4301 NORTH FAIRFAX DRIVE • ARLINGTON, VIRGINIA 22203
2001
STANDARD for
FORCEDCIRCULATION
AIR-COOLING
AND
AIR-HEATING
COILS
Standard 410
Price $20.00 (M) $40.00 (NM) ©Copyright 2001, by Air-Conditioning and Refrigeration Institute
Printed in U.S.A. Registered United States Patent and Trademark Office
IMPORTANT
SAFETY RECOMMENDATIONS
It is strongly recommended that the product be designed, constructed, assembled and installed in accordance with
nationally recognized safety requirements appropriate for products covered by this standard.
ARI, as a manufacturers' trade association, uses its best efforts to develop standards employing state-of-the-art and
accepted industry practices. However, ARI does not certify or guarantee safety of any products, components or
systems designed, tested, rated, installed or operated in accordance with these standards or that any tests conducted
under its standards will be non-hazardous or free from risk.
ARI CERTIFICATION PROGRAM PROVISIONS
Scope of the Certification Program
The Certification Program includes Forced-Circulation Air-Cooling Coils for application under non-frosting
conditions, and Forced-Circulation Air-Heating Coils, as defined in Section 3 of the standard.
Coils Included. This program applies only to coils intended:
a. For field installation (built-up systems)
b. For use in central station air-conditioning units
c. For use in central station heating or heating and ventilating units
Exclusion. It does not include:
a. Coils sold to original equipment manufacturers for inclusion in packaged units
b. Coils installed in packaged air-conditioning or heating units by the manufacturer
c. Special coils: Coils of fin or tube material of special configuration not having cataloged
performance data
Note: For the purpose of this program, a packaged unit is an assembly of components including coil(s) whose
rating is based on a test of the complete assembly.
Certified Ratings
The following Certification Program ratings are verified by test:
a. Average total cooling or heating capacity, Btu/h [W]
b. Air pressure drop through coil at standard air density, in H2O [kPa]
c. Water or aqueous ethylene glycol solution pressure drop through coil (including headers) at average fluid
density, ft of fluid [m of fluid]
Note:
This standard supersedes ARI Standard 410-91.
TABLE OF CONTENTS
SECTION PAGE
Section 1. Purpose .....................................................................................................................1
Section 2. Scope ........................................................................................................................1
Section 3. Definitions .................................................................................................................1
Section 4. Classifications ............................................................................................................3
Section 5. Test Requirements ................................................................................................... 10
Section 6. Rating Requirements................................................................................................ 14
Section 7. Minimum Data Requirements for Published Ratings ................................................. 24
Section 8. Symbols and Units ................................................................................................... 24
Section 9. Reference Properties and Conversion Factors........................................................... 27
Section 10. Marking and Nameplate Data................................................................................... 27
Section 11. Conformance Conditions.......................................................................................... 27
TABLES
Table 1. Range of Standard Rating Conditions.........................................................................2
Table 2. Required Laboratory Tests....................................................................................... 10
Table 3. Metal Thermal Conductivities .................................................................................. 20
Table 4. Conversion Factors .................................................................................................. 28
FIGURES
Figure 1. Combined Air Film and Metal Thermal Resistance for Dry Surface vs.
Air Film Thermal Resistance for Dry Surface ........................................................... 29
Figure 2. Total Metal Thermal Resistance of Fin and Tube Assembly
Based on Total Surface Effectiveness....................................................................... 30
Figure 3. Rating Data for Steam Coils..................................................................................... 31
Figure 4. Rating Data for Hot or Cold Water Sensible Heat Coils ........................................... 32
Figure 5. Rating Data for Cold Water Cooling and Dehumidifying Coils ................................. 33
Figure 6. Rating Data for Volatile Refrigerant Cooling and Dehumidifying
Coils ........................................................................................................................ 34
Figure 7. Temperature Correction Factor for Water Pressure Drop ......................................... 35
Figure 8. Air-Side Heat Transfer Coefficient Multiplier for Wet Surface.................................. 36
Figure 9. Surface Temperature Chart for Air Cooling and Dehumidifying Coil Application...... 37
Figure 10. Efficiency of Annular Fins of Constant Thickness..................................................... 38
Figure 11. Efficiency of Annular Fins of Constant Area for Heat Flow and Spiral Fins............... 39
Figure 12. Determination of RaW, fr and qt................................................................................ 40
Figure 13. Crossflow Air-Side Effectiveness ............................................................................. 41
Figure 14. Cross-Counterflow Air-Side Effectiveness ............................................................... 42
Figure 15. Counterflow Air-Side Effectiveness.......................................................................... 43
Figure 16. Aqueous Ethylene Glycol Solution Performance for Smooth Internal Tube Wall
Coils ........................................................................................................................ 44
Figure 17. Smooth Internal Tube Wall Heat Transfer Factor for Water ..................................... 45
APPENDICES
Appendix A. References - Normative............................................................................................ 46
Appendix B. References - Informative .......................................................................................... 47
ARI STANDARD 410-2001
1
FORCED-CIRCULATION AIR-COOLING
AND AIR-HEATING COILS
Section 1. Purpose
1.1 Purpose. The purpose of this standard is to establish
for Forced-Circulation Air-Cooling and Air-Heating
Coils: definitions; classifications; test requirements;
rating requirements; minimum data requirements for
Published Ratings; symbols and units; reference
properties and conversion factors; marking and
nameplate data; and conformance conditions.
1.1.1 Intent. This standard is intended for the
guidance of the industry, including manufacturers,
engineers, installers, contractors and users.
1.1.2 Review and Amendment. This standard is
subject to review and amendment as technology
advances.
Section 2. Scope
2.1 Scope. This standard applies to Forced-Circulation
Air-Cooling and Air-Heating Coils, as defined in Section
3 and classified in Section 4 of this standard, and for
application under non-frosting conditions.
This standard documents a fundamental means for
establishing coil performance by extension of laboratory
test data to other operating conditions and other coil sizes
and row depths.
Section 3. Definitions
All terms in this document shall follow the standard
industry definitions in the current edition of ASHRAE
Terminology of Heating, Ventilation, Air Conditioning
and Refrigeration unless otherwise defined in this
section.
3.1 Coil Line. For the purpose of this standard, a coil
line is defined as having the following in common:
a. Fluid (volatile refrigerant, water, steam or
aqueous ethylene glycol solution)
b. Tube size, spacing, arrangement (parallel or
staggered) or internal construction
c. Fin configuration (not spacing)
3.1.1 Examples of coil lines are:
a. Aqueous Ethylene Glycol Solution. If
conditions b and c of 3.1 are satisfied, the
following are types which may be part of one
line:
1. Continuous circuit type
2. Self-draining type
3. Cleanable type
b. Steam Distributing.
c. Steam Single-Tube.
d. Volatile Refrigerant. Direct expansion
coil with flow controlled by the expansion
valve.
e. Water. If conditions b and c of 3.1 are
satisfied, the following are types which may
be part of one line:
1. Continuous circuit type
2. Self-draining type
3. Cleanable type
3.2 Cooling Capacity. The capacity associated with the
change in air enthalpy which includes both the Latent
and Sensible Capacities expressed in Btu/h [W].
3.2.1 Latent Capacity. Capacity associated with a
change in humidity ratio.
3.2.2 Sensible Capacity. Capacity associated with a
change in dry-bulb temperature.
3.3 Forced-Circulation Air Coil. A coil for use in an air
stream whose circulation is caused by a difference in
pressure produced by a fan or blower.
3.3.1 Forced-Circulation Air-Cooling Coil. A heat
exchanger, with or without extended surfaces,
through which either cold water, cold aqueous
ethylene glycol solution or volatile refrigerant is
circulated, for the purpose of total cooling (sensible
cooling plus latent cooling) of a forced-circulation
air stream.
ARI STANDARD 410-2001
2
Table 1. Range of Standard Rating Conditions
Cooling Coils Heating Coils
Item
Volatile
Refrigerant
Cold
Water
Cold Ethylene
Glycol Solution Steam
Hot
Water
Hot Ethylene
Glycol Solution
Standard air face velocity,
std. ft/min [std. m/s]
200 to 800
[1 to 4]
200 to 800
[1 to 4]
200 to 800
[1 to 4]
200 to 1,500
[1 to 8]
200 to 1,500
[1 to 8]
200 to 1,500
[1 to 8]
Entering air dry-bulb temp.,
°F [°C]
65 to 100
[18 to 38]
65 to 100
[18 to 38]
65 to 100
[18 to 38]
-20 to 100
[-29 to 38]
0.0 to 100
[-18 to 38]
-20 to 100
[-29 to 38]
Entering air wet-bulb temp.,
°F [°C]
60 to 85
[16 to 29]
60 to 85
[16 to 29]
60 to 85
[16 to 29]
--
--
--
--
--
--
Tube-Side fluid velocity,
std. ft/s [std. m/s]
--
--
11.0 to 8.0
[0.3 to 2.4]
21.0 to 6.0
[0.3 to 1.8]
--
--
10.5 to 8.0
[0.1 to 2.4
20.5 to 6.0
[0.1 to 1.8]
Entering fluid temp., °F
[°C]
--
--
35 to 65
[1.7 to 18]
0.0 to 90
[-18 to 32]
--
--
120 to 250
[49 to 121]
0.0 to 200
[-18 to 93]
Saturated suction refrigerant
temp. at coil outlet, °F [°C]
30 to 55
[-1.1 to 13]
--
--
--
--
--
--
--
--
--
--
Minimum suction vapor
superheat at coil outlet,
°F [°C]
6.0
[3.3]
--
--
--
--
--
--
--
--
--
--
Steam pressure at coil inlet,
psig [kPa gage]
--
--
--
--
--
--
2.0 to 250.0
[14 to 1723]
--
--
--
--
Maximum superheat in
steam at coil inlet, °F [°C]
--
--
--
--
--
--
50
[28]
--
--
--
--
Concentration by mass, % -- -- 10 to 60 -- -- 10 to 60
Minimum fin surface
temperature, °F [°C]
> 32
[> 0.0]
> 32
[> 0.0]
> 32
[> 0.0]
> 32
[> 0.0]
> 32
[> 0.0]
> 32
[> 0.0]
Minimum tube wall surface
temperature, °F [°C]
> 32
[> 0.0]
> 32
[> 0.0]
> ethylene glycol
sol. freeze point
> 32
[> 0.0]
> 32
[> 0.0]
> ethylene glycol
sol. freeze point
1 On lower limit, Re shall exceed 3100 at twm. Predicted performance and actual performance in the water velocity range below the
tube-side fluid velocity listed above is expected to show variations in excess of currently accepted tolerances for the following
reasons:
1) Application of coils at low velocity can lead to excessive fouling.
