Experimental Thermal and Fluid Science 29 (2005) 511–521
www.elsevier.com/locate/etfs
A study of the heat transfer characteristics of a compact spiral coil
heat exchanger under wet-surface conditions
Paisarn Naphon, Somchai Wongwises
*
Fluid Mechanics, Thermal Engineering and Multiphase Flow Research Lab. (FUTURE), Department of Mechanical Engineering,
King MongkutÕs University of Technology Thonburi, Bangmod, Bangkok 10140, Thailand
Received 5 March 2004; accepted 16 July 2004
Abstract
The heat transfer characteristics and the performance of a spiral coil heat exchanger under cooling and dehumidifying conditions
are investigated. The heat exchanger consists of a steel shell and a spirally coiled tube unit. The spiral-coil unit consists of six layers
of concentric spirally coiled tubes. Each tube is fabricated by bending a 9.27 mm diameter straight copper tube into a spiral-coil of
five turns. Air and water are used as working fluids. The chilled water entering the outermost turn flows along the spirally coiled
tube, and flows out at the innermost turn. The hot air enters the heat exchanger at the center of the shell and flows radially across
spiral tubes to the periphery. A mathematical model based on mass and energy conservation is developed and solved by using the
Newton–Raphson iterative method to determine the heat transfer characteristics. The results obtained from the model are in reasonable agreement with the present experimental data. The effects of various inlet conditions of working fluids flowing through the
spiral coil heat exchanger are discussed.
2004 Elsevier Inc. All rights reserved.
Keywords: Heat transfer characteristic; Spiral coil heat exchanger; Enthalpy effectiveness; Humidity effectiveness
1. Introduction
Due to the curvature of the tube, a centrifugal force is
generated as fluid flows through the curved tubes. Secondary flows induced by the centrifugal force has significant ability to enhance the heat transfer rate. Helical
and spiral coils are known types of curved tubes which
have been used in a wide variety of applications for
example, heat recovery processes, air conditioning and
refrigeration systems, chemical reactors, food and dairy
processes. Heat transfer and flow characteristics in
curved tubes have been widely studied by researchers
both experimentally and theoretically. Garimella et al.
[1] presented average heat transfer coefficients of lami-
*
Corresponding author. Tel.: +662 470 9115; fax: +662 470 9111.
E-mail address: somchai.won@kmutt.ac.th (S. Wongwises).
0894-1777/$ - see front matter 2004 Elsevier Inc. All rights reserved.
doi:10.1016/j.expthermflusci.2004.07.002
nar and transition flows for forced convection heat
transfer in coiled annular ducts. Prabhanjan et al. [2]
compared the heat transfer rates between a helically
coiled heat exchanger and a straight tube heat exchanger. Due to complexity of the heat transfer processes
in the curved tubes, experimental studies are very difficult to handle. Numerical investigations are needed.
Bolinder and Sunden [3] solved the parabolized
Navier–Stokes and energy equations by using a finitevolume method. The steady, fully developed laminar
forced convective heat transfer in helical square ducts
for various Dean and Prandtl numbers were analyzed.
Zheng et al. [4] applied a control-volume finite difference
method with second-order accuracy for solving the
three-dimensional governing equations to analyze the
laminar force convection and thermal radiation in a participating medium inside a helical pipe. Acharya et al. [5]
numerically studied the phenomenon of steady heat
512
P. Naphon, S. Wongwises / Experimental Thermal and Fluid Science 29 (2005) 511–521
Nomenclature
A
D
Eh
Gmax
h
hr
i
J
k
M
n
Pr
r
Rc
Rn
T
U
a
Cp
De
Ew
hD
ifg
j
area
tube diameter, m
enthalpy effectiveness
mass flux based on minimum free flow area,
kg/m2s
heat transfer coefficient, W/m2 C
combined conductance through tube surface
and water inside tube, W/m2 C
enthalpy, kJ/kg
Colburn j factor
thermal conductivity, W/m C
mass flow rate per coil, kg/s
number of coil turns
Prandtl number
tube radius, m
coil characteristics, kg C/kJ
average radius of curvature of each coil turn,
m
temperature, C
overall heat transfer coefficient, W/m2 C
radius change per radian, m/radian
specific heat, kJ/(kg C)
Dean number
humidity effectiveness
mass transfer coefficient, kg/m2s
enthalpy of condensation, kJ/kg
number of segments
transfer enhancement in coiled-tube heat exchangers due
to chaotic particle paths in steady, laminar flow with
two different mixings. The velocity vectors and temperature fields were discussed. Lin and Ebadian [6] applied
the standard k–e model to investigate three-dimensional
turbulent developing convective heat transfer in helical
pipes with finite pitches. The effects of pitch, curvature
ratio and Reynolds number on the development of effective thermal conductivity and temperature fields, and
local and average Nusselt numbers were discussed. Sillekens et al. [7] employed the finite difference discretization to solve the parabolized Navier–Stokes and
energy equations. The effect of buoyancy forces on heat
transfer and secondary flow was considered. In their second paper, Rindt et al. [8] studied the development of
mixed convective flow with an axial varying wall temperature. The results were compared with the constant
wall temperature boundary conditions. Lemenand and
Peerhossaini [9] simplified the Navier–Stokes and energy
equations as a thermal model to predict heat transfer
rates in a twisted pipe of two tube configurations, helically coiled or chaotic.
