eq. (6)) is obtained by combining convection and radiation effects as shown in Eq. (11).
(11)
ho = hconv + hrad
To estimate the convection heat transfer coefficient, hconv, the modified Zukauskas correlation was used, Lee et al. [17]. This
correlation considers the current configuration of the airflow, flow crossed to the tubes and parallel to the wire (tube cross, see Fig. 1a),
through the correction coefficients Fc and Fp shown in Eq. (12). It also considers the relationship between the area of the tubes, Atp, and
the area of the wires, Awp, concerning the total area of the wire-on-tube condenser.
Fp = 0.063 · Re0.37
at , Fc = 1.3
(12)
Atp = π · Dtext · Ltp
(13)
Awp = π · Dw · Lwp
(14)
In this study, a total convective coefficient is considered, both for the tubes, ho,t, and for the wires, ho,w, indicated in Eqs. (15) and
(16), considering the geometric characteristics of the condenser.
(
(
)0.25
)
Prair
kair
Atp
0.36
ho,t = Fc · C · Renairt · Prair
·
·
·
(15)
Prs,air
Dtext Atp + 2 · Awp
(
0.36
·
ho,w = Fp · ηw · C · Renairw · Prair
Prair
Prs,air
)0.25
·
)
(
kair
Awp
·
Dw Atp + 2 · Awp
(16)
The constants C and n are defined in Table 3 for the magnitude of the Reynolds number obtained in each zone of the condenser
under study, Zukauskas [18]. The modified Zukauskas correlation was compared with other correlations, which is shown in section 4.
On the other hand, the radiation transfer coefficient is obtained by Eq. (17), where σ is the Stefan-Boltzman constant and εapp is the
apparent emissivity of the outer surface of the wire-on-tube condenser, which has considered a value of 0.88, Bansal and Chin [9].
hrad = εapp · σ ·
4
Tw4 − Tamb
Tw − Tamb
(17)
3.3. Internal heat transfer coefficient
To calculate the convective coefficient inside the tube (refrigerant side), representative correlations are used in each zone, con­
cerning the flow regime and the phase in which the refrigerant is. For the desuperheating and subcooling zones, the heat transfer
coefficient is approximated by the Kays and London correlation. It is used for single-phase flow in compact heat exchangers, where the
constants a and b depend on the flow regime of the refrigerant, Kays and London [19].
(18)
2
hdsh,sub = a · Gr · Cpr · Rebr · Prr− 3
For the analysis of the condensation process for the flow regime and the condenser configuration, a horizontal flow is considered
throughout the entire exchanger. Also, considering that low vapor speeds are handled (Reg < 35000), a stratified flow is defined where
the gravitational forces that act on the flow are of greater magnitude concerning the vapor shear forces, Incropera et al. [16]. Due to
these characteristics, the correlation of Chato, Dobson and Chato [20], is proposed for the calculation of the heat transfer coefficient in
the condensation zone as shown in Eq. (19).
Table 3
Values of the constants C and n for the Zukauskas correlation [18].
Reynolds number
C
n
1–40
40 – 1x103
1x103 – 2x105
2x105 – 1x106
0.75
0.52
0.26
0.076
0.4
0.5
0.6
0.7
7
Case Studies in Thermal Engineering 25 (2021) 100927
J.M. Belman-Flores et al.
)
(
g · ρf · ρf r − ρg r · kf 3r · hfg
hcond = 0.555 · [ r
)]0.25
(
μf r · Dt in · Tg − Tw
(19)
Where hfg is obtained as:
) 3
)
(
(
hfg = hg r − hf r + · Cpf r · Tg − Tw
8
(20)
Finally, the total heat dissipated by the multi-layer wire-on-tube condenser is obtained from the sum of the heat dissipated in each
of the areas analyzed. Furthermore, the total area of exchange is also estimated by adding the area of each zone.
Q = Qdsh + Qcond + Qsub
(21)
A = Adsh + Acond + Asub
(22)
3.4. Simulation strategy
Fig. 3 illustrates the simulation strategy of the model developed in the EES Software. It starts with the geometric parameters and
operating conditions. A structure of procedures and functions that facilitate the calculation of the thermodynamic properties for both
fluids in each of the zones mentioned above is proposed. The figure shows the coupling of each of the zones by estimating parameters
until reaching a determining factor on the total surface of the wire-on-tube condenser. Once the system of equations is adjusted and
solved, the output data are obtained, which will be validated with the experimental work.