2) Application of coils at low velocity can lead to possible air entrapment.
3) Differences in coil design/type affect the variation in low Re heat transfer coefficient.
2 On lower limit, Re shall exceed 700 at tgm.
Note: Numbers in [ ] are in SI Units
3.3.2 Forced-Circulation Air-Heating Coil. A heat
exchanger, with or without extended surfaces,
through which either hot water, hot aqueous ethylene
glycol solution or steam is circulated for the purpose
of sensible heating of a forced-circulation air stream.
3.4 Heating Capacity. The capacity associated with the
change in dry-bulb temperature expressed in Btu/h [W].
3.5 Laboratory Tests. Tests conducted by a
manufacturer on representative coils to determine basic
heat transfer and pressure drop characteristics that shall
be used in developing Published Ratings.
3.6 Published Ratings. A compilation of the assigned
values of those performance characteristics, under stated
rating conditions, by which a coil may be chosen to fit its
application. These values apply to all coils of like
nominal size and type (identification) produced by the
same manufacturer. As used herein, the term Published
Ratings includes the ratings of all performance
characteristics published in specifications, advertising or
other literature controlled by the manufacturer or
available through an automated rating/selection computer
procedure.
3.6.1 Application Ratings. Ratings determined at
conditions outside the range of standard rating
conditions.
ARI STANDARD 410-2001
3
3.6.2 Standard Ratings. Ratings within the range
of standard rating conditions (Table 1) and which
are accurate representations of test data.
3.7 "Shall" or "Should". Shall or "should" shall be
interpreted as follows:
3.7.1 Shall. Where "shall" or "shall not" is used for
a provision specified, that provision is mandatory if
compliance with the standard is claimed.
3.7.2 Should. "Should" is used to indicate
provisions which are not mandatory but which are
desirable as good practice.
3.8 Standard Air. Air weighing 0.075 lb/ft3 [1.2 kg/m3]
which approximates dry air at 70°F [21°C] and at a
barometric pressure of 29.92 in Hg [101.3 kPa].
3.9 Standard Coil Orientation. The standard coil
position is that of horizontal tubes and vertical coil face
with horizontal airflow.
3.10 Test Series. A group of related tests performed on
the same test coil.
3.11 Turbulators. Mechanical devices inside tubes used
to increase turbulence of fluids.
Section 4. Classifications
4.1 Coil Surface Dimensions, Terminology and Surface
Calculations.
4.1.1 Tube Arrangements and Types of Fin
Combinations.
4.1.1.1 Staggered tubes with:
a. Continuous flat plate fins
b. Continuous configurated plate
fins
c. Crimped spiral fins
d. Smooth spiral fins
e. Flat plate fins on individuallyfinned
tube
f. Configurated plate fins on
individually-finned tube
4.1.1.2 Parallel (in-line) tubes with:
a. Continuous flat plate fins
b. Continuous configurated plate
fins
c. Crimped spiral fins
d. Smooth spiral fins
e. Flat plate fins on individuallyfinned
tube
f. Configurated plate fins on
individually-finned tube
4.1.2 Dimensions, Terminology and Fin Efficiency
Calculations.
(Note: Equations in [ ] are in SI Units)
In the figures shown in 4.1.2.1, 4.1.2.2 and 4.1.2.3,
H applies as shown whether channel flanges are
turned inward or outward. Where an option is
offered in the measurement of any dimension, the
same basis shall be used to determine rating data as
used in the evaluation of test results.
Dimensions Lf and Ld for a configurated fin are
determined, at the option of the manufacturer, from
the blank fin sheet size prior to forming the
configuration providing no edge trimming is
performed after forming or from the finished fin size
after forming.
ARI STANDARD 410-2001
4
4.1.2.1 Staggered tubes and parallel (in-line)
tubes (as shown below) with continuous flat
plate or configurated plate fins.
4.1.2.2 Staggered tubes (as shown below) with
smooth or crimped spiral fins or with flat plate
or configurated plate fins on individually-finned
tube. Air baffles shown are to be considered
optional and H may be the distance between
channels as shown in 4.1.2.1.
ARI STANDARD 410-2001
5
4.1.2.3 Parallel (in-line) tubes (as shown
below) with flat plate or configurated plate fin
on individually-finned tube or with smooth or
crimped spiral fins.
ARI STANDARD 410-2001
6
4.1.2.4 Fin-Tube Assemblies.
a. Plate fins with collars touching
adjacent fin
Fin efficiency calculations:
5 . 0
÷ ÷
ø
ö
ç ç
è
æ
p
=
t
d f
e N
L L
x for continuous plate fin
5 . 0
÷ ÷
ø
ö
ç ç
è
æ
p
= d f
e
L L
x for individually-finned tube
2
2 f o
b
Y D
x
+
=
b e x x w - =
From the curve of
5 . 0
6 ÷
÷
ø
ö
ç ç
è
æ
f f
a
Y k
f
w
ú ú
û
ù
ê ê
ë
é
÷ ÷
ø
ö
ç ç
è
æ 5 . 0
2
f f
a
Y k
f
w for
various values of xe/xb, determine f (Figure 10)
b. Plate fins with collars not touching
adjacent fin Fin efficiency calculations same as for plate fins with
collars touching adjacent fin, except as follows:
2
f o
b
Y D
x
+
=
ARI STANDARD 410-2001
7
c. Plate fins without collars
Fin efficiency calculations same as for plate fins with
collars touching adjacent fin, except as follows:
2
o
b
D
x =
d. Smooth spiral fins
Fin efficiency calculations
2
f
e
D
x =
2
o
b
D
x = b e x x w - =
From the curve of
5 . 0
6 ÷
÷
ø
ö
ç ç
è
æ
r f
a
Y k
f
w
ú ú
û
ù
ê ê
ë
é
÷ ÷
ø
ö
ç ç
è
æ 5 . 0
2
r f
a
Y k
f
w for various values of xe/xb, determine f (Figure 11)
ARI STANDARD 410-2001
8
e. Crimped spiral fins Fin efficiency calculations same as for smooth spiral
fins except:
o
n n
r D
D Y
Y =
4.1.3 Equations for Determining Coil Areas and Surface Ratio.
(Note: Equations in [ ] are in SI Units)
4.1.3.1 Determination of As and Ap
a. Continuous plate fins for staggered and parallel tube arrangements
( ) ( )( )
÷ ÷
ø
ö
ç ç
è
æ - +
+
+
- =
84 . 45
2
68 . 91
2
72
2
c t h f o f o h d f
f s
L N N Y D Y D N L L
N A
( ) ( )( )
ú ú
û
ù
ê ê
ë
é
÷ ÷
ø
ö
ç ç
è
æ - +
+
+
- =
318344
2
636688
2
500000
2
c t h f o f o h d f
f
L N N Y D Y D N L L
N
( )
84 . 45
2 c o f f t t o t
p
L D Y N N L D N
A
- -
=
( )
úû
ù
êë
é - -
=
318344
2 c o f f t t o t L D Y N N L D N
b. Smooth spiral fins
( ) e f o f
t f
s Y D D D
N N
A 2
68 . 91
2 2 + - =
( )
ú úû
ù
ê êë
é
+ - = e f o f
t f Y D D D
N N
2
636688
2 2
( ) r f t
t o
p Y N L
N D
A - =
84 . 45
( )ú
û
ù
êë
é
- = r f t
t o Y N L
N D
318344
ARI STANDARD 410-2001
9
c. Crimped spiral fins
( ) ÷
÷
ø
ö
ç ç
è
æ
+
-
+ - = e f
n f
o n n
t f
s Y D
D D
D D D
N N
A
2 84 . 45
2 2
( )
ú ú
û
ù
ê ê
ë
é
÷ ÷
ø
ö
ç ç
è
æ
+
-
+ - = e f
n f
o n n
t f Y D
D D
D D D
N N
2 318344
2 2
( ) r f t
t o
p Y N L
N D
A - =
84 . 45
( )ú
û
ù
êë
é
- = r f t
t o Y N L
N D
318344
d. Plate fins on individually-finned tube
( ) ( )
÷ ÷
ø
ö
ç ç
è
æ +
+
+
- =
72 68 . 91
2
72
2
f d f f o d f
f t s
Y L L Y D L L
N N A
( ) ( )
ú ú
û
ù
ê ê
ë
é
÷ ÷
ø
ö
ç ç
è
æ +
+
+
- =
500000 636688
2
500000
2
f d f f o d f
f t
Y L L Y D L L
N N
( ) ( ) f f t
t f o
p Y N L
N Y D
A -
+
=
84 . 45
2
( ) ( )ú
û
ù
êë
é
-
+
= f f t
t f o Y N L
N Y D
318344
2
4.1.3.2 Determination of Af, Ao, Ai, B, Aix, Np, Nb and Le (all cases)
144
HL
Af =
úû
ù
êë
é =
1000000
HL
p s o A A A + =
84 . 45
t t i
i
L N D
A =
úû ù
êë
é
=
318344
t t i L N D
i o A A B / =
c i ix N D A 2 00545 . 0 =
[ ] c i N D2 7 10 x 85 . 7 - =
c t p N N N / =
1 - - = ih p b N N N
( ) b eb p s e N L N L L + = 833 . 0
( ) [ ] b eb p s N L N L + = 001 . 0
ARI STANDARD 410-2001
10
Table 2. Required Laboratory Tests
Type of Coil One Row Two Rows Three Rows or More
In-Line Tubes,
Flat Plate Fins
All Other Configurations
Steam (Distributing tube) Test Test No Test1 No Test1
Steam (Single tube) No Test2 No Test2 No Test2 No Test2
Hot Water No Test3 No Test4 No Test3 No Test3
All Cooling Test5 Test Test5 Test four-row, or fiverow,
or six-row coil
Aqueous Ethylene Glycol
Solution
Test same coil as used for sensible cooling tests
Where “No Test” is indicated, the manufacturer may, at his option, perform tests to establish performance factors, in
which case notes 1-4 below do not apply:
1 Steam ratings may be calculated using data from one-row tests.
2 The same steam ratings may be used as determined for steam distributing tube coil of same surface geometry.
3 The overall thermal resistance, R, may be determined by either of the following procedures:
(a) RaD is determined from steam coil tests, assuming a steam-side heat transfer coefficient, fv, of 2000 Btu /(h×ft2×°F)
[11360 W/(m2×°C)]. One-row steam coil tests shall be used to determine RaD for one-row hot water coils. Onerow
or two-row steam coil tests may be used to determine RaD for two-row hot water coils.