Compared to the numerous investigations in the
helically coiled tubes, there are few researches on the heat
Le
m
Nu
Q
Rmin
Re
t
x
Lewis number
total mass flow rate, kg/s
Nusselt number
heat transfer rate, W
minimum coil radius, m
Reynolds number
tube thickness, m
humidity ratio
Subscripts
a
air
i
inside
L
latent
max
maximum
o
outside
s
surface, wall
sat
saturated
w
water
avg
average
in
inlet
m
moist air
min
minimum
out
outlet
S
sensible
T
total
wv
water vapor
transfer and flow characteristics in the spirally coiled
tube in open literature. The most productive studies have
been continuously carried out by Ho et al. [10–12]. The
relevant correlations of the tube-side and air-side heat
transfer coefficients reported in literature were used in
the simulation to determine the thermal performance of
the spiral-coil heat exchanger under cooling and dehumidifying conditions. The simulation results were validated by comparing with measured data. Due to the
lack of the heat transfer coefficient correlations obtained
directly from the spirally coiled tube configuration, Naphon and Wongwises [13] proposed a correlation for
the average in-tube heat transfer coefficient for a spiral
coil heat exchanger under dehumidifying conditions. Recently, in their second and third papers (Naphon and
Wongwises [14,15]), mathematical models to determine
the performance and heat transfer characteristics of spirally coiled finned tube heat exchangers under wet-surface conditions and dry-surface conditions were
developed and investigated. There was reasonable agreement between the results obtained from the experiment
and those from the developed model.
As mentioned above, only a few works on the heat
transfer characteristics in spiral coil heat exchangers
P. Naphon, S. Wongwises / Experimental Thermal and Fluid Science 29 (2005) 511–521
have been reported. In the present study, the heat transfer characteristics and performance of a spiral coil heat
exchanger under cooling and dehumidifying conditions
which have never been investigated before, are studied.
The results obtained from the developed model are validated by comparing with measured data. In addition,
the effects of relevant parameters on the model prediction are also discussed.
513
Air inlet
Water outlet
Air outlet
Water inlet
2. Experimental apparatus and method
The experimental apparatus described in Naphon
and Wongwises [13] was used in the present study. A
schematic diagram of the experimental apparatus is
shown in Fig. 1. The test loop consists of a test section,
refrigerant loop, chilled water loop, hot air loop and
data acquisition system. The water and air are used as
working fluids. The test section is a spiral-coil heat exchanger which consists of a shell and spiral coil unit as
shown in Fig. 2. The test section and the connections
of the piping system are designed such that parts can
be changed or repaired easily. In addition to the loop
components, a full set of instruments for measuring
and controlling the temperature and flow rate of all fluids is installed at all important points in the circuit.
Air is discharged by a centrifugal blower into the
channel and is passed through a straightener, heater,
guide vane, test section, and then discharged to the
atmosphere. The purpose of straightener is to avoid
the distortion of the air velocity profile. The speed of
the centrifugal blower is controlled by the inverter. Air
velocity is measured by a hot wire anemometer. The test
channel is fabricated from zinc, with an inner diameter
of 300 mm and a length of 12 m. The channel wall is
insulated with a 6.40 mm thick Aeroflex standard sheet.
Fig. 2. Schematic diagram of the section of the spirally coiled tube
heat exchanger.
The inlet and outlet sections for hot air flowing through
the test section unit are shown in Fig. 2. The hot air
flows into the center core and then flows across the spiral coils, radially outwards the wall of the shell before
leaving the heat exchanger at the air outlet section
(Fig. 2). The inlet temperature of the air is raised to
the desired level by using electric heaters controlled by
a temperature controller. The entering and exiting air
temperatures of the heat exchanger are measured by
type T copper–constantan thermocouples extending inside the air channel in which the air flows. The 1 mm
diameter thermocouple probes are located at different
four positions at the same cross section, 60 cm upstream
of the heat exchanger inlet and also four positions at
50 cm downstream of the exit of the heat exchanger.
The inlet and outlet relative humidities of air are detected by humidity transmitters.
The chilled water loop consists of a 0.3 m3 storage
tank, an electric heater controlled by adjusting the voltage, a stirrer, and a cooling coil immerged inside a storage tank. R22 is used as the refrigerant in the cooling
Fig. 1. Schematic diagram of experimental apparatus.
