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Simplified Model for the Operation of Chilled Water
Cooling Coils Under Nonnominal Conditions
O. Morisot a , D. Marchio b & P. Stabat c
a ELYO Cylergie, France
b Centre of Energy Studies, Ecole des Mines de Paris, France
c Centre of Energy Studies, Ecole des Mines de Paris
Published online: 28 Feb 2011.
To cite this article: O. Morisot , D. Marchio & P. Stabat (2002): Simplified Model for the Operation of Chilled Water Cooling
Coils Under Nonnominal Conditions, HVAC&R Research, 8:2, 135-158
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VOL. 8, NO. 2
HVAC&R RESEARCH
APRIL 2002
Simplified Model for the Operation of
Chilled Water Cooling Coils
Under Nonnominal Conditions
O. Morisot, Ph.D.
D. Marchio, Ph.D.
P. Stabat
Student Member ASHRAE
This study presents a cooling coil model for calculating energy consumption in air-conditioned
buildings that has a minimal number of inputs. The model accurately determines the cooling
energy rate and dehumidification energy rate under nonnominal conditions, and takes into
account operation under variable air and water flows. In this manner, the model enhances the
simplified ASHRAE Toolkit model without requiring more input data. The main assumptions are
justified considering the common existing configurations of cooling coils in the air-conditioning
industry. The parameters of the model are identified from only one nominal rating point. The
model has been validated on a VAV facility with an average deviation of 5% for total energy
rate. Errors are mainly due to the assumption that the coil is either completely wet or dry even if
the surface is partially wet.
INTRODUCTION
One of the important models needed for estimating energy consumption of HVAC system is a
cooling coil model suitable for both cooling and dehumidification. HVAC systems very often
operate using only temperature control. The load induced by noncontrolled dehumidification is
not negligible compared to the yearly energy consumption and needs to be calculated. Building
indoor air humidity has to be predicted under nonnominal conditions. Moreover, the coil model
has to take into account the effect of variable air and water flows on heat transfer to accurately
compare the performance of various HVAC systems [e.g., Constant Air Volume (CAV) and
Variable Air Volume (VAV) systems, and variable speed pumps]. Moreover, the simplified
model operating under nonnominal conditions allows the production of training data for artifi-
cial neural networks used in the field of fault detection and diagnosis method applied to building
air-conditioning.
Existing models of cooling coils do not meet the following requirements for the building
energy consumption simulation:
• Coil characteristics determination using available data (the performance at a single rating
point is often the only piece of information given in catalogs by manufacturers)
• Dehumidification energy rate calculation under nonrating conditions
• Adaptability to variable airflow rate (VAV systems)
• Adaptability to variable water flow rate (water flow control devices or variable-speed pumps)
In this paper, a cooling coil model is developed based on the ASHRAE HVAC 2 Toolkit
simplified cooling coil model (Brandemuehl et al. 1993). The coil is modeled as a classical
Olivier Morisot in an engineer in energy and the environment at ELYO Cylergie, France. Dominique Marchio is a pro-
fessor at the Centre of Energy Studies, Ecole des Mines de Paris, France. Pascal Stabat is a doctoral student at the Centre
of Energy Studies, Ecole des Mines de Paris.
135

136
HVAC&R RESEARCH
Figure 1. Cooling Coil Representation for Building Air Conditioning
(Holmes 1988)
counterflow heat exchanger suitable for building air-conditioning with fins in counterflow
configuration or in crossflow configuration with at least four rows, as illustrated in Figure 1.
COOLING COIL MODEL
Local and Global Heat and Mass Transfer Exchange
In the cooling coil, there is a sensible thermal exchange between air and cooling fluid flowing
through the pipes. When the pipe surface temperature is below the air dew-point temperature, a
mass exchange occurs as illustrated in Figure 2. To analyze the airside heat transfer and mass
transfer, the following assumptions are made:
• Air and water are considered homogeneous outside the thermal and diffusion boundary layer
• Conduction heat transfer in material is negligible compared to convection heat transfer
• Air condensation film is assumed to be saturated air at film temperature Tcond
The total energy exchanged by the air over an incremental pipe surface (dA) can be expressed
with the convection coefficient hext between the air and pipe surface and the mass transfer coef-
ficient hmass
,
dQ = hextdA(Ta – Tcond) + hmasdA[wa(Hfg + cpvTa) – wcond(Hfg + cpvTcond)]
(1)
The total energy exchanged by the water flow over an incremental pipe surface (dA) can be
expressed with convection coefficient between water and pipe surface hint,
dQ = hintdA(Tcond – Tw)
(2)
As in the analysis performed by Threlkeld (1970), it is possible to aggregate the two compo-
nents’ temperature and humidity differences in an equivalent enthalpy difference. For a Lewis
value of unity (Sacadura 1993), considering the heat transfer coefficient, Equation (1) becomes

VOLUME 8, NUMBER 2, APRIL 2002
137
Figure 2. Heat and Mass Transfer in Cooling Coil
U
ext dA
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ
dQ =
(ha – hcondsat
)
(3)
cpa
In order to homogenize Equations (2) and (3), the air saturated enthalpy is assumed to be a
linear function of temperature:
∆hsat = cpsat∆T
(4)
Water is represented by the fictitious enthalpy of saturated air at water temperature, hwsat(Tw).
The coefficient cpsat has the dimensions of heat capacity and is assumed to be constant for the
considered range of temperature. Equation (2) becomes
Uint dA
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ
dQ =
[hcondsat(Tcond) – hwsat(Tw)]
(5)
cpsat
Using the fact that the exchanged energy rate is constant, the thermal resistance between air
and water can be considered as an addition of resistances in series as shown in Figure 3. The
equation of thermal and mass exchange is obtained by combining Equations (3) and (5):
dQ = UhdA(ha – hwsat
)
(6)
with
cpa
cpsat
Uint dAint
1
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ
=
+
(7)
U dA
Uext dAext
d

138
HVAC&R RESEARCH
Figure 3. Heat and Mass Transfer in Cooling Coil:
Representation Using Threlkeld (1970) Method
Two common techniques for thermal exchangers are applied to model heat and mass transfer
for the cooling coil: the effectiveness method NTU-ε and the log mean temperature difference,
∆Tlm. Both methods can be used when condensation occurs by using air enthalpy instead of air
temperature and fictitious saturated air enthalpy instead of water temperature (hwsat instead of
Tw). Both methods assume that the global exchange coefficient is constant for the heat and mass
exchanger.
Cooling Coil Parameter Identification
The purpose of the parameter identification process is to characterize the cooling coil from
available data. The most accurate approach for this process requires geometrical data, but in
some applications users do not have geometrical data and do not have the time to collect it. That
is the reason why CCDET model in ASHRAE Toolkit is rarely used by engineers for HVAC
design. The nominal rating, which is generally available, is very often the only datum available
to characterize the cooling coil.
As described previously, the internal and external heat exchange coefficients UAint and UAext
are characteristics of the cooling coil. They are respectively dependent on the water and airflow
rates. The data used at this step are extracted from one nominal rating point of the cooling coil.
The common exchanger calculation techniques are applied to the cooling coil with heat and
mass transfer described by Equation (6). The log mean enthalpy difference method is applied to
the counterflow heat exchanger (which is a good assumption for crossflow with at least four
rows).
Qrat = UAhrat∆hlmrat
(8)
(hai – hwosat) – (hao – hwisat
)
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ
=
∆hlmrat
(9)
h
ai – hwosat
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ
ln
h
ao – hwisat
Elmahdy and Mitalas (1977) demonstrated that a model based on this method has a maximal
error of 4% compared to experimental data. This calculation method is advocated by ARI Stan-
dard 410 for forced-circulation air-cooling and air-heating coils.
The purpose is to obtain UAh. To determine how UAh varies with airflow and waterflow
changes, estimate the internal and external heat transfer coefficients separately.