(b) RaD is determined from sensible cooling tests. One-row sensible cooling tests shall be used to determine RaD for
one-row hot water coils. One-row or two-row sensible cooling tests may be used to determine RaD for two- or
more-row hot water coils.
(c) For either (a) or (b) above, it is necessary to conduct isothermal water pressure drop tests per 5.4.7.
4 The air-side thermal resistance, RaD, may be determined as in 3 except that two-row coils shall be used.
5 A complete set of tests is not required, provided the air-side heat transfer coefficients, fa, as determined from a
sensible cooling water test series, are within 2.5% of those from four- or more-row tests. If this agreement exists for a
one-row coil, no test is required for a two-row coil.
Section 5. Test Requirements
5.1 Method for Laboratory Tests of Testing for Rating.
Forced-Circulation Air-Cooling and Air-Heating Coils
shall be tested in accordance with ANSI/ASHRAE
Standard 33.
5.2 Test Coils and Laboratory Tests.
5.2.1 Dimensional Requirements. All cooling and
heating coil Laboratory Tests shall be conducted
with a representative coil having a face area of 2 to
10 ft2 [0.19 to 0.93 m2].
5.2.2 Required Laboratory Tests. See Table 2.
5.2.3 Turbulators. If turbulators are offered as an
option to increase the heat transfer coefficient of the
fluid inside the coil tubes, only one coil need be
tested to establish the correlation between the tubeside
heat transfer coefficients, with and without
turbulators.
5.2.4 Fin Spacings. Air film heat transfer
coefficients and air-side pressure drops for various
fin spacings may be determined without testing
provided that the interpolated fin spacing is between
two spacings previously tested which are not more
than 8 fins/in [315 fins/m] apart.
5.2.5 Optional Changes from Test Coil.
5.2.5.1 Changes Requiring No Test. After
establishing the original Standard Ratings,
one or more of the following changes can be
made or offered as an option in a coil line
without changing Published Ratings, provided
that the calculated influence of any or all of
ARI STANDARD 410-2001
11
these changes does not reduce the capacity to
less than 97.5% of the corresponding
Standard Ratings.
a. Copper fin thickness may be decreased
up to 30% below aluminum fin
thickness
b. Fin thickness increase
c. Tube wall thickness between 0.016 and
0.049 in [0.406 and 1.254 mm]
d. Tube material, limited to types
normally used in comfort airconditioning,
such as copper, red brass,
admiralty metal, aluminum and cupronickel
If the calculated capacity is less than 97.5%,
new ratings shall be calculated and submitted
to ARI for approval.
5.2.5.2 Changes Requiring Tests. After
establishing the original Standard Ratings,
one or more of the following changes can be
made or offered as an option in one or more
coil lines with the same surface geometry,
provided a sensible cooling or heating Test
Series of four face velocities is run and the test
capacities are no less than 97.5% of the
corresponding Standard Ratings:
a. Fin material other than copper
b. Method of bonding
c. Tube wall thickness outside the range
of 5.2.5.1. c
d. Tube material other than as provided in
5.2.5.1.d
e. Fin thickness decrease
If the test capacities are less than 97.5% of
Standard Ratings, or if other changes such as
tube OD, tube spacing, fin configuration or
tube arrangement are made, a complete set of
Laboratory Tests shall be run and Published
Ratings shall be changed accordingly. If the
pressure drops are greater than 105% of
Standard Ratings, a series of pressure drop
tests shall be run and ratings shall be
published accordingly.
5.2.6 Refrigerant. Separate Laboratory Tests must
be conducted for each refrigerant covered by volatile
refrigerant coil ratings.
5.2.7 Aqueous Ethylene Glycol Solution Coils.
These coils shall have separate Laboratory Tests.
Aqueous ethylene glycol solution ratings shall not be
applied to other fluids.
5.2.8 Coil Orientations other than Standard.
Information should be available for determining
cooling and dehumidifying coil Application Ratings
for coil orientations other than the standard
orientation (see 3.9). Any such rating shall be
substantiated by adequate additional Laboratory
Tests.
5.3 Heat Transfer Rating Variables to be Determined by
Laboratory Tests.
5.3.1 Range of Heat Transfer Variables. The range
of heat transfer variables over which ratings may be
applied shall be limited strictly to the range included
in the Laboratory Tests; values shall not be
extrapolated outside the range covered in the
Laboratory Tests except for the following:
a. Initial air-to-tube side fluid temperature
difference for all coils
b. Inlet steam pressure for steam coils
c. Fluid velocity for water and aqueous
ethylene glycol solution coils
d. Fluid temperatures for water and aqueous
ethylene glycol solution coils
e. Fluid concentrations for aqueous ethylene
glycol solution coils
5.3.2 The heat transfer variables for the various coil
applications covered by this standard, which shall be
evaluated for their effect on thermal performance by
conducting Laboratory Tests, are described under
5.4.
5.4 Minimum Requirements for Laboratory Tests.
5.4.1 General Scope.
5.4.1.1 Air Velocity. All of the following
Test Series for specific coil applications,
except under 5.4.3.2.2, 5.4.6.3 and 5.4.7 shall
be made with at least four different standard
air face velocities, covering the complete
rating range of air speed in approximately
equally spaced velocity increments on a
logarithmic scale.
5.4.1.2 Fluid Velocity. For any test with
water coils except under 5.4.3.2.2 and 5.4.7, a
ARI STANDARD 410-2001
12
single fluid velocity should be used in the
range from 3 to 6 ft/s [0.9 to 1.8 m/s].
5.4.1.3 Air-Side Pressure Drop. The coil
air-side pressure drop for all dry and wet
surface tests shall be recorded per
ANSI/ASHRAE Standard 33.
5.4.2 Steam Heating Coils. The purpose of this
Test Series is to determine the variation in the
overall heat transfer resistance, R, with the standard
air face velocity, Va, and to determine the steam
pressure drop through the coil.
5.4.2.1 Steam Pressure. For any test, the
inlet steam pressure shall be 2 to 10 psig [14
to 69 kPa gage] with an inlet steam superheat
as specified in ANSI/ASHRAE Standard 33.
5.4.3 Water or Aqueous Ethylene Glycol Solution
Sensible Cooling Coils. To assure completely dry
air-side surface, the entering fluid temperature, tw1 or
tg1, for all tests shall be equal to or greater than the
entering air dew point temperature, t1dp.
5.4.3.1 Water Coil with Smooth Internal
Tube Walls. For coil designs with smooth
internal tube walls, the water film heat
transfer coefficient, fw, is initially known and
shall be calculated from curve fit Equation (8)
shown in Figure 17. Only a single Test Series
is required for the purpose of determining the
variation in the dry surface air film heat
transfer coefficient, fa, with standard air face
velocity, Va. (See 5.4.1.1 and 5.4.1.2.)
5.4.3.2 Water Coils with Tube Designs Other
than Smooth Internal Tube Walls. For coils
using tube designs with internal fins,
turbulators, etc., both the water and air film
heat transfer coefficients, as a function of the
respective fluid mass flow rate, are unknown.
Two Test Series are required for this type of
coil design.
5.4.3.2.1 Test Series Number 1. A
single Test Series, as described in
5.4.3.1, shall first be conducted on a
heat transfer surface whose design
and arrangement are the same in all
respects to the rated design except
that smooth internal tube walls are
used.
5.4.3.2.2 Test Series Number 2. A
single Test Series shall be conducted
on a heat transfer surface whose
design and arrangement are the same
as the rated design including internal
tube type geometry.
At least four tests with different
water velocities are required,
covering the complete rating range of
water velocity in approximately
equally spaced increments on a
logarithmic scale. For any test the
standard air face velocity may range
from 200 to 800 std. ft/min [1 to 4
std. m/s]. Use of high standard air
face velocities and close fin spacings
is recommended for accuracy
reasons.
For this Test Series, knowing the air
film heat transfer coefficients, fa,
determined under 5.4.3.2.1, the water
film heat transfer coefficients, fw,
may be determined as a function of
water velocity and water temperature.
The values of fw, thus determined,
shall be used both for analysis of
Laboratory Tests and for rating
purposes in lieu of water
performance for smooth tube coils
from Figure 17.
5.4.3.3 Aqueous Ethylene Glycol Solution
Coils with Smooth Internal Tube Walls. Two
series of tests shall be conducted.
5.4.3.3.1 Test Series Number 1. A
single Test Series with water, as
described in 5.4.3.1, shall first be
conducted on a heat transfer surface
whose design and arrangement are the
same in all respects to the rated design.
5.4.3.3.2 Test Series Number 2. Test
the same coil as in Test Series 1 except
that the tube side fluid shall be aqueous
ethylene glycol solution, 50% ± 5% by
mass, at temperatures between 45°F
[7.2°C] and 100°F [37.8°C]. A
minimum of eleven tests shall be
conducted to adequately define a
Colburn j-factor versus Re curve as
illustrated in Figure 16. Four test
ARI STANDARD 410-2001
13
points shall be below 2100 Re, three
test points between 2100 and 7000 Re
and four test points above 7000 Re. All
tests shall be conducted at one standard
air face velocity between 200 and 800
std. ft/min [1 to 4 std. m/s]. Use of
high air velocities and close fin
spacings is recommended for accuracy
reasons.
For this Test Series, with the air-side
heat transfer coefficients, fa, determined
under 5.4.3.3.1, the aqueous ethylene
glycol solution film heat transfer
coefficient, fg, may be determined.
Using the fluid properties in the
ASHRAE Handbook-Fundamentals, the
Colburn j-factor and Re can be
calculated and plotted as illustrated in
Figure 16. The curve(s) so defined by
the test points shall be used for tubeside
rating of aqueous ethylene glycol
solution coils.
The above shall be conducted using a
base coil with Ls/Di ratio between 70
and 90. Ratings for the range of Re
between 700 and 7000 shall be based
upon the Ls/Di ratio to the minus 0.4
power in the laminar flow region as
shown in Figure 16.
A second coil may be tested at a
different length and with a minimum of
four test points at Re below 2100 and
three test points between 2100 and
7000. The Ls/Di exponent so
determined (laminar region) may then
be used for rating purposes. The last
three points are used to more clearly
define the transition region.
Properties of pure aqueous ethylene
glycol solutions are representative of
most standard industrial inhibited
aqueous ethylene glycol solutions, but
do not apply to automotive radiator
antifreeze solutions.
5.4.3.4 Aqueous Ethylene Glycol Solution
Coils with Tube Designs Other Than Smooth
Internal Tube Walls. Two Test Series shall be
conducted.
5.4.3.4.1 Test Series Number 1.
Conduct tests with water identical to
those in 5.4.3.3.1.
5.4.3.4.2 Test Series Number 2.
Proceed identically as in 5.4.3.3.2
except that the coil tubes shall include
the internal fins, turbulators, etc.