514
P. Naphon, S. Wongwises / Experimental Thermal and Fluid Science 29 (2005) 511–521
coil. After the temperature of the water is adjusted to the
desired level, the chilled water is pumped out of the storage tank, and is passed through a filter, flow meter, test
section, and returned to the storage tank. The by-pass is
used for passing the excess water back to the water tank
for the experiments of low water flow rate. The flow rate
of the water is measured by a flow meter with a range of
0–10 GPM.
The spiral-coil heat exchanger consists of a steel shell
with a spirally coiled tube unit. The spiral-coil unit consists of six layers of spirally coiled copper tubes. Each
tube is constructed by bending a 9.27 mm diameter
straight copper tube into a spiral-coil of five turns.
The innermost and outermost diameters of each spiralcoil are 6.77 and 22.76 cm, respectively. Each end of
the spiral-coils is connected to the vertical manifold tube
with outer diameter of 15.9 mm. The dimensions of the
spiral-coil heat exchanger are listed in Table 1. The copper–constantan thermocouples are installed at the third
layer of the spiral-coil unit from the uppermost layer,
each with two thermocouples to measure the water temperature and wall temperature.
The water temperature is measured in five positions
with 1 mm diameter probes extending inside the tube
in which the water flows. Thermocouples are also
mounted at five positions on the tube wall surface to
measure the wall temperatures. Thermocouples are soldered into a small hole drilled 0.5 mm deep into tube
wall surface and fixed with special glue applied to the
outside surface of the copper tubing. With this method,
thermocouples are not biased by the fluid temperatures.
An overall energy balance was performed to estimate
the extent of any heat losses or gains from the surroundings. In the present study, only the data that satisfy the
energy balance conditions; jQw Qaj/Qavg is less than
0.05, are used in the analysis. The total heat transfer
rate, Qavg, is averaged from the air-side heat transfer
rate, Qa, and the water-side heat transfer rate, Qw.
Experiments were conducted with various temperatures
and flow rates of hot air and chilled water entering the
test section. The chilled water flow rate was increased
Table 1
Dimensions of the spirally coiled tube heat exchanger
Parameters
Dimensions
Outer diameter of tube, mm
Inner diameter of tube, mm
Innermost diameter of spiral coil, mm
Outermost diameter of spiral coil, mm
Number of coil turns
Number of spiral coils
Distance between the spiral coil layer, mm
Diameter of shell, mm
Length of shell, mm
Diameter of hole at air- inlet, mm
Diameter of closed plate at air-outlet, mm
9.3
7.8
67.8
227.6
5
6
13.7
300
250
65
230
Table 2
Experimental conditions
Variables
Range
Inlet-air temperature, C
Inlet-water temperature, C
Air mass flow rate, kg/s
Water mass flow rate, kg/s
50–60
10–20
0.01–0.08
0.08–0.24
Table 3
Uncertainty of measurement
Instruments
Accuracy
Uncertainty
Hot wire anemometer (air velocity, m/s)
Rotameter (water mass flow rate, kg/s)
Thermocouple type T
Data logger, (C)
Humidity transmitter (%RH)
2.0%
0.2%
0.1%
0.04%
0.5%
±0.23
±0.003
±0.03
±0.22
in small increments while the hot air flow rate, inlet
chilled water and hot air temperatures were kept constant. The flow rate of hot air was controlled by adjusting the speed of the centrifugal blower. An inverter was
used to control the speed of the motor for driving the
blower. The inlet hot air and chilled water temperatures
were adjusted to the desired level by using electric heaters controlled by temperature controllers. The system
was allowed to approach the steady state before data
were recorded. The steady state condition was reached
when the temperature and flow rates at all measuring
points no longer fluctuated. After stabilization, the variables at the locations mentioned above were recorded.
Temperatures at each position were measured five times.
Period of each measurement was five minutes. Finally,
temperature data at each position was averaged over
the time period. The range of experimental conditions
in this study and uncertainty of the measurement are
given in Tables 2 and 3, respectively.
3. Mathematical modelling
The heat transfer characteristics of the compact spiral
coil heat exchanger under wet-surface conditions can be
determined from the conservation equations of mass
and energy. The mathematical model is based on that
of Ho et al. [12] and, Naphon and Wongwises [14] with
the following assumptions:
• Flows of air and water are steady.
• There is no heat loss between the system and
surrounding.
• Air-side convective heat transfer coefficients at each
section of a coil turn in horizontal plane is equal.
• Water-side convective heat transfer coefficient at each
section of a coil turn in horizontal plane is equal.
P. Naphon, S. Wongwises / Experimental Thermal and Fluid Science 29 (2005) 511–521
• Thermal resistance of liquid film is neglected.
• Each completed coil turn is approximately circular.
• Thermal conductivity of the spirally coiled tube is
constant.