VOLUME 8, NUMBER 2, APRIL 2002
139
The airside heat exchange coefficient depends only on the airside coil geometry and on the
airflow conditions. Thus, a fictitious coil can be considered to have equivalent conditions on the
air side and infinite flow on the water side, as proposed in the simplified cooling coil model
CCSIM of ASHRAE HVAC 2 Toolkit (Brandemuehl et al. 1993). The fictitious saturated air
enthalpy of water, which is constant for the fictitious coil, is determined using inlet and outlet air
condition. This enthalpy corresponds to apparatus dew-point temperature of the real coil. Then,
the fictitious effectiveness of the cooling coil is calculated as follows:
h
ai – has
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ
εfictitious
=
(10)
h
ai – hadp
Considering the heat exchange resistance in Equation (7) and the NTU value in Equation (11),
and assuming that the internal resistance is negligible compared to external resistance (infinite
water flow rate), the UAext value is extracted from the effectiveness expression for coil with infi-
nite water flow as shown in Equation (12). The minimal capacity rate Cmin has the same unit as
the overall enthalpy heat transfer coefficient. The relations are
UAhrat
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ
NTU =
(11)
Cmin
εfictitious = 1 – e–NTU
(12)
(13)
Â
UAexrat = –macpaln(1 – εfictitious
)
The real value of the waterside heat transfer coefficient UAintrat is extracted from the global
and air-side coefficients using Equation (7). Using this approach, the characteristics of the cool-
ing coil (heat transfer coefficients for air side and liquid side) are calculated for the nominal rat-
ing point. It is now necessary to evaluate those coefficients for nonnominal conditions.
Performance Calculation
Outlet air and water temperatures are calculated from inlet conditions and heat transfer coeffi-
cients using the NTU-ε method applied to heat and mass transfer between air and water (Dewitt
and Incropera 1996).
In addition, it is necessary to determine whether the cooling coil is wet, dry, or partially wet.
The calculations under wet or dry conditions are based on the Braun (1988) method, which
shows that the performance of coils with partially wet surfaces can be approximated by assum-
ing either fully dry or fully wet conditions, whichever predicts the maximal heat transfer rate.
The assumption generally results in errors of less than 5% on total energy rate.
The approach of the simple model consists of calculating the impact of air and water mass
flow rate variation on the heat exchange coefficient. It is then necessary to identify the correla-
tion between the mass flow rates and the internal or external heat exchange coefficients. The
detailed correlations are simplified. First, the water-side heat transfer coefficient is evaluated.
Assuming the pipe conductive resistance is negligible compared with the convective resis-
tance, the internal heat transfer coefficient can be expressed as follows:
UAint = Ainthint
(14)

140
HVAC&R RESEARCH
As the inside area is constant for one coil, the heat transfer coefficient varies with the convec-
tion coefficient. The Dittus-Boelter correlation (ASHRAE 1994) is used to determine the con-
vection heat transfer coefficient hint for a one-phase fluid from the Nusselt number and for
Reynolds numbers larger than 2500:
Nuw = 0.023Re0w.8Prw0.4
(15)
with
dinthint
Gwdint
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ
µw
µwcpw
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ
λw
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ
Nuw
=
, Rew
=
, Prw =
(16)
λw
Thus,
Â
0.8
0.4
λe
µwcpw
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ
λw

mw




ꢀꢀꢀꢀꢀꢀꢀꢀ ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ
UAint = 0.023Aint
(17)


dint πdintµ

w
Rabehl et al. (1999) propose a method to fit coefficients or exponents of correlation. This
method needs 16 performance values to fit correctly. Indeed, this technique allows extension to
different heat transfer fluids, different temperature ranges and different temperature levels.
The model presented is applied only for a chilled water cooling coil. In the range of typical
temperatures for air conditioning (typically 5 to 12°C), the water properties viscosity µ and ther-
mal conductivity λ are assumed to be constant. Thus, for one coil (i.e., dint and Aint are constant),
the inside heat transfer coefficient depends only on water mass flow rate for turbulent flows. The
nonrating value can be calculated from rating value by identifying all the constant (or assumed
to be constant) values in Equation (17) using the known rating value as follows:
0.4

0.8 µ c


UAintrat
λe
1
w
pw

ꢀꢀꢀꢀꢀꢀꢀꢀ ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ
= 0.023Aint
(18)



 0.8
dint πdintµw
λw
mwrat
which leads to
UAintrat
 0.8
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ
UAint
=
mw
(19)
 0.8
mwrat
Second, concerning the airside heat transfer coefficient determination for nonnominal condi-
tions, the heat transfer coefficient is written using convection and fin resistances:
1
1
ꢀꢀꢀꢀꢀꢀꢀꢀꢀ ꢀꢀꢀꢀꢀꢀꢀꢀꢀ
UAext
=
=
+
(20)
(21)
(22)
Rext Rail
1
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ
Rext
hext Aext
1
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ
Rail
=
hext Asηail

VOLUME 8, NUMBER 2, APRIL 2002
141
Figure 4. Fin and Pipe Configuration
First, the convection heat transfer coefficient for cooling coils with dry fin area is determined.
This coefficient is calculated using the COLBURN factor j correlation presented in Equation
(23) (Elmahdy and Mitalas 1977). The values of the geometrical parameters describing fins and
pipes are explained in Figure 4.
hext,dry = jGacpaPra–2 ⁄ 3
(23)
(24)
Al
ꢀꢀꢀꢀꢀ
Gadh
j = c1Reca
Rea
=
Ga = ρav
2
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ
µa
aAa
4Aa
ꢀꢀꢀꢀꢀꢀꢀꢀꢀ
P
dh
=
Aa = (Pa – ea)(Ptt – de)
P = 2(Pa – ea) + 2(Ptt – de)
(25)
(26)
4P Plt
tt
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ
dail
=
la = 0.5(dail – de)
π
Where Pa is the fin spacing, Plt is the row spacing, Ptt is the distance between tubes, de is the
tube outside diameter, dail is the fin equivalent diameter and la is the fin equivalent height, as
shown in Figure 4.
The c1 and c2 coefficients as determined by Elmahdy and Biggs (1979) from geometry data
for 200 < Rea < 2000 are as follows:
0.141
0.065
ea
ꢀꢀꢀꢀꢀ
1a
dh
ꢀꢀꢀꢀ
ea








c1 = 0.159
(27)
(28)
0.049
0.077
ea
ꢀꢀꢀꢀꢀ
1a
Pa
ꢀꢀꢀꢀꢀ
ea







c2 = –0.323

This chosen correlation has been compared with other correlations of literature:

142
HVAC&R RESEARCH
Elmahdy and Biggs (1979)
j = c1Recd
200 < Red < 2000
2
21 coils with flat fins
and 4 to 8 rows
h
h
0.141
0.065
0.049
0.077
j is obtained at 10%
ea
ꢀꢀꢀꢀ
la
dh
ꢀꢀꢀꢀ
ea
ea
ꢀꢀꢀꢀ
la
Pa
ꢀꢀꢀꢀꢀ
ea
















c1 = 0.159
c2 = –0.323
Chuah et al. (1998)
j = c1Recd
200 < Red < 2000
2
1 coil with flat fins
and 3 rows
h
h
and 3 rows
0.141
0.065
0.049
0.077
ea
ꢀꢀꢀꢀ
la
dh
ꢀꢀꢀꢀ
ea
ea
ꢀꢀꢀꢀ
la
Pa
test and correction of
Elmahdy and Biggs (1979) on
a specific coil
