When positive boundary layer
interrupters (such as closely spaced
wire turbulators or internal ribs at right
angle to flow axis, etc.) are used, the
Ls/Di term will not affect the heat
transfer coefficient and only the base
coil tests are required.
5.4.4 Hot Water or Aqueous Ethylene Glycol
Solution Heating Coils. Tests on hot water or
aqueous ethylene glycol solution heating coils are
not required (see 5.2.2). Should any be tested, the
entering fluid temperature, tw1 or tg1, shall be 180°F
[82.2°C] or higher and the entering air dry-bulb
temperature, t1db, shall not exceed 100°F [37.8°C].
The purpose and minimum testing are the same as
given in 5.4.3.1 and 5.4.3.2 for smooth internal
tubes and other tube designs, respectively.
5.4.5 Cold Water Cooling and Dehumidifying
Coils. Two Test Series shall be conducted.
5.4.5.1 Dry Surface Sensible Heat Tests.
The purpose and minimum testing are
identical with those in 5.4.3.1 and 5.4.3.2 for
smooth tubes and other tube designs,
respectively.
5.4.5.2 Wet (Dehumidifying) Surface Tests.
The same test coil used for the procedure
under 5.4.5.1 shall be employed for these
tests.
5.4.5.2.1 Purpose. The purpose of
this Test Series is to establish
whether, under wet surface operating
conditions, any adjustments are
required in the air film heat transfer
coefficients, fa, as determined for dry
surface tests under 5.4.5.1. These
adjustments may, or may not, be
required, depending upon the
particular design and arrangement of
the heat transfer surface. Also, the
wet surface air-side pressure drop is
established by this Test Series.
ARI STANDARD 410-2001
14
5.4.5.2.2 Surface Condition. To
determine air film heat transfer
coefficients, fa, and air-side pressure
drop under completely wet surface
conditions, each test shall be
conducted with the entire air-side
surface actively condensing moisture.
This operating condition exists when
the air-side surface temperature, at
all locations throughout the coil, is
below the entering air dew point
temperature.
5.4.5.2.3 Range of Variables. For
each test, the range in each of the
following design variables shall fall
within the limits listed below:
tw1 = Entering water temperature:
35 to 55°F [1.7 to 12.8°C]
t1db - t1wb = Entering wet-bulb
depression
³ 6.0°F [3.3°C]
qs /qt = Air sensible heat ratio £ 0.75
t2wb - tw1 ³ 5.0 F [2.8°C]
5.4.6 Volatile Refrigerant Cooling and
Dehumidifying Coils. A complete Test Series, as
outlined below, shall be run with each volatile type
refrigerant for which tests are required (see 5.2.6).
Three series of tests shall be run on the same
prototype coil or coils.
5.4.6.1 Dry Surface Tests. Using cold
water, the first series of tests shall be
conducted as outlined under 5.4.5.1. This
requirement may be deleted if tests under
5.4.5.1 were previously completed.
5.4.6.2 Wet Surface Test. Using cold water,
a second series of tests shall be conducted as
outlined under 5.4.5.2. This requirement may
be deleted if tests under 5.4.5.2 were
previously completed.
5.4.6.3 Volatile Refrigerant Tests. Using
volatile refrigerant, the third series of tests
shall be conducted with at least two different
lengths of refrigerant circuits for a given coil:
a. A circuit closely approximating the
maximum equivalent length used
in the line of rated coils
b. A circuit whose length is no
greater than one-third of the
maximum equivalent length used
in the line of rated coils
For each of the two refrigerant circuit lengths,
a minimum of four tests are required. These
are to cover the complete range of refrigerant
loading per circuit in approximately equal
increments of capacity on a logarithmic scale,
and conducted with a constant liquid
temperature in the range of 108 to 112°F
[42.2 to 44.4°C] entering the control device
and up to 55°F [12.8°C] saturated coil outlet
refrigerant temperature.
5.4.6.4 Evaluation. The above eight tests
shall serve to evaluate the effects of
refrigerant loading per circuit on both the coil
circuit saturated refrigerant pressure drop and
the refrigerant evaporating film heat transfer
coefficient.
5.4.6.5 General Recommendations. For any
test, the standard air face velocity, Va, may
range from 200 to 800 std. ft/min [1 to 4 std.
m/s]. The surface shall be operated either
completely dry or completely wet in order to
simplify the data reduction procedure.
5.4.6.6 Outlet Superheat. Refrigerant outlet
vapor superheat, for any test, is to be
maintained per ANSI/ASHRAE Standard 33.
5.4.7 Isothermal Water Pressure Drop For All
Water Coils. For each water coil tested, the water
pressure drop through the coil shall be determined
under isothermal operating conditions. Tests shall
be made with at least four different water velocities
as specified in 5.4.3.2.2.
5.4.8 Isothermal Pressure Drop for Ethylene Glycol
Solution Coils. For each ethylene glycol solution
coil tested, the pressure drop through the coil shall
be determined under isothermal operating
conditions. Conduct at least four tests at Re below
1000 and at least four tests at Re above 4000. To
complete the pressure drop curve, extrapolate the
two resulting data curves to find the intersection in
the 1000 to 4000 Re region. Additional tests may be
run in the 1000 to 4000 Re region to complete the
pressure drop curve.
ARI STANDARD 410-2001
15
Section 6. Rating Requirements
6.1 Ratings. Ratings for Forced-Circulation Air-Cooling
and Air-Heating Coils consist of Standard Ratings and
Application Ratings used in the selection or application
of coils. They are usually given for a range of conditions
encountered in practice, so that the rating at any desired
condition may be selected directly or by interpolation.
6.1.1 Ratings shall include pressure drop data and
performance characteristics produced under specified
conditions, or means for calculating specific coil
requirements.
6.1.2 Ratings may be presented in the form of
curves, tables, charts or automated rating/selection
computer procedures.
6.1.3 Ratings shall be developed using basic
performance characteristics obtained from
Laboratory Tests in accordance with this standard.
6.2 Heat Transfer Equations for Laboratory Test
Reduction and for Ratings. The initial test data
reduction procedure and calculations for the
determination of:
a. Both fluid flow rates
b. The average or rated sensible and/or total heat
transfer capacity
c. Entering and leaving fluid conditions
d. Both fluid pressure drops
are given in ANSI/ASHRAE Standard 33 both for air
sensible heating or cooling and air cooling and
dehumidifying coils.
6.2.1 Metal Thermal Resistance of External Fins
and Tube Wall for All Applications. The total metal
thermal resistance, Rm, to heat flow through the
external fins and the prime tube wall is calculated as
follows:
Rm = Rf + Rt (1)
where the constant tube metal thermal resistance, Rt, is,
÷ ÷ø ö
ç çè
æ
=
i
o
t
i
D
D
k
BD
t R ln
24
=
ú úû
ù
ê êë
é
÷ ÷ø
ö
ç çè
æ
i
o
t
i
D
D
k
BD
ln
2
and where the variable fin metal thermal resistance,
Rf, based on total external surface effectiveness, h, is
( ) aD f R R ÷ ÷
ø
ö
ç çè
æ -
=
h
h 1
(for dry surface) (2)
÷ ÷
ø
ö
ç ç
è
æ
÷ ÷ø
ö
ç çè
æ -
=
m"
c
R R p
aW f h
h 1
(for wet surface) (2a)
o
p s
A
A A +
=
f
h (3)
The influence of m" on RaW, as shown in Equation
(2a), is based on a derivation by Brown (Reference
A1.7) which was applied to wet coil theory by Ware-
Hacha (Reference A1.18) to determine its implicit
effect on Rf.
6.2.2 Sensible Heat Air Coils. Equations relating
the average or rated sensible heat capacity, qs, to
both air- and tube-side fluid, by a material heat
balance, are given in applicable paragraphs in
ANSI/ASHRAE Standard 33.
The identical sensible heat capacity, qs,
corresponding to this material heat balance, in terms
of the overall heat transfer rate between fluids is:
R
t A
q m o
s
D
= (4)
where, for clean surfaces,
R = RaD + Rm + Rw (or Rv or Rg or Rr) (5)
t
aD
m aD R
R
R R + = +
h
(6)
and, for cold and hot water Laboratory Test
reduction (Rffa = 0) and ratings (manufacturer may
chose to use fouling factor allowances, see Reference
A.1.2 for typical values):
÷ ÷ø
ö
ç çè
æ
+ = ffa
w
w R
f
B R
1
(7)
For steam:
v
v f
B
R = (7a)
For cold and hot aqueous ethylene glycol solution
Laboratory Test reduction (Rffa = 0) and ratings
ARI STANDARD 410-2001
16
(manufacturer may chose to use fouling factor
allowances, see Reference A1.2 for typical values):
÷ ÷
ø
ö
ç ç
è
æ
+ = ffa
g
g R
f
B R
1
(7b)
For volatile refrigerant:
r
r f
B
R = (7c)
For all water coils with surface designs employing
smooth internal tube walls, the tube-side water film
heat transfer coefficient, fw, where the Re exceeds
3100, is determined using the curve fit Equation (8)
shown in Figure 17 .
For water coils using tube geometries other than
smooth internal walls, the tube-side water film heat
transfer coefficient, fw, is determined by test as in
5.4.3.2.2. For steam coils, the tube-side steam film
heat transfer coefficient, fv, is evaluated as described
in Table 2, note 3. For volatile refrigerant coils, the
tube-side refrigerant film heat transfer coefficient, fr,
is evaluated as described in 6.3.6. For aqueous
ethylene glycol solution coils, the tube-side aqueous
ethylene glycol solution film heat transfer
coefficient, fg, is evaluated as described in 6.4.7.