3.1. Air-side heat transfer
When the surface temperature of the spirally coiled
heat exchanger is below the dew-point temperature of
the in-coming air, a portion of the vapor in the humid
air stream is condensed on the coil surface and removed
as liquid. By considering the control volume of each segment in Fig. 3, the total heat transfer rate is determined
from the sum of latent and sensible heat as follows:
dQT ¼ dQS þ dQL
ð1Þ
where dQT, dQS, and dQL are the total heat, sensible
heat and latent heat, respectively.
dQS ¼ ho dAo ðT a;in T s Þ
ð2Þ
where ho is the air-side heat transfer coefficient, dAo is
the outside surface area, Ta,in is the inlet-air temperature, and Ts is the tube surface temperature.
The heat released is given by the following latent heat
transfer rate:
dQL ¼ dM wv ifg
C p;m ¼ C p;a þ xa C p;wv
515
ð6Þ
Substituting Eq. (6) into Eq. (5) and assuming Le is
approximately equal to 1, we get
ho dAo
dQT ¼
ð7Þ
ðia;in isat;s Þ
C p;m
where ia, in is the inlet enthalpy of air, and isat, s is the
enthalpy at saturated conditions at tube surface
temperature.
3.2. Water-side heat transfer
The heat transfer rate in terms of the water flow rate
can be given as
dQT ¼ M w C p;m dT w
ð8Þ
The heat transfer rate to the water can be expressed as
dQT ¼ hr dAo ðT s T w Þ
ð9Þ
where
1
tdAo
dAo
¼
þ
hr kAave dAi hi
ð10Þ
where t is the tube thickness, Aave is the average surface
area, and hr is the combined conductance through the
tube surface and water inside tube.
ð3Þ
where ifg is the enthalpy of condensation and dMwv is
the mass transfer rate of the water vapor, defined as
dM wv ¼ hD dAo ðxa;in xsat;s Þ
ð4Þ
where hD is the mass transfer coefficient, xa,in is the inlet
humidity ratio of air, and xsat,s is the humidity ratio at
saturated conditions at the tube surface temperature.
Substituting Eqs. (2)–(4) into Eq. (1) gives
ho
1
dQT ¼
C p;m ðT a;in T s Þ þ ðxa;in xsat;s Þifg
Le
C p;m dAo
ð5Þ
where the Lewis number, Le, is defined by Le ¼ hDhCop;m
The specific heat of the moist air, Cp,m, is the sum of
the specific heat of dry air and water vapor
3.3. Energy balance
Considering the energy balance over the control volume for each segment, we get
ho dAo
ðia;in isat;s Þ ¼ hr dAo ðT s T w Þ
C p;m
Rearranging gives
ho
ðT s T w Þ
¼ Rc
¼
hr C p;m ðia;in isat;s Þ
isat;s ¼ 10:90748 þ 1:22045T s þ 0:05652T 2s
Ta,out , ia,out, ωa,out
Wate r flow
j+1
Tube wall
j
j-1
dθ
Rn-1
1
n-1
n
n+1
Tw,in
Tw,out
Water flow
2
3
Ts,out
Air flow
Air flow
ð12Þ
The enthalpy of the saturated air, isat,s, at the wet surface
temperature in Eq. (12) is determined from a equation
used by Ho and Wijeysundera [12]:
Air flow
Air flow
ð11Þ
Ta,in, ia,in, ω a,in
Ts,in
Air flow
Fig. 3. Schematic diagram of simulation approach and control volume of each segment.
ð13Þ
516
P. Naphon, S. Wongwises / Experimental Thermal and Fluid Science 29 (2005) 511–521
Substituting Eq. (13) into Eq. (12) and rearranging, we
get
1
0:05652T 2s þ 1:22045 þ
Ts
Rc
Tw
þ 10:90749 ia;in ¼0
ð14Þ
Rc
The energy balance over the control volume for each
segment may be written in terms of the water flow rate
as follows:
T s;out þ T s;in T w;out T w;in
hr dAo
2
2
¼ M w C p;w ðT w;out T w;in Þ
On rearranging, we get
1
ðb½T s;out þ T s;in T w;in ½b 1Þ
T w;out ¼
ðb þ 1Þ
ð15Þ
hr dAo
2M w C p;w
1
þ 1:22045 þ
T s;in
Rc
T w;in
þ 10:90749 ia;in ¼0
Rc
0:05652T 2s;in
ð22Þ
for 300 < De < 2200, Pr P 5
The air-side heat transfer coefficient correlation of the
spirally coiled heat exchanger for wet-surface conditions
was also developed from the same experimental data of
Naphon and Wongwises [13]. The equation is as follows:
ho
Pr2=3 ¼ 0:135Re0:318
o
Gmax C p;m
ð17Þ
for Reo < 6000
In addition, the spiral coil heat exchanger configurations and properties of working fluids, as well as the
operating conditions, are also needed. The iteration
process is described as follows:
ð19Þ
Substituting Eq. (16) into Eq. (18) we get
1
b
2
0:05652T s;out þ 1:22045 þ T s;out
Rc Rcðb þ 1Þ
1
þ 10:90749 ia;in ½bT s;in ðb 1ÞT w;in ¼ 0
Rcðb þ 1Þ
ð20Þ
4. Solution method
The spiral-coil unit consists of six layers of spirally
coiled tubes. Each coiled tube is divided into five circular
coil turns having the following mean radius:
Rn ¼ ðRmin þ ð2n 1ÞapÞ
hi d i
¼ 27:358De0:287 Pr0:949
k
J¼
Eq. (14) can be written in term of Ts,out and Ts,in, as
follows:
1
0:05652T 2s;out þ 1:22045 þ
T s;out
Rc
T w;out
þ 10:90749 ia;in ¼0
ð18Þ
Rc
and
Nui ¼
ð16Þ
where
b¼
segment of the innermost coil turn and then is done segment by segment along the circular coil turn. In order to
solve the model, relevant tube-side and air-side heat
transfer coefficients are needed. The following correlation proposed by Naphon and Wongwises [13] for the
spirally coiled tube is used to predict tube-side heat
transfer coefficients.