ꢀꢀꢀꢀꢀ
ea
c1 = 0.101
c2 = –0.323
Mirth and Ramadhyani (1993)
j = 0.13Re–d0.33
900 < Red < 1700
5 coils with flat fins
and 4 and 8 rows
h
h
Wang, Fu, et al. (1997)
18 coils with sinusoidal fins
and 1 to 4 rows
j is obtained at 10%
1.201
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ
j =
400 < Red < 8000
[ln(Reσd )]
e
e
with s = Aa/Al
Wang, Hsieh, et al. (1997)
9 coils with flat fins
and 2 to 6 rows
j = 0.4Re–d 0.468 + 0.0407Nε0.159N –1.261
200 < Red < 4000
e
e
j is obtained at 10%
Turaga et al. (1988)
j = 0.053ε–0.24Re–d0.18
300 < Red < 1500
10 coils with flat fins
and 3 to 8 rows
h
h
McQuiston (1978)
–0.15
P P
10 coils with flat fins
and 4 rows
j is obtained at 10%
–0.4 4
lt tt

ꢀꢀ ꢀꢀꢀꢀꢀꢀ ꢀꢀꢀꢀꢀꢀ
σ
j = 0.0014 + 0.2618(Red
)


e
π dh de
with s = Aa/Al
Results of the comparison are given in Figure 5. As the purpose is to express UAext from
rating value UAextrat, j/jnom is plotted on Figure 5. All results are close except those of Turaga
et al. (1988). The correlation of Wang, Fu et al. (1997) relative to coils with sinusoidal fins is in
good agreement with the others; jnom is larger but only j/jnom is relevant.
Second, the fin efficiency is evaluated following Taborek et al. (1983) using the equivalent
circular fin of diameter dail:
tanh(αL)
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ
ηail
=
(29)
(30)
(31)
αL
2hext
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ
α =
λ
ailea
dail
ꢀꢀꢀꢀꢀꢀꢀꢀ
de
dail
ꢀꢀꢀꢀꢀꢀꢀꢀ
de



– 1 1 + 0.35 ln




L = 0.5de


VOLUME 8, NUMBER 2, APRIL 2002
143
Figure 5. Comparison of Correlations for Air Side (Dry Conditions)
Third, the convection heat transfer coefficient for the cooling coil with wet fin area is deter-
mined. A corrective factor based on air velocity is introduced to take condensation into account
(Threlkeld 1970):
hext,wet = Cf hext,dry
(32)
with Cf calculated from an experimental correlation considering 600 < Re < 2000,
Cf = 0.626(5.08 × 10–3
)
0.101v0f .101
(33)
where vf is the air velocity in minimal section, vf = Ga/ra m/s, with Ga mass flow rate per square
metre.
All of these expressions require geometrical data that are often unknown at the HVAC design
phase or that require too much time to be determined. It is necessary to determine UAext using a
simplified approach. Experimental results suggest a correlation for hext expressed as
hext = aVab
(34)
A survey of seven different cooling coil manufacturers’ products shows that at the present
time the cooling coil technology applied to building air conditioning is not significantly varied.
Indeed, all manufacturers’ products are similar: cooling coil with pipes and flat aluminum plate
fins, as shown in Figure 1. Typically, the pipes are copper. Some coils have tube and fins of
other material, but these coils are used in specific applications (operation with salt water, etc).
The number of rows ranges from two to eight. For fewer than three rows, the assumption of
counterflow exchanger is no longer valid, but this kind of cooling coil is not common. Fifty dif-
ferent cooling coil configurations have been found in manufacturers’ catalogs (Table 1). For
industrial applications, some coils can have different geometric characteristics such as a fin
spacing of 15 mm, for example.

144
HVAC&R RESEARCH
Table 1. Possible Existing Geometrical Configurations for Seven Cooling Coil Manufacturers
Coils Described
ea, mm
Ptt × Plt , mm
Pa, mm
de, mm
Coil 1
0.12
30 × 30
60 × 30
1.6, 2, 2.5, 3
1.6, 2, 2.5, 3, 4
15.8 (5/8 in.)
Coil 2
Coil 3
0.12
0.12
30 × 30
Standard 2.2
Other available up to 4 mm
25 × 25
30 × 30
60 × 30
Standard 2.5
1.6, 2, 2.5, 3.0, 4.0
9.5 (3/8 in.)
(1/2 in.)
15.8 (5/8 in.)
Coil 4
0.12
25 × 25
30 × 30
Standard 2.2
Coil 5
Coil 6
Coil 7
0.18
0.12
0.12
30 × 30
30 × 30
25 × 25
30 × 30
2, 3, 4
2.3, 2.5
2.1
(5/8 in.)
9.5 (3/8 in.)
15.8 (5/8 in.)
Figure 6. Typical Values of Fin Efficiency for Cooling Coil in Building
In the configurations presented, the maximal value for αL is considered. The extreme realis-
tic values of parameters of Equations (30) and (31) are taken to be hext = 100 W/(m·K), λail
200 W/(m·K) (aluminum), ea = 0.12 mm, and L = 10.1 mm.
=
The L value is calculated using a 30 by 60 mm configuration of 5/8 in. pipes, which is the
existing configuration giving the highest L value. Those values give a maximum realistic value
for αL of 0.9. Figure 6 shows that for the range of αL of 0 to 0.9 m–1, the fin efficiency values
vary from 1 to 0.8 and the slope of the variation is low. So, the fin efficiency can be considered
as a constant. The narrow range of values of fin efficiency is due to the fact that the price of the
fins is attributed to implementation, and that the cost of high-efficiency fins is actually low. So it
is logical for the manufacturer to propose very efficient fins (more than 85%). With those
assumptions, Equations (20) to (22) and (29) to (31) are simplified as indicated in Equation (35):
UAext = Acorhext
(35)

VOLUME 8, NUMBER 2, APRIL 2002
145
Figure 7. Statistic Distribution of c2 Values for Range of Cooling Coils
in Air-Conditioning Industry
Considering Equations (20) to (28) and a constant fin efficiency value, UAext varies only with
the airflow rate. One should now determine the exponent b of the airflow rate as in Equation
(34). It depends only on c2 with the factor j provided by Equation (24) in the Reynolds number
range [200 to 2000]. For all the 50 cooling coil configurations presented in Table 1, the c2 coef-
ficient is evaluated using Equation (28). The resulting distribution of the c2 values is plotted in
Figure 7 for the complete gamut of cooling coils. The variation range of c2 value is –0.34 to
–0.31. Thus, a default mean c2 value can be defined:
c2 = – 0.33
(36)
This default value corresponds to the following configuration, which is very common in
building air-conditioning applications: Ptt = 30 mm, Plt = 30 mm, Pa = 2.5 mm, ea = 0.12 mm.
Figure 7 depicts the distribution of c2 weighed by the sales of each product. To have a more real-
istic distribution of the exponent c2, the common coils (standard product) have been arbitrarily
weighted by 0.8 and the unusual coils by 0.2. These values correspond to the fact that manufac-
turers produce about 80% of standard products and 20% of nonstandard products. About 50% of
the most common cooling coils have a c2 value of –0.33.
With this default value of c2, the outside heat transfer in wet conditions UAext becomes
UAext = bv0a.77
(37)
Equation (37) is the condensed expression of Equations (20) to (33) according to the assump-
tions made. In dry conditions, the corrective factor Cf expressed in Equation (33) does not apply
and the outside heat transfer UAext is then
UAext = bv0a.67
(38)
The experimental Nüsselt correlation determined by Mirth (1994) for the dry cooling coil
agrees with the value obtained by this method in the case of dry regime.
Nu = 0.13 – Re0.67Pr1/3
(39)