For water coils:
ix
w
w A
w
V
224500
=
úû
ù
êë
é
=
ix
w
A
w
927 . 998
For aqueous ethylene glycol solution coils:
ix g
g
g A
w
V
r 3600
=
ú úû
ù
ê êë
é
=
ix g
g
A
w
r
For counterflow cold water coils:
( ) ( )
÷ ÷ø
ö
ç çè æ
-
-
- - -
= D
1 2
2 1
1 2 2 1
ln
w db
w db
w db w db
m
t t
t t
t t t t
t (9)
For counterflow cold aqueous ethylene glycol
solution coils:
( ) ( )
÷ ÷
ø
ö
ç ç
è
æ
-
-
- - -
= D
1 2
2 1
1 2 2 1
ln
g db
g db
g db g db
m
t t
t t
t t t t
t (9a)
For counterflow hot water coils:
( ) ( )
÷ ÷ø
ö
ç çè
æ
-
-
- - -
= D
db w
db w
db w db w
m
t t
t t
t t t t
t
2 1
1 2
2 1 1 2
ln
(10)
For counterflow hot aqueous ethylene glycol solution
coils:
( ) ( )
÷ ÷
ø
ö
ç ç
è
æ
-
-
- - -
= D
db g
db g
db g db g
m
t t
t t
t t t t
t
2 1
1 2
2 1 1 2
ln
(10a)
For thermal counterflow volatile refrigerant coils:
( ) ( )
÷ ÷
ø
ö
ç ç
è
æ
-
-
- - -
= D
g rc db
r db
g rc db r db
m
t t
t t
t t t t
t
2 2
1 1
2 2 1 1
ln
(11)
For steam coils (single-tube):
( )
÷ ÷
ø
ö
ç ç
è
æ
-
-
-
= D
db vmg
db vmg
db db
m
t t
t t
t t
t
2
1
1 2
ln
(12)
For steam coils (distributing):
( )
÷ ÷
ø
ö
ç ç
è
æ
-
-
-
= D
db g v
db g v
db db
m
t t
t t
t t
t
2 2
1 2
1 2
ln
(12a)
For other tube circuiting arrangements see 6.4.2.
6.2.3 Cooling and Dehumidifying Air Coils. The
method used in this standard to calculate wet surface
coil performance is, with some modifications,
similar to the method outlined in Technical Standard
BCMI-TS4044 (Reference A1.6) with basic theory as
presented by McElgin and Wiley (Reference A1.15).
ARI STANDARD 410-2001
17
Enthalpy
Temperature Coil Depth
Enthalpy
Temperature
Other investigators by converting the basic dual
potential, used in the method described in this
standard, to an equivalent single potential, have
developed other similar rating methods (Reference
A1.18 and Appendix B).
6.2.3.1 Sensible Heat Ratio. The ratio of airside
sensible-to-total heat is calculated as
follows:
( )
2 1
2 1 /
h h
t t c
q q db db p
t s -
-
= (13)
The ratio, qs /qt, is used as an index to define the
type of procedure required for calculating
ratings as follows:
a. If qs/qt < 0.95, use the equations listed
in the remainder of 6.2.3.
b. If qs /qt ³ 0.95, use the conventional dry
surface, sensible heat transfer equations
listed under 6.2.2.
6.2.3.2 Total Heat Capacity or Total External
Surface Area Requirements. Depending upon
operating conditions, the coil air-side surface
may operate either completely wet or a portion
of the coil may operate with dry surface. For the
case where all surface is completely wet, all
surface temperatures, ts, of the coil are below the
entering air dew-point temperature, t1dp. For the
case where the surface temperatures, ts, of a part
of the coil are above the entering air dew-point
temperature, t1dp, this portion of the coil surface
area, AD, operates dry with the remainder of the
coil surface area, AW, wet or actively condensing
moisture. For this latter case, the coil surface
area requirements are separately calculated for
the dry and wet parts of the coil.
For the wet part of the coil, the wet surface area,
AW, or the corresponding total heat capacity, qtW,
is calculated by using the mean air enthalpy
difference between the air stream and that
corresponding to the coil surface temperature.
Equations relating the average or rated total heat
capacity, qt, to both air- and tube-side fluid, by a
material heat balance, are given in applicable
paragraphs of ANSI/ASHRAE Standard 33.
The identical total heat capacity, qt,
corresponding to this material heat balance, for
the general case where a portion of the coil
surface area operates dry is:
aW p
m W m D
t R c
h A
R
t A
q
D
+
D
= (14)
where:
tD
m D q
R
t A
=
D
= Dry surface capacity
tW
aW p
m W q
R c
h A
=
D
= Wet surface capacity
t tW tD q q q = + = Total heat capacity required
The qtD term in Equation (14) is omitted if the
entire air-side surface is actively condensing
moisture.
For counterflow water coils :
Graphic representation of Equations (15) and
(16)
( ) ( )
÷ ÷ø
ö
ç çè
æ
-
-
- - -
= D
wB Bdb
w db
wB Bdb w db
m
t t
t t
t t t t
t
2 1
2 1
ln
(15)
( ) ( )
÷ ÷ø
ö
ç çè
æ
-
-
- - -
= D
2 2
2 2
ln
s
sB B
s sB B
m
h h
h h
h h h h
h (16)
For thermal counterflow volatile refrigerant
coils:
ARI STANDARD 410-2001
18
Enthalpy
Temperature
Coil Depth
Graphic representation of Equations (15a) and
(16a)
( ) ( )
÷ ÷
ø
ö
ç ç
è
æ
-
-
- - -
= D
rBg Bdb
r db
rBg Bdb r db
m
t t
t t
t t t t
t
1 1
1 1
ln
(15a)
( ) ( )
÷ ÷ø
ö
ç çè
æ
-
-
- - -
= D
2 2
2 2
ln
s
sB B
s sB B
m
h h
h h
h h h h
h (16a)
For aqueous ethylene glycol solution coils:
Graphic
representation of Equations (15b) and (16b)
( ) ( )
÷ ÷
ø
ö
ç ç
è
æ
-
-
- - -
= D
gB Bdb
g db
gB Bdb g db
m
t t
t t
t t t t
t
2 1
2 1
ln
(15b)
( ) ( )
÷ ÷ø
ö
ç çè
æ
-
-
- - -
= D
2 2
2 2
ln
s
sB B
s sB B
m
h h
h h
h h h h
h (16b)
In the above equations, hs2 refers to the enthalpy
of saturated air at the surface temperature for the
leaving air-side of the coil.
6.2.3.3 The Coil Characteristic. The coil
characteristic is in terms of the individual
thermal resistances:
aW p
w m
R c
R R
C
+
= (for water) (17)
aW p
r m
R c
R R
C
+
= (for volatile refrigerant) (17a)
aW p
g m
R c
R R
C
+
= (for aqueous ethylene glycol
solution) (17b)
And also, for any point condition within the wet
surface region, such as the terminal differences,
the coil characteristic is used to obtain the
correct division between the air-side enthalpy
difference, h-hs, and tube-side temperature
difference, ts-tw, ts-trg, or ts-tg, as follows:
s
w s
h h
t t
C
-
-
= (for water) (18)
s
rg s
h h
t t
C
-
-
= (for volatile refrigerant) (18a)
s
g s
h h
t t
C
-
-
= (for aqueous ethylene glycol
solution) (18b)
C is calculated from Equations (17), (17a) or
(17b) using known values of RaW, Rm and Rw, Rr
or Rg. Then with known values of h and tw, tr or
tg at a given position within the wet surface
region, the corresponding values of ts and hs
may be exactly calculated from Equations (18),
(18a) or (18b) by trial and error using air
enthalpy tables. A direct method for finding ts
and hs, to closely approximate the exact solution
given by Equations (18), (18a) or (18b) may be
obtained by use of a universal Surface
Temperature Chart, such as shown in Figure 9.
6.2.3.4 Dry-Wet Boundary Determination for
Partially Dry Surface. Under operating
conditions where a portion of the coil is
operating dry, the boundary condition between
the dry and wet surface regions is established by
calculating the air stream enthalpy, hB, at this
point.
For counterflow water coils:
y C
Ch yh t t
h dp w dp
B +
+ + -
= 1 1 2 1 (19)
For thermal counterflow volatile refrigerant
coils:
y C
Ch yh t t
h dp r dp
B +
+ + -
= 1 1 1 1 (19a)
ARI STANDARD 410-2001
19
For aqueous ethylene glycol coils:
y C
Ch yh t t
h dp g dp
B +
+ + -
= 1 1 2 1 (19b)
where:
2 1
1 2
h h
t t
y w w
-
-
= (for water coils) (20)
2 1
2 1
h h
t t
y g rc r
-
-
= (for volatile refrigerant coils)(20a)
2 1
1 2
h h
t t
y g g
-
-
= (for aqueous ethylene glycol
solution coils) (20b)
If hB ³ h1, the entire coil surface area is wet and
AD = 0. Only the wet surface area, AW, is
calculated for this condition. If hB < h1, part of
the surface is operating dry. For this condition,
the dry, AD, and wet, AW, surface areas are
separately calculated.
The air dry-bulb temperature at the dry-wet
boundary is:
÷ ÷
ø
ö
ç ç
è
æ -
- =
p
B
db Bdb c
h h
t t 1
1 (21)
The total heat load for the dry surface region is:
( ) B a tD h h w q - = 1 60 (22)
( ) [ ] B a h h w - = 1 1000
The total heat load for the wet surface region is:
tD t tW q q q - = (23)
The cold water temperature at the dry-wet
boundary with counterflow coils is:
÷ ÷
ø
ö
ç çè
æ
- =
pw w
tD
w wB c w
q
t t 2 (24)
The cold aqueous ethylene glycol solution
temperature with counterflow coils is:
÷ ÷
ø
ö
ç ç
è
æ
- =
pg g
tD
g gB c w
q
t t 2 (24a)
6.2.3.5 Determination of Leaving Air Dry-Bulb
Temperature. If tÿ ³ t1dp, the coil surface is dry
and the leaving air dry-bulb temperature shall be
calculated using the method described in 6.2.2.
For wet or partially wet coil surface, the leaving
air dry-bulb temperature, t2db, shall be calculated
as follows:
aD a
o
aD a p
o
R w
A
R w c
A
c
58 . 14 60
= = (25)
úû
ù
êë
é
=
ú úû
ù
ê êë
é
=
aD a
o
aD a p
o
R w
A
R w c
A
1017 1000
and also:
s db
s db
s
s c
t t
t t
h h
h h
-
-
=
-
-
= -
1
2
1
2 e (26)
The saturated air enthalpy, hÿ, corresponding to
the effective coil surface temperature, tÿ, is:
÷ ÷ø
ö
ç çè æ
-
-
- = -c s
h h
h h
e 1
2 1
1 (27)
The leaving air dry-bulb temperature, t2db, is
then calculated as follows:
( ) c
s db s db t t t t - - + = e 1 2 (28)
6.2.3.6 Determination of Sensible and Latent
Heat Capacities. The air-side sensible, qs, and
total, qt, heat capacities are calculated from
applicable equations in ANSI/ASHRAE
Standard 33.
6.3 Reduction of Laboratory Test Data to Determine
Parameters for Ratings. The Forms referenced herein
are contained in ARI OM-410 Addendum (Reference
A1.3).
6.3.1 Coil Physical Data Calculations. Procedure
for calculation of coil physical data and fin efficiency
upon which both analysis of Laboratory Tests and
preparation of ratings are based, is detailed in ARI
OM-410 Addendum Form 410-1 and is based on
equations listed under 4.1.