3.5. Propagation of errors
An analysis of the uncertainty associated with the estimation of the parameters from the measurements was carried out. The EES
software was used to calculate the relative errors in the output parameters, specifically in the heat transfer, Q, by using the
Fig. 3. Flowchart for the model of the multilayer wire-on-tube condenser.
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J.M. Belman-Flores et al.
methodology included in the same software (Taylor and Kuyatt [21]). For heat transfer, a maximum error of ± 0.8% was obtained;
temperatures are a direct measurement. This analysis reflects a greater foundation in the reliability of the results and the validation of
the model presented.
4. Results discussion
This section presents the validation of the model developed for the wire-on-tube condenser. Validation is focused on comparing the
output parameters of the model (Fig. 3) with those estimated or measured experimentally. It should be remembered that the exper­
imental study was based on real refrigerators operating under different conditions (Table 2).
Fig. 4 illustrates the thermal capacity of the multi-layer wire-on-tube condenser, on one hand, the capacity obtained by the model,
and on the other hand, the capacity obtained by experimental measurements. The figure presents the results of the two test re­
frigerators operating on R134a and R600a. Likewise, the comparison between different correlations used to estimate the external heat
transfer coefficient is shown, where the modified Zukauskas correlation represents a better coupling to the model. It can be observed
that the model predicts the thermal capacity within a maximum marginal error of ±5%, a smaller error than that published in previous
works for a WTC (Bansal and Chin [9]). Therefore, the model approximates heat dissipation very adequately.
In Fig. 4 the thermal behavior of both refrigerants can also be observed, in which the R134a reflects a higher thermal capacity,
reaching a maximum value of 310W. While the refrigerator operating with R600a remains below 250W for different operating
conditions.
Meanwhile, Fig. 5 shows the prediction of the refrigerant temperature at the outlet of the condenser. It can be observed that the
model’s prediction is below a relative error of ±0.5K, for both refrigerators. The refrigerator with R600a has higher temperatures than
R134a. Fig. 6 illustrates the prediction of air temperature at the outlet of the wire-on-tube condenser. We can see that the model
predicts again within a maximum error of ±0.5K.
The model prediction for these three parameters has shown relative errors below ±5% for the thermal capacity and errors of ±0.5K
for the air and refrigerant outlet temperatures. Consequently, an adequate approximation of the model developed in this study for the
multi-layer wire-on-tube condenser can be confirmed.
4.1. Parametric analysis
According to the proper characterization of the condenser, in this section, a possible application of the model is presented to
simulate the influence of the main geometrical parameters on the thermal capacity of the multi-layer wire-on-tube condenser. This
application could guide the design engineer in the decision-making process. Among the parameters evaluated are the tube diameter, Dt,
wire diameter, Dw, tube pitch, St, and wire pitch, Sw.
Fig. 7 illustrates the behavior for the thermal capacity of the condenser when varying the diameter of the tube and wire for both
refrigerators working with R134a and R600a. For this simulation, the length of the tube, the wire pitch and tube pitch are considered
constant. In general, it is observed that as the tube diameter increases, Dt, the thermal capacity of the wire-on-tube condenser rises. The
most significant increase is observed in a range of 0.0045 < Dt < 0.006 m; for larger pipe diameters, the increase in thermal capacity is
Fig. 4. Prediction of wire-on-tube condenser thermal capacity and comparison between correlations. Zukauskas [18], Hilpert [16], Churchill and
Bernstein [16], Perkins and Lepert [22], Whitaker [16], Fand and Keswani [23].
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Case Studies in Thermal Engineering 25 (2021) 100927
J.M. Belman-Flores et al.
Fig. 5. Prediction of refrigerant temperature at wire-on-tube condenser outlet.
Fig. 6. Prediction of air temperature at wire-on-tube condenser outlet.
Fig. 7. Thermal capacity of wire-on-tube condenser vs tube and wire diameters.
practically insubstantial. In contrast, the increase in wire diameter, Dw, causes a growth in thermal capacity. The increase in both
geometric parameters presents an increase in the heat transfer surface, consequently, there is a rise in the thermal capacity, reaching a
maximum thermal capacity for both refrigerants (250W for R600a and 340W for R134a) due to the physical limitation of other
geometric parameters. Finally, the figure shows a higher thermal capacity for the condenser with R134a, for example, on average there
is a difference of about 85 W between the capacities of both refrigerants. It must be considered that the refrigerant charge is different in
both refrigerators.