146
HVAC&R RESEARCH
Figure 8. Architecture of Cooling Coil Model
The multiplier coefficient b in Equation (38) depends on thermal properties (viscosity, heat
capacity, and conductivity) and on geometrical data. For typical cooling coil air temperature
variation (15 to 30°C), the viscosity, heat capacity, and conductivity are assumed to be constant.
Thus, b is identified for a rating point for a specific cooling coil and is a constant for this cooling
coil. The volume airflow rate at inlet of the cooling coil is used instead of air velocity in order to
reduce the cooling coil data needed.
UA



extrat
0.77
V 0.77
(40)
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ
UAext
=


a
V
arat
To make the calculations less complicated and to avoid an iterative process, the outside heat
transfer correlation used for all cases (wet, dry, and partially wet) is Equation (40), which is spe-
cific for a wet regime. The effects of this assumption and of the default value for c2 are dis-
cussed later.
The model architecture is illustrated in Figure 8. Both pairs of model characteristics (UAextrat
,
Â
Â
Varat and UAintrat, merat ) are calculated from the nominal rating point values (i.e., maTaiwai for
Â
air conditions, mwTwi for water conditions, and QratQsenrat for outlet conditions). Then, using the
characteristic values, the performance of the cooling coil is calculated from air and water inlet
conditions for nonnominal operation.
SENSITIVITY TO ERRORS
The main assumptions of the model are integrated into the airside heat transfer correlation.
For the UAext correlation, Mirth and Ramadhyani (1993) have shown that errors in experimental
heat transfer rates are amplified when the convective heat exchange coefficient is determined. In
contrast, the error is reduced when predicting heat transfer using a heat transfer coefficient cor-
relation. Indeed, as demonstrated by Mirth and Ramadhyani (1993), a 20% uncertainty in the
heat exchange coefficient results in an uncertainty of less than 5% in the predicted coil heat
transfer rate. This effect is illustrated by the expression of the NTU-e relation for a counterflow
exchanger considering the range of NTU values.
The effects on the calculated energy rate of the main assumptions made are determined first
using various methods, including the statistical Monte Carlo method. Second, the estimation of
the uncertainty induced from characterization data is evaluated.

VOLUME 8, NUMBER 2, APRIL 2002
147
As described in Aude et al. (1997), a probability density is assigned to all the uncertain inputs
of the model. For each simulation, one value is selected randomly for each input based on its
probability of occurrence. Assuming the inputs are normally distributed, the extreme values are
less likely to be selected that the central value. Because all the inputs are perturbed simulta-
neously, this method fully accounts for any interactions between the inputs. The process is
repeated many times and, after several simulations, the standard deviation of each output of the
model can be estimated. The accuracy of the standard deviation estimation depends only on the
number of simulations.
Â
Â
All the uncertain parameters (Tai, wai, ma , Twi, and mw ) are simultaneously perturbed. For
each set of random input data, the simulation is carried out. For instance, standard deviation
σTao on output air temperature Tao is shown in Figure 9. This standard deviation depends on the
number of simulations carried out. Figure 9 shows σTao as a function of the number of simula-
tions for 10% uncertainty on cooling coil input data (see Table 2). The standard deviation sTao
first varies between maximum and minimum values, then converges as the number of simula-
tions increases. At 5000 simulations, convergence is reached; therefore, the following sensitivity
analysis is carried out to 5000 simulations. The uncertainty on the standard deviation of the out-
puts is 15% for 100 simulations, 4% for 750 simulations, and 1% for 5000 simulations. This
method is easy to use and well adapted for complex models for which analytical methods of
uncertainty prediction are not applicable, but requires long computer time.
The main assumption of the model is the air-side heat transfer correlation, and particularly on
the default value for c2. Using the statistic distribution of the parameter c2 for the complete com-
mercial gamut as presented in Figure 7, the probability density of c2 is evaluated for the 5000
simulations. The Monte Carlo method is applied with this probability density as an input for the
parameter c2 value. The nominal rating point used to determine the parameters of the cooling
Table 2. Uncertainty on Input Data
Â
Â
Variables
Tai
°C
wai
kg/kg
0.01118
10%
ma
Twi
°C
mw
Units
kg/s
0.6
kg/s
0.4
Values
23.1
2.3°C
9
Absolute/relative uncertainty
10%
0.9°C
10%
)LJXUHꢀꢁꢂ Evolution of Standard Deviation σ
According to
Number of Simulations in Monte Carlo Method

148
HVAC&R RESEARCH
Table 3. Nominal Rating Point
Â
Â
Â
Inputs
ma
Tai
wai
mw
Twi
°C
9
Q
Qsen UAextrat Varat UAintrat mwrat
Units
kg/s
°C
kg/kg kg/s
W
W
W/K
m3/s
W/K
kg/s
Rating point
0.85 23.1 0.01118 0.636
28 0.013 0.3
8508 6499
Operation point 0.3
6
1633
0.726 2427 0.636
)LJXUHꢀꢃꢄꢂ Impact of c Assumption on Energy Rate Uncertainties
coil and the operation point applied to the cooling coil for the simulation are presented in the
Table 3. The operation point, and particularly the airflow rate, is largely different from the nom-
inal rating point in order to magnify the induced error on the UAext calculation.
The relative uncertainty calculated using a normal law hypothesis for the c2 distribution is
3%. The order of magnitude for the relative uncertainties for the outlet conditions and total and
latent energy rates is roughly 0.2%. The probability densities of the two energy rates are pre-
sented in Figure 10. Notice that the reduced centered variable is introduced as follows:
X – X
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ
Xred cent
=
(41)
X
The uncertainty prediction calculation shows that the default value for the c2 parameter
induces a minor uncertainty on the outputs of the cooling coil model and produces a very small
effect on the energy rate calculation.
In order to reduce the complexity of the calculation, the outside correlation UAext used for the
calculation assumes the coil completely wet. This assumption does not mean the model always
considers condensation. The deviation introduced by this method is the difference between the
calculation made with a wet UAext value compared to a dry value for a cooling coil operating
under dry conditions. The deviation on UAext is presented in Figure 11 for different values of
inlet conditions, airflow rate, and water flow rate. The deviation on UAext implies a deviation on
the result of total energy rate about four times smaller. The uncertainties on total energy rate
introduced by the use of wet correlation for all cases are always lower than 3%. Using the wet
correlation agrees with the accuracy required by the global method and prevents time-expensive
iterations that are not desirable if the model is to be integrated in building simulation program.
To evaluate the error induced by the wet or dry determination method, the detailed model of
ASHRAE Toolkit is used as a reference model. Indeed, this model calculates the heat transfer
coefficient on the air and water sides from geometric coil data and from flow characteristics.
The proportion of wet surface is calculated using the iterative method in the case of a partially
wet regime. The model is applied to a typical 9000 m3/h air handler cooling coil. The coil has