ð21Þ
where Rmin is the minimum coil radius, n is the number
of coil turns, and a is of radius change per radian.
Each circular coil turn can be divided into several segments as shown in Fig. 3. The calculation begins at the
ð23Þ
• The outlet-water temperature is assumed.
• Eqs. (16), (19) and (20) are solved simultaneously by
using the Newton–Raphson method to obtain the
inlet-tube temperature, (Ts,in), outlet-tube surface
temperatures, (Ts,out), water temperature, (Tw,in), at
Segment 1.
• The heat transfer rate, (Q), and the outlet-air temperature, (Ta,out), are calculated.
• The computation described above is next performed
at segment 2 and then the remaining segments in turn
until the last one.
• The same computation is performed at the next circular coil.
• The computation is terminated when the calculation
at the last segment of the outermost coil turn is
finished.
• The calculated water temperature at the last segment
of the outermost coil turn is compared with the inletwater temperature (initial condition). If the difference
is within 106, the calculations is ended, and if not,
another outlet-water temperature value of the first
segment at the innermost coil turn is tried and the
computations are repeated until convergence is
obtained.
5. Results and discussion
Fig. 4 shows the variation of the outlet-air temperatures with air mass flow rate obtained from the experiment for the different water mass flow rates of 0.11
P. Naphon, S. Wongwises / Experimental Thermal and Fluid Science 29 (2005) 511–521
60
25
Mathematical model
0.11
0.19
50
45
40
35
o
30
Ta,in = 50 C
o
T w,in = 11.5 C
25
ω a,in = 0.04
0.01
0.02
0.03
0.04
0.05
0.06
0.07
Air mass flow rate (kg/s)
and 0.19 kg/s. At an inlet-air temperature of 50 C, inletwater temperature of 11.5 C and inlet-air humidity ratio
of 0.04, the outlet-air temperature tends to increase as
air mass flow rate increases. At the same air mass flow
rate, the outlet-air temperature at mw = 0.11 kg/s seems
slightly higher than that at mw = 0.19 kg/s. However,
the effect of the water mass flow rate on the outlet-air
temperature in the present experiment is quite low.
The average difference between the measured data is
4.4%. The present numerical results are validated by
comparing with experimental data. It can be noted that
the model slightly underpredicts the present measured
data at low air mass flow rate region. The low flow rate
of air, together with the temperature which is higher
than the ambient air downstream, causes the measured
outlet-air temperatures to be higher than the calculated
ones. Fig. 5 shows the variation of the outlet-air temperature with air mass flow rate for the different inlet-air
60
o
Outlet air temperature ( C)
o
Ta,in ( C)
Experiment
Mathematical model
50
55
50
45
40
35
Tw,in = 11.5 oC
m w = 0.11 kg/s
ωa,in = 0.04
30
25
20
0.00
0.01
0.02
0.03
0.04
Experiment
Mathematical model
0.11
20
0.19
15
10
5
0.00
o
T a,in = 50 C
o
T w,in = 11.5 C
ω a,in = 0.04
0.01
0.02
0.03
0.04
0.05
0.06
0.07
Air mass flow rate (kg/s)
Fig. 4. Variation of the outlet-air temperatures with air mass flow rate
for different water mass flow rates.
55
m w (kg/s)
o
o
Outlet air temperature ( C)
Experiment
O utle t wa ter temp eratur e ( C )
m w (kg/s)
55
20
0.00
517
0.05
0.06
0.07
Air mass flow rate (kg/s)
Fig. 5. Variation of the outlet-air temperatures with air mass flow rate
for different inlet-air temperatures.