The thermal capacity of the condenser is also affected by the tube pitch and wire pitch, as shown in Fig. 8, which represents the
behavior for the two heat exchangers working with R134a and R600a. In addition, the behavior of the heat exchange surface A, with
respect to the variation of geometric parameters is also illustrated. In Fig. 8a it can be seen that with the increase of the tube pitch there
is a rise in the thermal capacity of the wire-on-tube condenser, this rise is due to a slight increase in the length of the tube therefore the
surface increases. According to the variation of the tube pitch from 0.022 to 0.029, there is a 20% increase in the heat exchanger area,
which represents an increment of 15 W for both condensers.
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J.M. Belman-Flores et al.
Fig. 8. Thermal capacity of wire-on-tube condenser vs tube and wire pitches.
Regarding the wire pitch, Fig. 8b shows a variation of 2.5 mm–5 mm, the decrease in the wire pitch causes an increment in the
thermal capacity and in the heat exchange surface. As the wires approach each other, the air flow begins to isolate in an enclosed space,
thus reducing the convective effect and therefore the combined heat transfer coefficient. Thus, the rise in heat transfer is due to the
increase in the area by the wires.
4.2. Convection heat transfer coefficient
Alternatively, the model can also be used to analyze the variation of the external heat transfer coefficient. Such behavior is shown in
Fig. 9 for changes in the Reynolds number of both the tube case (Fig. 9a) and wire case (Fig. 9b). The blue lines in Fig. 9a represent the
behavior of the heat transfer coefficient when varying the Reynolds number, in which the air velocity varies in a range of 2–5 m/s, also
showing the influence of the pipe diameter over the heat transfer coefficient. As expected, as the Reynolds number increases, the
convective heat transfer coefficient rises, while the increment of the pipe diameter causes an insignificant increase in the convective
coefficient (black dotted lines). For example, the most notable change is observed at high speeds (5 m/s) where the increase in pipe
diameter from 4.5 mm to 6.0 mm, represents a 3% increase in the heat transfer coefficient.
As for Fig. 9b, it is observed that the heat transfer coefficient increases as the Reynolds number on the wire case increases, for a wire
diameter of 1.6 mm the convective coefficient increases up to 93% from a speed of 2 m/s (Reynolds number of 200) to 5 m/s (Reynolds
number of 500). In contrast, the increase in the wire diameter causes a reduction in the convective coefficient (black dotted lines),
where there is a narrowing of the cross-section through which the air flow circulates, which would also physically generate an increase
in the speed of the air. The most abrupt changes in the convective coefficient are obtained in high Reynolds numbers (speeds of 5 m/s).
5. Conclusions
In this work, the thermal behavior of a multilayer wire-on-tube condenser has been researched through the development of a
physical model programmed in the EES software. This was validated with stationary experimental data obtained with real re­
frigerators. The behavior of the condenser was characterized in three zones associated with the state of the refrigerant: desuperheating,
condensation, and subcooling, where energy balances were made, and the ε-NTU method was used. Also, the model incorporated
empirical correlations for the air side and refrigerant side heat transfer coefficients.
In general, the model proposed in this work was able to predict the thermal behavior in a very adequate way, since the output
parameters of the model represented a maximum error of ±5% for heat transfer and ±0.5K for refrigerant and air outlet temperatures.
Therefore, the model was used as a simulation tool to analyze the influence of the geometric parameters input to the model on the
energy transfer and the convective heat transfer coefficient. In the results, it was observed that the tube and wire diameters, as well as
the tube pitch and wire pitch, affect to a certain extent the heat dissipation, the heat exchange surface, and the convective coefficient.
Finally, the model can be proposed for simulation, design optimization, or retrofit analysis with alternate refrigerants. Also, the
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J.M. Belman-Flores et al.
Fig. 9. Convection heat transfer coefficient vs Reynolds number, a) tube case, b) wire case.
model can analyze the effect of several design parameters, including the variation in airspeed, thus showing a greater panorama when
making decisions in the engineering of these refrigeration systems.
CRediT author contribution statement
J.M. Belman-Flores: conceptualization, methodology, investigation, visualization, formal analysis, writing. Y. Heredia-Aricapa:
conceptualization, software, formal analysis, writing. Juan J. García-Pabón: Investigation, review. A. Gallegos-Muñoz: investiga­
tion, review. J. Serrano-Arellano: review. C. Gutiérrez Pérez-Reguera: review.
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.
Acknowledgements
We acknowledge University of Guanajuato for their sponsorship in the realization of this work. We also want to thank the Company
Mabe TyP (through César Gutiérrez) for the donation of the refrigerators in the performing of the tests.
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