VOLUME 8, NUMBER 2, APRIL 2002
149
Figure 11. Deviation Caused by Use of Wet Correlation in Dry Conditions
Figure 12. Difference Between Detailed and Simplified Model for Energy Rate and
Latent Energy Rate: Cooling Coil Under Partially Wet Conditions
smooth copper tubes (15.3 mm ID for 1 mm of thickness) with flat aluminum plate fins. The coil
is 4 rows deep and 22 tubes high, with 25 mm tube spacing. Moreover, the coil has a face area of
2.2 m2, with an external heat transfer surface of 178.6 m2 and internal heat transfer area of
11.3 m2. The fins are 0.19 mm thick and the fin diameter is 38 mm. There are 288.714 fins per
metre. Calculations are made for an airflow variation from 30% to 100% of its rating value
(1) for a cooling coil using a water temperature control device (5 to 7°C) and (2) using a flow
regulation device (25 to 100%). Entering air and humidity conditions of moist air vary from
24°C and 8 g/kg to 30°C and 10 g/kg. The results of the calculation of the energy rates are pre-
sented in Figures 12 and 13 for a partially wet cooling coil. The average relative difference
observed is 1.5% on total energy rate, with a maximum relative difference of 4.7%.
For the latent energy rate due to condensation, there are two main cases, attributed to the
method used to perform the calculation:
• For a condensation energy rate less than 2 kW (corresponding to 20% of the nominal value of
latent energy rate), the simplified model considers the coil to be completely dry and considers
the exchanged latent energy rate as the sensible energy rate. As a consequence, the overesti-
mation on the sensible energy rate is 1.7% on average, with a maximum of 4.3%.
• For condensation energy rates over 2 kW, the simplified model considers the cooling coil to
be completely wet. Between 2 kW and approximately 5 kW, the latent energy rate is underes-
timated. The mean difference is 14% and the maximum difference is 35%. For values over
5 kW, the latent energy rate is overestimated. The average difference is 5% and the maximum
difference is 9%.

150
HVAC&R RESEARCH
Figure 13. Deviation Between Simplified and Detailed Models for
Partially Wet Conditions, %
Figure 14. Errors Introduced by Data Characterization: Parameter Identification
Thus, the difference of the energy rate required from the chilled water is 1.5% on average,
corresponding to the difference in the total energy rate. On the other hand, the difference in
ambient conditions (indoor temperature and humidity) is more important due to the difference in
distribution between the sensible and latent energy rates. The maximum difference in outlet air
temperature is 24% and on outlet humidity is 13%. The average difference for both temperature
and humidity under partially wet regime is less than 2%.
In the global HVAC system consumption estimation, the error introduced by the hypothesis
on the partially wet regime is reduced. Indeed, if the model for a time step underestimates dehu-
midification, an artificial increase of the indoor humidity will be induced. So, at the next step,
since the air will be more humid, the model will overestimate the dehumidification and will par-
tially compensate for the error of the previous step.
After validating the main assumptions of the model, the next step is to determine the uncer-
tainties induced by the use of nominal rating point values and the associated uncertainties. The
nominal rating point includes seven variables. The uncertainty of each variable is given by the
French Standard for fan coils (NF Standard E 38). The values, which are similar to American
standard value for testing cooling coils, are summarized in Figure 14. Some uncertainties are
expressed in percentage and others in absolute values. It is necessary that only independent vari-
ables should be used to introduce uncertainties.

VOLUME 8, NUMBER 2, APRIL 2002
151
Figure 15. Errors Introduced by Data Characterization: Performance Calculation
Normal laws are considered for all input variables to determine the air and water exchange
coefficients linked to the associated flow rate. The probability density of the output agrees with
the assumption of normal laws. The uncertainties calculated during the parameter identification
process are summarized in Figure 14. This figure shows that uncertainties are important when
calculating air-side exchange coefficient from a fictitious effectiveness using Equation (13),
which results from the use of the logarithmic function for a value near zero.
The Monte Carlo method is applied to consider the calculated density probability for the
parameters and constant values for the inputs that are different from the rating point. The
method and values used to study the error propagation and the uncertainties of the outputs of the
model are summarized in Figure 15. The results indicate that the method using a nominal rating
point is accurate, provided that the measurements at rating point meet the requirements for stan-
dard precision. Indeed, the use of the NTU-ε expression reduces the uncertainties caused by out-
side exchange coefficient.
EXPERIMENTAL VALIDATION OF THE MODEL
The experimental setup used to validate the model is presented in Figure 16. The setup con-
sists of a variable air volume system. The air was circulated by two variable-speed centrifugal
fans (1500 to 4500 m3/h), one for supply air and one for exhaust air. The coil was controlled
with a temperature-control device. Particular attention was devoted to measurement of airflow
rate. The supply airflow rate was measured with a hot-wire anemometer at four places in the cir-
cular duct. The calculated error of the airflow rate measurement is 3%, including error of the
method and error of the sensors. The water flow rate uncertainty is 0.05 m3/s. Uncertainties are
0.2°C for air and water temperature measurements, and the relative uncertainty is 1.5% for abso-
lute air humidity. The experiments are made for an airflow variation from 30 to 100% of its rat-
ing value for the cooling coil using a water temperature control device (7 to 12°C). Inlet air
temperature and humidity conditions vary from 17°C and 45 g/kg to 24°C and 72 g/kg. The
nominal rating point used to characterize the model is taken from measurement. Input data are
represented on Figure 17 and details are given in the Appendix.
The coil is equipped with sinusoidal fins. Its characteristics are presented in Table 4. The cal-
culations of uncertainties are carried out for the measurements using the Monte Carlo method.
This leads to a 200 W (5%) error on total energy rate and 130 W (9%) error on latent energy
rate. It should be noted that, in this case, latent energy rate is not calculated from condensation
flow rate, which was not measured, but from outlet air conditions. Figures 18 and 19 present the
results of the comparison for energy rate and temperature. Concerning total energy rate, the

Figure 16. Experimental Apparatus

VOLUME 8, NUMBER 2, APRIL 2002
153
Figure 17. Experimental Input Data
Table 4. Coil Characteristics
Number of rows
4
Number of circuits
22
Duct height parallel to the tubes, m
Duct width, m
Outside tube diameter, m
Inside tube diameter, m
Thermal conductivity of tube material, W/(m·K)
Thickness of individual fin, m
0.61
0.638
0.0127
0.0109
389
0.0002
0.0018
305
Spacing between individual fins, m
Number of fins
Thermal conductuivity of fins, W/(m·K)
Distance between centers of tubes in a row, m
Distance between centerlines of tube rows, m
Specific heat of water + 20% ethylene glycol, J/(kg·K)
200
0.029
0.026
3800
calculated value fits into the measured value with a mean absolute relative error of 3%, includ-
ing wet and partially wet operation. The absolute error on energy rate is in the range of value of
the uncertainties on measured energy rate ( 200 W). Moreover, the outlet air temperature given
by the model agrees with the measured temperature with a mean absolute error of 0.3°C, with a
maximal and minimal error of respectively 1°C and –0.5°C. Concerning the latent energy rate,
(1) operation under wet conditions (1.8 to 2.45 kW) is well represented by the model and intro-
duces a mean relative error of 3%; and (2) during operation under partially dry and wet condi-
tions (0 to 0.7 kW), the latent energy rate is underestimated because of the method used to
perform the calculation. This phenomenon occurs for low values of latent energy rate, and the
induced error has a minimal influence on the building energy consumption estimation, as
explained previously.