ARI STANDARD 410-2001
20
Table 3. Metal Thermal Conductivities
Material Temperature
°F [°C]
Thermal Conductivity, k
Btu×ft/(h×ft2×°F)
[103 W×mm/(m2×°C)]
Aluminum Alloy 1100 Temper O
Aluminum Alloy 3003 Temper O
Aluminum Alloy 3003 Temper H18
Copper (C11000)
Copper (C12200)
Red Brass (85-15%, C23000)
Cupronickel (90-10%, C70600)
Cupronickel (70-30%, C71500)
Admiralty (C44300, C44400, C44500)
Steel-Carbon (SAE 1020)
Stainless Steel 304, 304L, 316, 316L
Stainless Steel 410 and 420
Stainless Steel 347 and 321
77 [25]
77 [25]
77 [25]
68 [20]
68 [20]
68 [20]
68 [20]
68 [20]
68 [20]
212 [100]
212 [100]
212 [100]
212 [100]
128.3 [221.7]
111.7 [193.0]
89.2 [154.1]
226.0 [390.5]
196.0 [338.7]
92.0 [159.0]
26.0 [44.9]
17.0 [29.4]
64.0 [110.6]
30.0 [51.8]
9.4 [16.2]
14.4 [24.9]
9.3 [16.1]
See References A1.9 and A1.11.
6.3.2 Calculation of Metal Thermal Resistance for
Fin and Tube Assembly. Calculation procedure for
establishing the metal thermal resistance, Rm, is
detailed in Form 410-1, and is based on equations
listed under 6.2.1. No experimental data are
required for these calculations. Metal thermal
conductivities for use in Form 410-1 are contained in
Table 3.
Rm consists of two resistances in series: (a) the
variable thermal resistance, Rf, of the external fins
based on total surface effectiveness for either dry or
wet surface, and (b) the constant thermal resistance,
Rt, of the prime tube wall. Depending upon tube
design, Rt may or may not be negligible.
An illustrative plot of (RaD+ RmD) vs. RaD is shown
in Figure 1 and is for dry surface application only.
This plot is used for analysis of either Laboratory
Test results or ratings of sensible heat coils.
An illustrative plot of Rm vs. faD for dry surface coils
or Rm vs. faW for wet surface coils is shown in Figure
2.
For wet surface, the term, m"/cp, is determined from
Figure 8. The data illustrated in Figure 2 are used to
determine Rm in either the analysis of Laboratory
Test results or for ratings of all coil types.
All calculations of the fin thermal resistance, Rf,
shall be based on the fin efficiencies, f, as developed
in Reference A1.10. This data by Gardner for
annular shaped fins with both constant fin thickness
and constant fin cross-sectional area designs are
shown, respectively, in Figure 10 and Figure 11.
For non-circular shaped fins, the fin segmentation
method, described in References A1.8 and A1.16,
may be used to compute the fin thermal resistance,
Rf. The fin efficiency of the individual fin segments
shall be based on data by Gardner from Figure 10 or
Figure 11.
6.3.3 Air Sensible Heat Steam Coils. Calculation
procedure for determining the performance factors
for steam coil ratings derived from Laboratory Tests,
is detailed in Form 410-2. This analysis is based on
the applicable heat transfer equations under 6.2.2.
This procedure also includes parameters, based on
experimental results, used to determine coil air-side
pressure drop. The steam pressure drop inside tubes
is determined by the calculation procedure as
detailed in Form 410-3.
From analysis of Laboratory Tests on steam coils as
outlined in Forms 410-2 and 410-3, the following
plots of experimental data are used for ratings as
illustrated in Figure 3:
a. a V R vs.
b. a
r
st V
N
p
vs.
D
c.
c
v
vmg e
tv
N
w
v L
p
vs.
D
ARI STANDARD 410-2001
21
A typical thermal diagram for steam coils with fluid
temperature designations is shown on the last page
of Form 410-2.
6.3.4 Air Sensible Heat Hot and Cold Water Coils.
Calculation procedure for determining the
performance factors for both air sensible heat hot
and cold water coil ratings derived from Laboratory
Tests, is detailed in Form 410-2. This analysis is
based on the applicable heat transfer equations under
6.2.2. This procedure also includes parameters,
based on experimental results, used to determine coil
air-side pressure drop. The water pressure drop
inside tubes is determined by the calculation
procedure as detailed in Form 410-3.
From analysis of Laboratory Tests on air sensible
heat hot or cold water coils as outlined in Form 410-
2 and 410-3, the following plots of experimental data
are used for ratings as illustrated in Figure 4 along
with water performance for smooth internal tube
coils from Figure 17.
a. a aD V R vs.
b. ( ) a mD aD V R R vs. +
c. a
r
st V
N
p
vs.
D
d. w
t e
Lt V
F L
h
vs.
For tube designs other than smooth internal tube
walls, water performance from 5.4.3.2 shall be used.
The factors, Ft and Fh, shown in Figure 7, are used
to correct the tube circuit and header pressure drop,
respectively, for other average water temperatures at
constant mass flow.
Typical thermal counterflow diagrams for hot and
cold water coils with fluid temperature designations
are shown on the last page of Form 410-2.
6.3.5 Cold Water Cooling and Dehumidifying
Coils. Calculation procedure for determining the
performance factors for cold water cooling and
dehumidifying coil ratings, derived from Laboratory
Tests, is detailed in Form 410-2. This analysis is
based on the applicable heat transfer equations under
6.2.3. Separate procedures are included for
conditions where the coil surface is either completely
wet or completely dry. A parameter, based on test
results, is included to determine wet surface coil airside
pressure drop. Besides wet surface air-side
pressure drop, the basic purpose of this series of tests
is to determine values of the wet surface air film
thermal resistance, RaW, over the rated range of coil
standard air face velocity, Va, and to establish
whether RaW differs from the corresponding dry
surface value, RaD, at a given standard air face
velocity. RaW and RaD at a given value of Va may or
may not be the same depending upon the particular
coil surface design and arrangement.
From analysis of Laboratory Tests on cold water
cooling and dehumidifying coils as outlined in
Forms 410-2 and 410-3, the following plots of
experimental data are used for ratings as illustrated
in Figure 5 along with water performance for smooth
tube coils from Figure 17:
a. a aW V R vs.
b. a
r
sw V
N
p
vs.
D
Also shown in Figure 5 are the following data from
Figure 4 (see 6.3.4) based on dry surface tests which
are also applicable for partially wet surface
operation:
c. a aD V R vs.
d. a
r
st V
N
p
vs.
D
e. w
t e
Lt V
F L
h
vs.
For tube designs other than smooth internal tube
walls, water performance from 5.4.3.2 shall be used.
The factors, Ft and Fh, shown in Figure 7, are used
to correct the tube circuit and header pressure drop,
respectively, for other average water temperatures at
constant mass flow.
A typical thermal counterflow diagram for cold
water cooling and dehumidifying coils is shown on
the last page of Form 410-6. This diagram
illustrates the condition where a part of the coil
surface is operating dry. Air enthalpies, the
temperature conditions of fluids and surface, and the
dry-wet boundary conditions are illustrated as used
in the analysis given in Forms 410-2 and 410-3.
6.3.6 Volatile Refrigerant Cooling and
Dehumidifying Coils. Calculation procedure for
determining the performance factors for volatile
refrigerant cooling and dehumidifying coil ratings,
derived from Laboratory Tests, is detailed in Form
ARI STANDARD 410-2001
22
410-4. This analysis is based on the applicable heat
transfer equations under 6.2.3. Separate procedures
are included for conditions where the coil surface is
either completely wet or completely dry. The basic
purpose of this series of tests is to determine the
refrigerant evaporating film heat transfer
coefficients, fr, and the refrigerant pressure drops,
Dprc, through the coil tube circuit.
From analysis of Laboratory Tests on volatile
refrigerant cooling and dehumidifying coils as
outlined in Forms 410-4, the following plots of
experimental data are used for ratings as illustrated
in Figure 6.
a.
c
t
r N
q
R vs.
b.
c
r
g rc e
rc
N
w
v L
p
vs.
2
D
Also shown in Figure 6 are the following data from
Figure 5 determined from water coil tests and
previous calculations.
c. a
r
st V
N
p
vs.
D
d. a
r
sw V
N
p
vs.
D
e. a aD V R vs.
f. a aW V R vs.
A typical thermal counterflow diagram for volatile
refrigerant cooling and dehumidifying coils is shown
on the last page of Form 410-6. This diagram
illustrates the condition where a part of the coil
surface is operating dry. Air enthalpies, the
temperature conditions of fluids and surface, and the
dry-wet boundary conditions are illustrated as used
in the analysis given in Form 410-4.
6.3.7 Aqueous Ethylene Glycol Solution Coils.
Calculation procedure for determining the
performance factors for aqueous ethylene glycol
solution coil ratings, derived from Laboratory Tests,
is detailed in Form 410-7. This analysis is based on
the applicable heat transfer equations of Figure 16.
The procedure is for conditions where the coil
surface is completely dry. The basic purpose of this
series of tests is to determine the aqueous ethylene
glycol solution tube-side heat transfer performance (j
and fg) and friction factor, f’.
From analysis of Laboratory Tests on aqueous
ethylene glycol solution coils as outlined in Forms
410-7, the following plots of experimental data are
used for ratings as illustrated in Figure 16.
a. j vs. Re
b. f' vs. Re
Also used for aqueous ethylene glycol solution coil
ratings are the following data from Figure 5
determined from water coil tests and previous
calculations.
c. a aD V R vs.
d. a aW V R vs.
e. ( ) a mD aD V R R vs. +
f. a
r
st V
N
p
vs.
D
g. a
r
sw V
N
p
vs.
D
A typical thermal counterflow diagram for aqueous
ethylene glycol solution coils is shown on the last
page of Form 410-9. This diagram illustrates the
condition where a part of the coil surface is
operating dry. Air enthalpies, the temperature
conditions of fluids and surface, and the dry-wet
boundary conditions are illustrated as used in the
analysis given in Forms 410-7.
6.4 Standard Ratings.
6.4.1 Tolerances. Standard Ratings shall be such
that any coil selected at random will have a total
capacity, when tested, not less than 95% of its
published total capacity. Published values of air-side
pressure drop, under test, shall not be exceeded by
more than 10%, or 0.02 in H2O [5 Pa], whichever is
greater. Published values of tube-side pressure drop,
under test, shall not be exceeded by more than 10%,
or 1.0 ft of fluid [0.3048 m of fluid], whichever is
greater.
6.4.2 Computations. Computations for Standard
Ratings shall be based on heat transfer coefficients
and coil characteristics obtained by Laboratory Tests.