Fig. 6. Variation of the outlet-water temperatures with air mass flow
rate for different water mass flow rates.
temperatures of 50 and 55 C. As expected, the inletair temperature has significant effect on the outlet-air
temperature.
Fig. 6 shows the variation of the outlet-water temperatures with air mass flow rate for the different water
mass flow rates of 0.11 and 0.19 kg/s. For an inlet-water
temperature of 11.5 C, inlet-air temperature of 50 C,
and inlet-air humidity ratio of 0.04, the increase of the
heat transfer rate resulted in an increase of the outletair temperature (Fig. 5) has a significant effect on the increase of the outlet-water temperature. As the outlet-air
temperature increases, the temperature difference between inlet-and outlet-air temperature decreases. Therefore, the air mass flow rate must be increased for
keeping the heat transfer rate equal to the water side.
Therefore, it can be clearly seen that the outlet-water
temperature increases with increasing air mass flow rate.
At the same inlet-air and-water temperatures, inlet-air
humidity ratio and air mass flow rate, the outlet-water
temperature at lower water flow rate is higher than that
at higher water flow rate. This is because at a specific air
mass flow rate, inlet-air and-water temperatures the
water mass flow rate slightly affects the outlet-air temperature. In other words, the heat transfer rate absorbed
by the chilled water is mainly dependent on the mass
flow rate and the outlet-water temperature. Therefore
the lower water flow rate gives the higher water-outlet
temperature. Considering Fig. 7, which shows the effect
of inlet-air temperature on the outlet-water temperature,
it is clearly seen that at the same air mass flow rate, the
outlet-water temperature at Ta,in = 50 C is lower than at
Ta,in = 55 C. The reason for this is similar to the one as
described above. At a specific inlet-water temperature,
inlet-air humidity ratio, and water and air mass flow
rates, the increase of the outlet-water temperature results in the increases of the outlet-air temperature and
the heat transfer rate. Again, in order to keep the heat
518
P. Naphon, S. Wongwises / Experimental Thermal and Fluid Science 29 (2005) 511–521
25
20
Ta,in (oC)
Mathematical model
o
Experiment
Tube surface temperature ( C )
Ta,in (oC)
o
O u t l e t w a t e r t em p e r a t u r e ( C )
25
50
55
15
10
5
0.00
Tw,in = 11.5oC
m w = 0.11 kg/s
ωa,in = 0.04
0.01
0.02
0.03
0.04
0.05
0.06
20
Mathematical model
15
o
10
5
0.00
0.07
Experiment
50
55
Tw,in = 11.5 C
m w = 0.11 kg/s
ωa,in = 0.04
0.01
0.02
Air mass flow rate (kg/s)
0.03
0.04
0.05
0.06
0.07
Air mass flow rate (kg/s)
Fig. 7. Variation of the outlet-water temperatures with air mass flow
rate for different inlet-air temperatures.
Fig. 9. Variation of the tube surface temperatures with air mass flow
rate for different inlet-air temperatures.
transfer rate equal to the water-side heat transfer rate,
the inlet-air temperature must be increased. Considering
the results obtained from the present model and those
obtained from the experiment, it can be clearly seen
from figure that the predicted outlet-water temperature
is higher than the measured one. This may be due to
the fact that the thermal resistance of the liquid film that
covers the tube surface is not included in the mathematical model causing higher heat transfer rate from hot air
to chilled water.
Figs. 8 and 9 show the variations of the tube surface
temperatures with air mass flow rate. The tube surface
temperature is measured at the 3rd layer from the uppermost layer in five positions in which the water flows. It
can be seen from both figures that the trends of the tube
surface temperature are similar to those of the outletwater temperature curves as shown in Figs 6 and 7. It
can be clearly seen that the water mass flow rate and
the inlet air temperature have insignificant effects on
the tube surface temperature. Again, considering the
predicted and measured results, it is found that the
model overpredicts the measured data. It may be because, in experiment, the tube surface is chilled by the
liquid film.
Figs. 10 and 11 illustrate the variations of the enthalpy effectiveness and humidity effectiveness with air
mass flow rate, respectively at Tw,in = 11.5 C, mw =
0.11 kg/s, xa,in = 0.04, for different inlet-air temperatures
of 50 and 55 C. For the whole range of inlet-water temperature, it is found that the tube surface temperatures is
always lower than the dew-point temperature of the air.
This results in condensing out of the moisture. The total
load-removal performance and the latent load-removal
performance of the spiral coil heat exchanger can be presented in terms of the enthalpy effectiveness and humidity effectiveness, respectively, as follows
1.0
m w (kg/s) Experiment
Ta,in (oC)
Mathematical model
20
Enthalpy effectiveness
0.11
o
Tube surface temperature ( C )
25
0.19
15
o
Ta,in = 50 C
Tw,in = 11.5oC
ωa,in = 0.04
10
5
0.00
0.01
0.02
0.03
0.04
0.06
0.07
Air mass flow rate (kg/s)
Fig. 8. Variation of the tube surface temperatures with air mass flow
rate for different water mass flow rates.