154
HVAC&R RESEARCH
Figure 18. Experimental Validation on Energy Rate and Latent Energy Rate
Figure 19. Experimental Validation on Outlet Air Temperature and
Outlet Water Temperature
The experimental validation demonstrates the accuracy of the model and sheds light on the
precautions that should be taken for a good use of the model. The model is well adapted to the
global building energy consumption. Other applications of the model are feasible, after allowing
for the relative inaccuracy in modeling partially wet regimes.
CONCLUSION
The proposed method for modeling cooling coils can be easily integrated into methods for
estimating the energy use in buildings. The three main advantages of the model are
• Detailed cooling coil geometrical data are not required; only one nominal rating point is used
to characterize the coil.
• The model is accurate under nonnominal conditions.
• The noncontrolled dehumidification energy rate is estimated correctly.
Therefore, this model allows the real operating performance of the cooling coil to be taken
into account without significant computational efforts. This model has been integrated in the
ConsoClim method (Morisot et al. 1997) for estimating building energy consumption.
120(1&/$785(
A
Aint
Al
air-side exchange area, m2
water-side exchange area, m2
airflow maximal area, m2
airflow area, m2
As
Acor
airflow fin area, m2
air-side exchange area corrected by fin
efficiency, m2
Aa
cpa
specific heat of air, J/(kg·K)

VOLUME 8, NUMBER 2, APRIL 2002
155
c
c
c
specific heat of saturated air, J/(kg·K)
Pr
P
P
Q
Re
T
Prandtl number
specific heat of liquid water, J/(kg·K)
specific heat of water vapor, J/(kg·K)
coefficient for j factor from COLBURN
correlation
minimal capacity rate between air and
water, kg/s
transverse tube spacing, m
longitudinal tube spacing, m
total energy rate, W
Reynolds number
temperature, K
overall enthalpy heat transfer coefficient,
W/K
c , c
C
UA
d
inside pipe diameter, m
d
d
d
e
air-side hydraulic diameter, m
outside tube diameter, m
equivalent circular fin diameter, m
fin thickness, m
enthalpy of saturated air at apparatus
dew-point temperature, J/kg
convection heat transfer coefficient on
air-side, W/(m ·K)
convection heat transfer coefficient for
wet coil, W/(m ·K)
convection heat transfer coefficient for dry
coil, W/(m ·K)
convection heat transfer coefficient on
liquid-side, W/(m ·K)
mass transfer coefficient, kg/(m ·s)
enthalpy of air, J/kg
enthalpy of saturated air at liquid
temperature, J/kg
heat of vaporization at 0°C, J/kg
mass flux (flow/area), kg/(m ·s)
factor of COLBURN correlation
equivalent fin height, m
mass air flow rate, kg/s
PDVVꢁZDWHUꢁIORZꢁUDWHꢂꢁNJꢃV
FRQGHQVDWLRQꢁIORZꢁUDWHꢂꢁNJꢃV
number of rows of the coil
fin thermal resistance, K/W
fin air-side convection resistance, K/W
Nusselt number
UA
UA
v
v
Va
w
air-side heat transfer coefficient, W/K
liquid-side heat transfer coefficient, W/K
front face velocity, m/s
front water velocity, m/s
specific dry air volumetric flow rate, m /s
humidity ratio, kg/kg dry air
variable
average value of the population of X
variable
log mean enthalpy difference, J/kg
constant
hadp
h
h
h
h
X
X
∆hlm
α
ε
coil effectiveness or fin factor
εfictitious coil effectiveness of fictitious coil with
infinite water flow rate
fin efficiency
h
h
h
ηail
λa
λw
µa
µw
νa
thermal air conductivity, W/(m·K)
thermal water conductivity, W/(m·K)
dynamic air viscosity, Pa/s
dynamic water viscosity, Pa/s
kinematic air viscosity, m2/s
air density, kg/m3
Hfg
G
j
ρa
ρw
l
m
mw
mcond
water density, kg/m3
Â
Âa
Subscripts
i
o
a
Â
inlet
outlet
air
water
N
R
R
Nu
NTU
P
w
cond
rat
sat
condensation film
related to the nominal rating point
at saturation
number of transfer unit
fin spacing, m
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ginia: Air-Conditioning and Refrigeration Institute.
ASHRAE. 1994. 1994 ASHRAE Handbook—Fundamentals. Atlanta: American Society of Heating,
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Aude, P., P. Depecker, and J. Virgone. 1997. Building Thermal Modelling: An Example of Radiative
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Brandemuehl, M.J., S. Gabel, and I. Andersen. 1993. A Toolkit for Secondary HVAC System Energy Calcu-
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Boulder.
Braun, J.E. 1988. Methodologies for the Design and Control of Central Cooling Plants. Ph.D. dissertation,
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156
HVAC&R RESEARCH
Chuah, Y.K., C.C. Hung, and P.C. Tseng. 1998. Experiments on the Dehumidification Performance of a
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Finned Tube Heat Transfer Surfaces with Staggered Tubes. ASHRAE Transactions 84(1):294-309.
Mirth, D.R. 1994. Experimental Studies and Mathematical Modeling of Chilled-Water Cooling Coils.
Ph.D. dissertation, Purdue University, West Lafayette, Indiana.
Mirth, D.R. and S. Ramadhyani. 1993. Prediction of Cooling Coil Performance Under Condensing Condi-
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Morisot, O. 2000. Modèle de batterie froide à eau glacée adapté à la maitrise des consommations d’éner-
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Sacadura, J.F. 1993. Initiation aux Transferts Thermiques. 4th edition. Paris: Tec et Doc Lavoisier.
Taborek, J., G.F Hewitt, and N. Afgan. 1983. Heat Exchangers: Theory and Practice. New York: Hemi-
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tice-Hall.
Turaga, M, S. Lin, and P.P. Fazio. 1988. Correlations for Heat Transfer and Pressure Drop Factors for
Direct Expansion Air Cooling and Dehumidifying Coils. ASHRAE Transactions 94(2):616-630.
Wang, C.C, Y.C. Hsieh, and Y.T. Lin. 1997. Performance of Plate Finned Tube Heat Exchanger Under
Dehumidifying Conditions. Journal of Heat Transfer 119:109-117.
Wang, C.C., W.L. Fu, and C.T. Chang. 1997. Heat Transfer and Friction Characteristics of Typical Wavy
Fin-and-Tube Heat Exchanger. Experimental Thermal and Fluid Science 14:176-186.
Appendix: Experimental Data
Â
Â
Â
Â
Tao, wao, Two, mw Tai, wai,
m , Twi, Tao, wao, Two, mw Tai, wai, ma Twi,
, ,
a
,
°C g/kg da °C kg/s °C g/kg da kg/s °C °C g/kg da °C kg/s °C g/kg da kg/s °C
11.3 8.33 10.3 0.639 22.8 11.2
11.3 8.31 10.3 0.639 22.8 11.3
11.2 8.29 10.2 0.639 22.8 11.3
11.2 8.3 10.2 0.639 22.8 11.3
11.2 8.29 10.1 0.639 22.8 11.4
11.2 8.29 10.1 0.639 22.8 11.4
11.2 8.25 10 0.639 22.7 11.4
11.2 8.26 10 0.639 22.7 11.4
11.2 8.26 10 0.639 22.7 11.4
0.30 8.0 11.4 8.36 11.4 0.639 17.6
0.30 7.9 11.5 8.43 11.5 0.639 17.6
0.30 7.8 11.4 8.38 11.5 0.639 17.6
0.30 7.8 11.5 8.42 11.6 0.639 17.6
0.30 7.7 11.5 8.43 11.6 0.639 17.6
0.30 7.7 11.5 8.43 11.6 0.639 17.6
0.30 7.6 11.6 8.49 11.7 0.639 17.6
0.30 7.6 11.6 8.49 11.7 0.639 17.6
8.8 0.30 10.5
9.0 0.30 10.6
8.7 0.30 10.6
8.7 0.30 10.7
8.6 0.30 10.8
8.6 0.30 10.8
8.7 0.30 10.9
8.7 0.30 10.9
8.7 0.37 11.3
8.8 0.37 11.3
8.6 0.37 11.0
8.7 0.37 10.6
8.6 0.37 10.5
0.30 7.6 12
0.37 8.3 12
8.68 12.1 0.639 17.3
8.69 12.1 0.639 17.3
12.2 8.85 10.9 0.639 23
12.2 8.84 10.9 0.639 23
12.2 8.86 10.9 0.639 23
12.2 8.83 10.8 0.639 23
11.3
11.2
11.3
11.3
0.37 8.3 11.8 8.54 11.9 0.639 17.3
0.37 8.3 11.6 8.46 11.6 0.639 17.3
0.37 8.2 11.5 8.42 11.5 0.639 17.3