In this standard, expressions for logarithmic mean
effective differences, Dtm and Dhm, are only
illustrated for the case of thermal counterflow
between the air- and tube-side fluids, as defined
under 6.2.2 and 6.2.3.2. It shall be the responsibility
of the manufacturer to include appropriate
allowances to these logarithmic mean effective
ARI STANDARD 410-2001
23
differences for those coil designs where the tube
circuiting arrangement causes deviations from the
thermal counterflow relationships described in this
standard.
In publishing Standard Ratings, it shall be the
responsibility of the manufacturer to include
appropriate allowances for the effects of tube
pressure drop, condensate accumulation, etc., on coil
capacity.
6.4.3 Air Sensible Heat Steam Coils. A suggested
method for rating air sensible heat steam coils is
shown on Form 410-5.
Standard Ratings for determining either number of
rows, Nr, requirements or sensible heat capacity, qs,
for specific job conditions may be obtained by use of
the following data:
a. Performance factors as illustrated in Figure
3
b. Applicable heat transfer equations in 6.2.2
c. Manufacturer established steam pressure
drop parameters (headers, nozzles, tube
entrance and exit, and equivalent length of
coil circuit per return bend)
6.4.4 Air Sensible Heat Hot and Cold Water Coils.
This method of rating the sensible cooling coils is for
application where the air sensible heat ratio, qs/qt ³
0.95. For conditions where, qs/qt < 0.95, use the wet
surface, total heat method described in 6.4.5. A
suggested method for rating air sensible heat hot and
cold water coils is shown on Form 410-5.
Standard Ratings for determining either number of
rows, Nr, requirements or sensible heat capacity, qs,
for specific job conditions may be obtained by use of
the following data:
a. Performance factors as illustrated in Figure
4
b. Water performance for smooth internal tube
wall coils from Figure 17. For tube designs
other than smooth internal tube walls, water
performance from 5.4.3.2 shall be used.
c. Applicable heat transfer equations in 6.2.2
d. Ft and Fh in Figure 7
e. Manufacturer established water pressure
drop parameters (headers, nozzles, tube
entrance and exit, and equivalent length of
coil circuit per return bend)
6.4.5 Cold Water Cooling and Dehumidifying
Coils. This method of rating is for application
where the air sensible heat ratio, qs/qt < 0.95. For
conditions where qs/qt ³ 0.95, use the dry surface,
sensible heat method described in 6.4.4. A
suggested method for rating cold water cooling and
dehumidifying coils is shown on Form 410-6.
Standard Ratings for determining either total
external surface area, Ao, requirements or total heat
capacity, qt, for specific job conditions may be
obtained by use of the following data:
a. Performance factors as illustrated in Figure
5
b. Water performance for smooth internal tube
wall coils from Figure 17. For tube designs
other than smooth internal tube walls, water
performance from 5.4.3.2 shall be used.
c. Applicable heat transfer equations in 6.2.2
and 6.2.3
d. m”/cp in Figure 8 for wet surface
e. Rm for dry and wet surface as illustrated in
Figure 2
f. Ft and Fh in Figure 7
g. Universal surface temperature chart in
Figure 9
h. Manufacturer established water pressure
drop parameters (headers, nozzles, tube
entrance and exit, and equivalent length of
coil circuit per return bend)
6.4.6 Volatile Refrigerant Cooling and
Dehumidifying Coils. This method of rating is for
application where the air sensible heat ratio, qs/qt <
0.95.
For conditions where qs / qt ³ 0.95, use the dry
surface, sensible heat method described in 6.4.4
except for the following change of data
a. Use the plot for Rr as illustrated in Figure 6
instead of Figure 17.
b. Use the plot for Dpr / (Levrc2g) as illustrated
in Figure 6 instead of the plot for hL t/ (LeFt)
in Figure 4.
c. Use manufacturer established refrigerant
instead of water pressure drop parameters
(headers, nozzles, tube entrance and exit,
and equivalent length of coil circuit per
return bend)
Standard Ratings for determining either total
external surface area, Ao, requirements or total heat
capacity, qt, for specific job conditions may be
obtained by use of the following data:
ARI STANDARD 410-2001
24
a. Performance factors as illustrated in Figure
6
b. Applicable heat transfer equations in 6.2.2
and 6.2.3
c. m"/cp in Figure 8 for wet surface
d. Rm for dry and wet surface as illustrated in
Figure 2
e. Universal surface temperature chart in
Figure 9
f. Manufacturer established refrigerant
pressure drop parameters (headers, nozzles,
tube entrance and exit, and equivalent
length of coil circuit per return bend)
6.4.7 Aqueous Ethylene Glycol Solution Coils. The
method of rating aqueous ethylene glycol solution
coils is identical to that described in 6.4.4 and 6.4.5
for water coils except the j and f’ factors in Figure 16
must be used to determine the tube-side performance
data. Suggested methods for rating sensible heat
coils and cooling and dehumidifying coils are shown
on Forms 410-8 and 410-9, respectively.
Section 7. Minimum Data Requirements for
Published Ratings
7.1 Minimum Data Requirements for Published Ratings.
As a minimum, Published Ratings shall include all
Standard Ratings. All claims to ratings within the scope
of this standard shall include the statement “Rated in
accordance with ARI Standard 410”. All claims to
ratings outside the scope of this standard shall include
the statement “Outside the scope of ARI Standard 410”.
Wherever Application Ratings are published or printed,
they shall include a statement of the conditions at which
the ratings apply.
Where applicable, the following information, or the
means for determining it, based on tests, shall be
published or made available through an automated
rating/selection computer procedure within the range of
rating conditions specified in Table 1.
a. Manufacturer’s name and address
b. Model, size and/or type
c. Heating/cooling medium
d. All applicable input information specified in
Table 1
e. Standard air volumetric flow rate, scfm [std.
m3/s]
f. Air pressure drop through coil at standard air
density (dry and wet surface), in H2O [kPa]
g. Total cooling capacity (dehumidifying coils
only), Btu/h [W]
h. Sensible heating/cooling capacity, Btu/h [W]
i. Leaving air dry-bulb temperature, °F [°C] or for
heating coils, air dry-bulb temperature rise, °F
[°C]
j. Leaving air wet-bulb temperature, °F [°C]
k. Standard water or aqueous ethylene glycol
solution volumetric flow rate, sgpm [std. m3/s]
l. Water or aqueous ethylene glycol solution
fouling factor allowance, h×ft2×°F/Btu [m2×°C/W]
m. Leaving water or aqueous ethylene glycol
solution temperature or water or ethylene glycol
solution temperature difference, °F [°C]
n. Water or aqueous ethylene glycol solution
pressure drop through coil (including headers)
at average fluid density, ft of fluid [m of fluid]
o. Subcooled refrigerant liquid temperature
entering liquid control device, °F [°C]
The preceding information shall be published or made
available at a barometric pressure of 29.92 in Hg [101.3
kPa] and may also be published or made available at
other barometric pressures, providing these pressures are
clearly identified.
Section 8. Symbols and Units
(Dimensionless unless otherwise noted)
8.1 Letter Symbols.
A - Area, ft2 [m2]
Ai - Total internal surface area, ft2 [m2]
Ao - Total external surface area, ft2 [m2]
Ap - Primary surface area, which consists of the
exposed external tube area (if any) plus the
external fin collar area, if used, less the area under
the fins corresponding to the fin root thickness, ft2
[m2]
As - Secondary surface area (net fin area), ft2 [m2]
1. Flat Plate Fins. The secondary surface area
is
the sum of the areas of the fin sheets minus
the areas of the tube holes. Any fin collar
areas are excluded (see 4.1.3.1).
2. Configurated Plate Fins. The secondary
surface area is determined in the same way as
for a flat plate except the area dimensions, Lf
and Ld, are determined, at the option of the
manufacturer, from the blank fin sheet size
prior to forming the configuration provided no
edge trimming is performed after forming, or
from the finished fin size after forming (see
4.1.2).
ARI STANDARD 410-2001
25
3. Spiral Fins. The secondary surface area
consists of the exposed lateral and outside fin
edge areas, calculated on the basis of an
annular type fin, which neglects the helical fin
pitch. For crimped fins, the lateral area is
composed of the actual developed area of the
crimped fin portion plus any smooth annular
area at the outer extremities of the fin (see
4.1.3.1).
B - Ratio of total external coil surface area to the total
internal surface area, Ao/Ai
C - Coil characteristic, lb×°F/Btu [kg×°C/kJ] [as
defined in Equations (17), (17a), (17b), (18), (18a)
and (18b) in 6.2.3.3]
c - Heat transfer exponent (as defined in Equation
(25) in 6.2.3.5)
co - Heat transfer exponent (as defined in Figures 13,
14 and 15)
cp - Specific heat at constant pressure of air-water
vapor mixture, 0.240 + 0.444W, Btu/(lb dry air×°F)
[1.005 + 1.859W, kJ/(kg dry air×°C)]. To simplify
calculation and rating procedures, a constant value
of cp = 0.243 [1.017] may be used for cooling
calculations and a constant value of cp = 0.241
[1.009] may be used for heating calculations.
cpg - Specific heat at constant pressure of aqueous
ethylene glycol solution, Btu/(lb×°F) [kJ/(kg×°C)]
cpw - Specific heat at constant pressure of water,
Btu/(lb×°F) [kJ/(kg×°C)]. To simplify calculation
and rating procedures, a constant value of cpw =
1.000 [4.187] may be used.