Mathematical model
0.6
0.4
o
0.2
0.05
Experiment
50
55
0.8
0.0
0.00
Tw,in = 11.5 C
mw = 0.11 kg/s
ωa,in = 0.04
0.01
0.02
0.03
0.04
0.05
0.06
0.07
Air mass flow rate (kg/s)
Fig. 10. Variation of the enthalpy effectivenesses with air mass flow
rate for different inlet-air temperatures.
P. Naphon, S. Wongwises / Experimental Thermal and Fluid Science 29 (2005) 511–521
1.0
1.0
o
Experiment
Mathematical model
mw (kg/s) Experiment
50
55
Enthalpy effectiveness
Humidity effectiveness
Ta,in ( C)
0.8
0.6
0.4
0.2
0.0
0.00
519
Tw,in = 11.5 oC
mw = 0.11 kg/s
ωa,in = 0.04
0.01
0.02
0.8
0.19
0.6
0.4
o
0.2
0.03
0.04
0.05
0.06
0.0
0.00
0.07
Ta,in = 50 C
Tw,in = 11.5oC
ωa,in = 0.04
0.01
0.02
Air mass flow rate (kg/s)
Humidity effectiveness; Ew ¼
xa;in xa;out
xa;in xsat;s
0.05
0.06
0.07
1.0
ð24Þ
m w (kg/s) Experiment Mathematical model
ð25Þ
The humidity ratio of saturated air, xsat,s, at the wetsurface conditions can be obtained from the correlation
given by Laing et al. [16]
xsat;s ¼ ð3:7444 þ 0:3078T s þ 0:0046T 2s
þ 0:0004T 3s Þ 103
0.04
Fig. 12. Variation of the enthalpy effectivenesses with air mass flow
rate for different water mass flow rates.
ð26Þ
It is found from Figs. 10 and 11 that the enthalpy
effectiveness and the humidity effectiveness decrease
with increasing air mass flow rate for a given inlet-water
temperature, inlet-air humidity ratio, and water mass
flow rate. Increasing of the air mass flow rate directly affects the outlet enthalpy, ia,out, enthalpy of saturated air,
isat,s, outlet humidity ratio, xa,out, and humidity ratio of
saturated air, xsat,s. However, the increases of the outlet
enthalpy and outlet humidity ratio of air are larger than
those of the enthalpy of saturated air and humidity ratio
of saturated air. Therefore, the enthalpy effectiveness
and humidity effectiveness tend to decrease with increasing air mass flow rate. It can be noted that the air inlet
temperature has an insignificant effect on the enthalpy
effectiveness and humidity effectiveness. However, at a
given lower air mass flow rate, higher inlet-air temperature may lead to a slight increase in enthalpy effectiveness and humidity effectiveness. The average
discrepancies between experimental data are about
4.8% and 8.7%, respectively. Figs. 12 and 13 show the
variation of enthalpy effectiveness with air mass flow
rate and that of humidity effectiveness with air mass flow
rate, respectively. It can be clearly seen from the experimental that the water mass flow rate show an insignifi-
Humidity effectiveness
ia;in ia;out
ia;in isat;s
0.03
Air mass flow rate (kg/s)
Fig. 11. Variation of the humidity effectivenesses with air mass flow
rate for different inlet-air temperatures.
Enthalpy effectiveness; Eh ¼
Mathematical model
0.11
0.11
0.8
0.19
0.6
0.4
0.2
0.0
0.00
Ta,in = 50oC
Tw,in = 11.5 oC
ωa,in = 0.04
0.01
0.02
0.03
0.04
0.05
0.06
0.07
Air mass flow rate (kg/s)
Fig. 13. Variation of the humidity effectivenesses with air mass flow
rate for different water mass flow rates.
cant effect on the enthalpy effectiveness and humidity
effectiveness. The average difference between experimental data are 5% and 5.5%, respectively. The uncertainties
of the experimental enthalpy and humidity effectivenesses are between 0.34–0.56% and 0.5–0.93%, respectively. In general, the shape of the predicted and
observed enthalpy effectiveness and humidity effectiveness profiles agree well.