VOLUME 8, NUMBER 2, APRIL 2002
157
Appendix: Experimental Data (Continued)
Â
Â
Â
Â
Tao, wao, Two, mw Tai, wai,
m , Twi, Tao, wao, Two, mw Tai, wai, ma Twi,
, ,
a
,
°C g/kg da °C kg/s °C g/kg da kg/s °C °C g/kg da °C kg/s °C g/kg da kg/s °C
12.2 8.85 10.9 0.639 23 11.3 0.37 8.3 11.4 8.37 11.3 0.639 17.4
0.37 8.2 11.4 8.4 11.3 0.639 17.4
0.37 8.2 11.4 8.37 11.2 0.639 17.4
0.37 8.1 11.2 8.3 11.1 0.639 17.4
8.7 0.37 10.3
8.8 0.37 10.2
9.0 0.37 10.0
8.8 0.37 9.9
8.3 0.41 9.9
8.3 0.41 9.8
8.3 0.41 10.4
8.5 0.41 10.4
8.6 0.41 10.5
8.4 0.41 10.6
8.5 0.41 10.7
8.5 0.41 10.7
8.5 0.41 10.8
8.1 0.47 10.1
8.5 0.47 10.3
8.6 0.47 10.4
8.5 0.47 10.5
8.5 0.47 10.6
8.4 0.47 10.7
8.4 0.47 10.8
8.6 0.47 10.8
8.6 0.47 10.9
7.2 0.52 10.6
7.2 0.52 10.7
7.3 0.52 10.7
7.3 0.52 10.9
7.3 0.52 11.0
7.3 0.52 11.0
7.3 0.52 11.1
7.2 0.52 11.2
7.3 0.52 11.3
7.3 0.58 11.3
7.3 0.58 10.7
7.3 0.58 10.6
7.2 0.58 10.4
7.3 0.58 10.3
7.3 0.58 10.2
7.3 0.58 10.1
7.2 0.58 10.0
7.3 0.58 9.9
7.4 0.63 10.3
7.4 0.63 10.2
7.3 0.63 10.1
7.3 0.63 10.0
7.3 0.63 10.0
12.1 8.82 10.8 0.639 22.9 11.2
12.1 8.78 10.8 0.639 22.9 11.1
12.1 8.79 10.7 0.639 22.9 11.2
12.1 8.77 10.6 0.639 22.9 11.2
12.8 9.19 11.6 0.639 23.1 11.3
12.7 9.15 11.5 0.639 23.1 11.2
12.8 9.19 11.5 0.639 23.1 11.3
12.8 9.19 11.5 0.639 23.1 11.4
12.7 9.15 11.4 0.639 23.1 11.3
12.7 9.12 11.4 0.639 23.1 11.2
12.7 9.14 11.4 0.639 23.1 11.2
12.7 9.15 11.4 0.639 23.1 11.3
12.7 9.13 11.3 0.639 23.1 11.3
13.4 9.55 12 0.639 23.3 11.4
13.4 9.52 11.9 0.639 23.3 11.4
13.4 9.49 11.9 0.639 23.2 11.3
13.4 9.49 11.9 0.639 23.2 11.3
13.4 9.49 11.8 0.639 23.2 11.3
13.4 9.49 11.8 0.639 23.2 11.3
13.4 9.49 11.9 0.639 23.2 11.3
13.3 9.46 11.8 0.639 23.2 11.2
13.9 9.84 12.4 0.639 23.5 11.5
13.9 9.8 12.4 0.639 23.4 11.4
13.9 9.78 12.3 0.639 23.4 11.4
13.9 9.78 12.3 0.639 23.4 11.4
13.8 9.76 12.3 0.639 23.4 11.4
13.9 9.78 12.3 0.639 23.4 11.4
13.9 9.78 12.3 0.639 23.4 11.4
13.8 9.77 12.3 0.639 23.3 11.4
13.8 9.74 12.2 0.639 23.3 11.4
14.2 9.97 12.6 0.639 23.6 11.3
14.2 9.96 12.6 0.639 23.6 11.2
14.3 9.98 12.6 0.639 23.6 11.3
14.3 9.99 12.6 0.639 23.6 11.3
14.3 9.98 12.6 0.639 23.6 11.3
14.3 9.99 12.6 0.639 23.6 11.3
14.3 9.98 12.6 0.639 23.6 11.3
14.2 9.97 12.6 0.639 23.5 11.3
14.2 9.98 12.6 0.639 23.5 11.3
14.6 10.2 12.9 0.639 23.6 11.3
14.6 10.1 12.8 0.639 23.6 11.3
14.6 10.2 12.9 0.639 23.6 11.4
14.6 10.2 12.9 0.639 23.6 11.4
14.6 10.1 12.8 0.639 23.6 11.3
0.37 8.0 11.2 8.18 11 0.639 17.3
0.41 8.9 11.1 8.14 10.9 0.639 17.3
0.41 8.8 11.4 8.28 11.4 0.639 17.2
0.41 8.8 11.5 8.37 11.4 0.639 17.2
0.41 8.8 11.6 8.43 11.5 0.639 17.2
0.41 8.7 11.6 8.36 11.6 0.639 17.2
0.41 8.7 11.6 8.41 11.7 0.639 17.2
0.41 8.7 11.7 8.44 11.7 0.639 17.2
0.41 8.7 11.7 8.46 11.8 0.639 17.2
0.41 8.6 11.8 8.08 11.6 0.639 19.5
0.47 9.2 11.9 8.42 11.8 0.639 19.4
0.47 9.1 12
0.47 9.1 12
0.47 9.1 12
0.47 9.0 12
8.55 11.9 0.639 19.2
8.45 11.9 0.639 19
8.45 12 0.639 18.9
8.44 12 0.639 18.7
0.47 9.0 12.1 8.43 12.1 0.639 18.5
0.47 9.1 12.1 8.57 12.1 0.639 18.4
0.47 9.0 12.1 8.57 12.1 0.639 18.3
0.52 9.4 12.4 7.24 12.2 0.639 19.9
0.52 9.4 12.5 7.21 12.3 0.639 19.9
0.52 9.3 12.5 7.27 12.3 0.639 19.9
0.52 9.3 12.6 7.31 12.5 0.639 19.9
0.52 9.3 12.6 7.25 12.6 0.639 19.8
0.52 9.3 12.6 7.29 12.6 0.639 19.8
0.52 9.3 12.7 7.31 12.7 0.639 19.9
0.52 9.3 12.8 7.22 12.7 0.639 19.8
0.52 9.2 12.9 7.27 12.8 0.639 19.8
0.58 9.5 13.1 7.3
13 0.639 20.1
0.58 9.5 12.8 7.28 12.5 0.639 20.1
0.58 9.5 12.7 7.27 12.4 0.639 20
0.58 9.5 12.5 7.24 12.2 0.639 20
0.58 9.5 12.5 7.25 12.1 0.639 20
0.58 9.5 12.4 7.27 12 0.639 20
0.58 9.5 12.4 7.3
12 0.639 20
0.58 9.5 12.3 7.22 11.9 0.639 20
0.58 9.5 12.2 7.27 11.8 0.639 20
0.63 9.7 12.8 7.36 12.3 0.639 20.4
0.63 9.7 12.7 7.36 12.2 0.639 20.4
0.63 9.7 12.7 7.29 12.1 0.639 20.4
0.63 9.7 12.6 7.27 12.1 0.639 20.4
0.63 9.6 12.6 7.3
12.1 0.639 20.4