A number of graphs can be drawn from the output of
the simulation but, because of the space limitation, only
typical results are shown. Fig. 14 illustrates the variation
of the predicted outlet-air temperatures with air mass
flow rate for various water mass flow rates. It can be
clearly seen from figure that the outlet-air temperature
increases rapidly in the low air mass flow rate region
and then increases moderately as air mass flow
rate increases. In addition, the decrease of outlet-air
520
P. Naphon, S. Wongwises / Experimental Thermal and Fluid Science 29 (2005) 511–521
40
Ta,in = 60oC
Tw,in = 10 oC
ωa,in = 0.04
50
45
m w (kg/s)
40
0.05
0.10
0.15
0.50
35
30
0.00
0.02
Ta,in = 60oC
Tw,in = 10oC
ωa,in = 0.04
35
o
Tube surface temperature ( C)
55
o
Outlet air temperature ( C)
60
0.04
0.06 0.08
0.10
0.16
0.12 0.14
30
25
20
15
mw (kg/s)
0.05
0.10
0.15
0.50
10
5
0
0.18
0.00
0.02
0.04
Air mass flow rate (kg/s)
Ta,in (oC)
0.50
50
60
70
80
0.45
0.40
0.35
0.25
Tw,in = 10oC
mw = 0.15 kg/s
ωa,in = 0.04
0.20
0.00
0.02
0.30
0.04
0.06 0.08
0.10
0.12 0.14
0.16
0.18
Air mass flow rate (kg/s)
Fig. 17. Variation of the enthalpy effectivenesses with air mass flow
rate for different inlet-air temperatures.
0.60
o
Tw,in = 10 C
mw = 0.15 kg/s
ωa,in = 0.04
25
20
o
Ta,in ( C)
15
50
60
70
80
10
5
0.02
0.04
Ta,in ( oC)
0.55
Humidity effectiveness
o
Tube surface temperature ( C)
0.18
0.55
40
0
0.00
0.16
0.12 0.14
Fig. 16. Variation of the tube surface temperatures with air mass flow
rate for different water mass flow rates.
Enthalpy effectiveness
temperature becomes relatively smaller as water mass
flow rate increases.
Fig. 15 shows the effect of inlet-air temperature on
the tube surface temperature. At a specific inlet-air temperature, the tube surface temperature generally increases with increasing air mass flow rate, however,
the increase of the tube surface temperature at higher
inlet-air temperatures is higher than at lower ones for
the same range of air mass flow rates. In addition, at
any air mass flow rate, the tube surface temperature increases relatively constantly with increasing inlet-air
temperature. The effect of water mass flow rate on the
tube surface temperature is shown in Fig. 16. It can be
found that at a specific air mass flow rate, the tube surface temperature decreases as water mass flow increases.
Figs. 17 and 18 show the variations of the enthalpy
effectivenesses and humidity effectivenesses with air
mass flow rate for various inlet-air temperatures, respec-
30
0.10
Air mass flow rate (kg/s)
Fig. 14. Variation of the outlet-air temperatures with air mass flow
rate for different water mass flow rates
35
0.06 0.08
0.06 0.08
0.10
0.12 0.14
0.16
0.45
0.40
0.35
0.30
0.25
0.18
Air mass flow rate (kg/s)
Fig. 15. Variation of the tube surface temperatures with air mass flow
rate for different inlet-air temperatures.
50
60
70
80
0.50
0.20
0.00
o
Tw,in = 10 C
mw = 0.15 kg/s
ωa,in = 0.04
0.02
0.04
0.06 0.08
0.10
0.12 0.14
0.16
0.18
Air mass flow rate (kg/s)
Fig. 18. Variation of the humidity effectivenesses with air mass flow
rate for different inlet-air temperatures.
P. Naphon, S. Wongwises / Experimental Thermal and Fluid Science 29 (2005) 511–521
tively. It should be noted that the enthalpy effectiveness
and humidity effectiveness decrease with increasing air
mass flow rate. These effectivenesses decrease rapidly
in the low air mass flow rate region and then decrease
moderately as the air mass flow rate increases. For a
specific air mass flow rate at constant inlet-air andwater temperatures, both effectivenesses increase with
increasing inlet-air temperature. The same explanation
described above for Figs. 17 and 18 can be given.
6. Conclusions
New experimental data from the measurement of the
heat transfer characteristics and the performance of a
spiral coil heat exchanger under cooling and humidifying conditions are presented. The results obtained from
the developed model are validated by comparing with
the measured data. The effects of the inlet conditions
of the working fluids flowing through the spirally coiled
heat exchanger are discussed. The following conclusions
can be given:
• There is reasonable agreement between the results
obtained from the experiment and those from the
developed model.
• Air mass flow rate and inlet-air temperature have significant effect on the increase of the outlet-air andwater temperatures.
• The outlet-air and water temperatures decrease with
increasing water mass flow rate.
• The enthalpy effectiveness and humidity effectiveness
decrease as the air and water mass flow rates increase.
• The enthalpy effectiveness and humidity effectiveness
increase as the inlet-air temperature increases.
Acknowledgements
The authors would like to express their appreciation
to the Thailand Research Fund (TRF) for providing
financial support for this study. The authors also wish
to acknowledge Miss Supajaree Maroongruang, Mr.
Anucha Kasikapast and Mr. Chanit Somphol, for their
assistance in some of the experimental work.
521
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