158
HVAC&R RESEARCH
Appendix: Experimental Data (Continued)
Â
Â
Â
Â
Tao, wao, Two, mw Tai, wai,
m , Twi, Tao, wao, Two, mw Tai, wai, ma Twi,
,
,
,
a
°C g/kg da °C kg/s °C g/kg da kg/s °C °C g/kg da °C kg/s °C g/kg da kg/s °C
14.5 10.1 12.8 0.639 23.6 11.3
14.5 10.1 12.8 0.639 23.6 11.3
14.6 10.1 12.8 0.639 23.6 11.3
14.5 10.1 12.8 0.639 23.6 11.3
14.8 10.3 12.9 0.639 23.4 11.3
14.8 10.2 12.9 0.639 23.4 11.2
14.8 10.3 12.9 0.639 23.5 11.3
14.8 10.3 12.9 0.639 23.5 11.3
14.8 10.3 12.9 0.639 23.5 11.3
14.7 10.2 12.8 0.639 23.4 11.2
14.9 10.3 12.9 0.639 23.5 11.4
14.9 10.3 13 0.639 23.5 11.3
14.8 10.3 12.9 0.639 23.5 11.3
14.9 10.3 12.7 0.639 23.1 11.2
0.63 9.6 12.5 7.21 11.9 0.639 20.3
0.63 9.6 12.4 7.26 11.8 0.639 20.3
0.63 9.6 12.4 7.27 11.8 0.639 20.3
7.2 0.63 9.8
7.3 0.63 9.7
7.3 0.63 9.7
7.3 0.63 9.6
7.2 0.69 9.8
7.1 0.69 9.8
7.1 0.69 9.7
7.2 0.69 9.5
7.3 0.69 10.2
7.2 0.69 10.3
7.3 0.69 10.5
7.1 0.69 10.6
7.2 0.69 10.7
7.1 0.75 10.3
7.0 0.75 10.2
6.9 0.75 10.1
6.9 0.75 10.0
7.0 0.75 9.9
7.0 0.75 9.8
7.0 0.75 9.7
7.1 0.75 10.0
7.1 0.75 10.4
7.0 0.80 9.8
7.0 0.80 9.7
7.1 0.80 9.8
7.1 0.80 9.7
7.0 0.80 9.5
6.9 0.80 9.5
7.0 0.80 10.2
7.0 0.80 10.3
6.9 0.80 10.4
7.0 0.85 10.2
7.0 0.85 10.1
7.1 0.85 10.0
7.1 0.85 10.0
7.0 0.85 9.9
7.0 0.85 9.9
7.0 0.85 9.8
7.1 0.85 9.7
7.1 0.85 9.7
0.63 9.6 12.4 7.3
11.7 0.639 20.3
0.69 9.7 12.8 7.21 12 0.639 20.5
0.69 9.7 12.8 7.13 12 0.639 20.5
0.69 9.7 12.8 7.15 11.9 0.639 20.5
0.69 9.7 12.7 7.21 11.8 0.639 20.5
0.69 9.7 13
7.29 12.4 0.639 20.5
0.69 9.6 13.1 7.23 12.4 0.639 20.5
0.69 9.6 13.2 7.27 12.6 0.639 20.5
0.69 9.7 13.2 7.14 12.7 0.639 20.4
0.69 9.7 13.3 7.17 12.8 0.639 20.4
0.75 9.4 13.4 7.07 12.6 0.639 20.7
0.75 9.4 13.3 7.02 12.5 0.639 20.7
0.75 9.4 13.3 6.93 12.4 0.639 20.7
0.75 9.5 13.2 6.95 12.3 0.639 20.6
0.75 9.4 13.2 6.96 12.2 0.639 20.6
0.75 9.4 13.1 6.98 12.2 0.639 20.6
0.75 9.5 13.1 7.03 12.1 0.639 20.6
0.75 9.4 13.2 7.09 12.3 0.639 20.6
0.75 9.4 13.4 7.06 12.7 0.639 20.6
0.80 9.2 13.5 6.97 12.3 0.639 21
0.80 9.3 13.4 7.01 12.2 0.639 21
0.80 9.3 13.5 7.08 12.3 0.639 21
0.80 9.3 13.4 7.08 12.2 0.639 21
0.80 9.3 13.3 7.00 12.1 0.639 21
0.80 9.3 13.3 6.87 12.1 0.639 21
0.80 9.4 13.6 6.95 12.7 0.639 21
0.80 9.3 13.7 6.98 12.8 0.639 21
0.80 9.4 13.7 6.94 12.8 0.639 20.9
0.85 8.8 13.9 7.03 12.8 0.639 21.1
0.85 8.8 13.8 7.03 12.7 0.639 21
0.85 8.8 13.8 7.09 12.6 0.639 21.1
0.85 8.9 13.8 7.06 12.6 0.639 21.1
0.85 8.9 13.7 6.99 12.5 0.639 21.1
0.85 9.0 13.7 6.99 12.5 0.639 21.1
0.85 9.0 13.7 7.01 12.4 0.639 21.1
0.85 9.0 13.7 7.07 12.4 0.639 21.1
0.85 9.0 13.7 7.06 12.4 0.639 21.1
0.30 10.4
14.8 10.2 12.7 0.639 23
14.8 10.2 12.7 0.639 23
14.8 10.2 12.8 0.639 23
14.8 10.2 12.7 0.639 23
14.8 10.2 12.7 0.639 23
14.8 10.2 12.7 0.639 23
14.8 10.2 12.7 0.639 23
14.8 10.2 12.7 0.639 23
11.1
11.1
11.1
11.1
11.1
11.1
11.1
11.1
15.1 10.4 12.7 0.639 23.2 11.3
15.2 10.5 12.8 0.639 23.3 11.4
15.2 10.5 12.8 0.639 23.3 11.4
15.1 10.4 12.7 0.639 23.2 11.3
15.1 10.4 12.8 0.639 23.2 11.3
15.1 10.4 12.7 0.639 23.2 11.3
15.2 10.4 12.8 0.639 23.2 11.3
15.1 10.4 12.7 0.639 23.1 11.2
15.1 10.4 12.8 0.639 23.1 11.2
15.0 10.3 12.3 0.639 22.5 11.2
15.1 10.4 12.3 0.639 22.7 11.3
15.0 10.3 12.3 0.639 22.8 11.2
15.1 10.4 12.4 0.639 22.9 11.1
15.1 10.4 12.4 0.639 23
15.1 10.4 12.5 0.639 23
11.2
11.2
15.2 10.4 12.5 0.639 23.1 11.2
15.1 10.4 12.5 0.639 23.1 11.1
15.2 10.4 12.5 0.639 23.1 11.2
11.3 8.32 11.3 0.639 17.6
8.8