D - Diameter, in [mm]
E - Air-side effectiveness (as defined in Figures 13, 14
and 15)
Fa - Air-side pressure drop correction factor
Ft - Temperature correction factor for water pressure
drop inside smooth tubes at mean temperature, twm,
of operating condition
Fh - Temperature correction factor for header water
pressure drop at mean temperature, twm, of
operating condition
f - Heat transfer coefficient (air-side is referred to
total external area, Ao; all others are referred to
total internal area, Ai), Btu/(h×ft2×°F) [W/(m2×°C)]
f' - Friction factor for aqueous ethylene glycol solution
coils
G - Mass velocity lb/(h×ft2) [kg/(s×m2)]
H - Coil face height (as illustrated in 4.1.2), in [mm]
h - Enthalpy, Btu/lb [kJ/kg] (when applied to air,
Btu/lb dry air [kJ/kg dry air])
hL - head loss at average liquid density, ft of liquid [m
of liquid]
Dh - Enthalpy difference, Btu/lb dry air [kJ/kg dry air]
j - Colburn heat transfer factor
k - Material thermal conductivity, Btu×ft/(h×ft2×°F)
[W×mm/(m2×°C)] (see Table 3)
L - Length, in [mm]
Le - Total equivalent length of tube circuit, ft [m]
Leb - Equivalent length of tube circuit per return bend,
in [mm]
M - Air-to-fluid heat capacity ratio (as defined in
Figures 13, 14, and 15)
m” - Slope of saturated air temperature-enthalpy curve
at the coil surface temperature, ts, Btu/(lb×°F)
[kJ/(kg×°C)]
N - Number of
P - Absolute pressure (psia or in Hg abs) [kPa abs]
p - Gage pressure (psi or in Hg or in H2O) [kPa gage]
Dp - Difference in pressure (psi or in H2O ) [kPa]
Pr - Prandtl number
QaSTD - Standard air volumetric flow rate (standard air
density = 0.075 lb/ft3 [1.2 kg/m3]) which
approximates dry air density at 70°F [21.1°C]
and 14.696 psia [101.325 kPa abs], scfm [std.
m3/s]
QwSTD - Standard water volumetric flow rate (standard
water density = 62.361 lb/ft3 [998.927 kg/m3])
which approximates water density at 60°F
[15.6°C] and 14.7 psia [101.325 kPa abs], sgpm
[std. m3/s]
QgSTD - Standard aqueous glycol solution volumetric
flow rate (standard aqueous glycol solution
density = 62.361 lb/ft3 [998.927 kg/m3]) which
approximates water density at 60°F [15.6°C]
and 14.696 psia [101.325 kPa abs], sgpm [std.
m3/s]
q - Heat transfer capacity, Btu/h [W]
R - Thermal resistance, referred to total external area,
Ao, h×ft2×°F/Btu [m2×°C/W]
Re - Reynolds Number
shf - Continuous plate fin hole spacing across coil face,
in [mm]
shr - Continuous plate fin hole spacing in direction of
air flow, in [mm]
stf - Tube spacing across coil face, in [mm]
str - Tube spacing in direction of air flow, in [mm]
St - Stanton Number
t - Temperature, °F [°C]
Dt - Temperature difference, °F [°C]
U - Overall heat transfer coefficient, referred to the
total external surface area, Ao, Btu/(h×ft2×°F)
[W/(m2×°C)]
Va - Standard air face velocity, std. ft/min [std. m/s]
Vg - Average aqueous ethylene glycol solution velocity
inside tubes at average aqueous ethylene glycol
solution density, ft/s [m/s]
Vw - Standard water velocity inside tubes, std. ft/s [std.
m/s]
ARI STANDARD 410-2001
26
v - Specific volume, ft3/lb [m3/kg]
W - Humidity ratio of air-water vapor mixture, lb
water vapor/lb dry air [kg water vapor/kg dry air]
w - Height of equivalent annular fin, xe-xb, in [mm]
(when no subscript is used)
- Mass flow rate (when used with subscript), for air
lb dry air/min [kg dry air/s], for water, refrigerant
and aqueous ethylene glycol solution- lb/h [kg/s]
x - Radius, in [mm]
xg - Composition by mass of aqueous ethylene glycol
solution, %
xr - Mass fraction of volatile refrigerant vapor
Y - Fin thickness, in [mm]
y - Ratio of fluid temperature rise to air enthalpy
drop, lb×°F/Btu [kg×°C/kJ] (see Equations (20),
(20a) and (20b))
h - Total external surface effectiveness
f - Fin efficiency
r - Density, lb/ft3 [kg/m3]
m - Dynamic viscosity at mean bulk temperature,
lb/(ft×h) [mPa×s]
mtw - Dynamic viscosity at mean tube wall temperature,
lb/(ft×h) [mPa×s]
8.2 Subscripts.
8.2.1 Numerical subscripts:
0 - Refers to conditions entering liquid
control device
1 - Refers to conditions entering coil
2 - Refers to conditions leaving coil
8.2.2 Letter subscripts are used to further identify
the letter symbols. They are:
a - Air-side
B - Conditions at dry-wet boundary
b - Fin root (when used with symbol, x)
- Return bends (when used with symbol, N)
c - Assumed value (when used with symbol,
A)
- Plate fin external collar (when used with
symbol, L)
- Tube circuits (when used with symbol, N)
D - Dry surface
d - Plate fin depth in direction of air flow
(when used with symbol, L)
- At outer edge of spiral fin at Df (when
used with symbol, Y)
db - Dry-bulb
dp - Dew point (when used with symbol, t)
- Saturated air at t1dp (when used with
symbol, h)
e - Outside edge of spiral fin (when used
with symbol, Y)
- Outside, or equivalent annular area of
non-circular fin or of annular or spiral fin
(when used with symbol, x)
f - Across coil face (when used with symbol,
s)
- Coil face (when used with symbol, A)
- Outside diameter of spiral fin (when used
with symbol, D)
- Fins in net finned tube length (when used
with symbol, N)
- Plate fin length perpendicular to direction
of tubes exposed to the air flow (when
used with symbol, L)
- Plate fins of constant thickness (when
used with symbol, Y)
- Saturated liquid (when used with
symbols, hr, tc, tr , and tv)
ffa - Fouling factor allowance for water and
aqueous ethylene glycol solution coil
ratings. See Reference A1.2 for typical
values.
g - Aqueous ethylene glycol solution
- Saturated vapor (when used with symbols
hr, tr, tv, vr, and vv)
h - Holes in plate fin
i - Inside tube
ih - intermediate headers
m - Logarithmic mean (when used with Dh or
Dt)
- Mean or average (may be combined with
other subscripts)
- Metal (when used with symbol, R)
n - Crimped spiral fin neutral diameter
(when used with symbol, D)
- Crimped spiral fin thickness at neutral
diameter (when used with symbol, Y)
o - Outside tube (when used with symbol, D)
p - Tube passes per tube circuit
r - Coil rows in direction of air flow (when
used with symbols, N)
- Fin root for spiral fins with constant
metal area for heat flow (when used with
symbol, Y)
- Refrigerant (all other symbols)
rc - Volatile refrigerant coil circuit
rh - Volatile refrigerant coil suction header
s - Coil surface (when used with symbol, t)
- Saturated air at coil surface temperature,
ts, (when used with symbol, h)
- Sensible heat (when used with symbol, q)
- Straight tube (when used with symbol, L)
- Static (when used with symbol, P)
ARI STANDARD 410-2001
27
ÿ - Effective coil surface (when used with
symbol, t)
- Saturated air at effective coil surface
temperature, tÿ (when used with symbol,
h)
st - Isothermal dry surface air-side, at
standard air density
sw - Wet surface air-side, at standard air
density
t - Net finned tube (when used with symbol,
L)
- Total (when used with symbol, q)
- Tube (when used with symbols hL, k, R, N
and s)
tw - Tube wall
v - Steam
W - Wet surface
w - Water
wb - Wet-bulb
x - Cross section
Where no letter subscript follows cp , h or t these
symbols designate air-water vapor mixture
properties.
8.3 Superscripts.
8.3.1 Numerical superscripts denote the power to
which a number or symbol is raised.
Section 9. Reference Properties and Conversion
Factors
9.1 Reference Properties. The thermodynamic
properties of water and steam shall be obtained from
References A1.13 or A1.14. All other properties shall be
obtained from the ASHRAE Handbook - Fundamentals.
9.2 Metric Conversion Factors. For conversion factors
from I-P to SI units of measure, see Table 1 of
ANSI/ASHRAE Standard 33 and Table 4 in this
standard. (Note: Equations in [ ] are in SI Units)
Section 10. Marking and Nameplate Data
10.4 Marking and Nameplate Data. As a minimum,
nameplate shall display the manufacturer's name and
identify designation, such as model or type.
Section 11. Conformance Conditions
11.1 Conformance. While conformance with this
standard is voluntary, conformance shall not be claimed
or implied for products or equipment within its Purpose
(Section 1) and Scope (Section 2) unless such claims
meet all of the requirements of the standard
ARI STANDARD 410-2001
28
Table 4. Conversion Factors
Item I-P SI
Conversion
Unit Name
Conversion Factor
I-P x Factor = SI
Dynamic Viscosity lb/(h×ft) mPa×s millipascal second 0.41338
Heat Transfer Capacity Btu/h kW kilowatt 0.00029307
Heat Transfer Coefficient Btu/(h×ft2×°F) W/(m2×°C)
watt per square meter
degree Celsius
5.6783
Mass Flow Rate lb/h kg/s kilogram per second 0.000126
Mass Velocity lb/(h×ft2) kg/(m2×s)
kilogram per square
meter second
0.0013562
Pressure Drop Parameter lb2/(in2×ft4) kPa×kg/m4 kilopascal kilogram per
meter4 362.35
Thermal Conductivity Btu×ft/(h×ft2×°F
)
W×mm/(m2×°C
)
watt millimeter per
square meter degree
Celsius
1730.7
Thermal Resistance h×ft2×°F/Btu m2×°C/W
square meter degree
Celsius per watt
0.17611
ARI STANDARD 410-2001
29
RaD = Air Film Thermal Resistance for Dry Surface,
h × ft2 × °F / Btu
Figure 1.
Combined Air Film and Metal Thermal Resistance for Dry Surface
vs.
Air Film Thermal Resistance for Dry Surface
Illustrating performance factors as determined from laboratory tests
RAD + RmD = RAD / h + Rt = Combined Air Film and Metal Thermal Resistance for Dry Surface, h × ft2 °F / Btu
ARI STANDARD 410-2001
30
Dry Surface Area: fa = faD = 1 / RaD
For Wet Surface Area: fa = ÷
÷
ø
ö
ç ç
è
æ
÷ ÷ø
ö
ç çè
æ
=
p aW
aW c
m"
R
f
1
Note: Determine ÷
÷
ø
ö
ç ç
è
æ
p c
m"
from Figure 8
fa = Air-Side Heat Transfer Coefficient,
Btu/(h × ft2 × °F)
Figure 2. Total Metal Thermal Resistance of Fin and Tube Assembly Based on Total Surface
Effectiveness
Illustrating performance factors as determined from laboratory tests
ARI STANDARD 410-2001
31
Va - Standard Air Face Velocity, std. ft/min
c
N
v
w 100
- Steam Mass Flow Rate Per Tube Circuit, 100 lb/(h × tube circuit)
Figure 3. Rating Data for Steam Coils
Illustrating performance factors as determined from laboratory tests
ARI STANDARD 410-2001
32
100 Vw – Standard Water Velocity Inside Tubes, 100 std. ft/s
Va – Standard Air Face Velocity, std. ft/min
Figure 4. Rating Data for Hot or Cold Water Sensible Heat Coils
Illustrating performance factors as determined from laboratory tests
ARI STANDARD 410-2001
33
100 Vw – Standard Water Velocity Inside Tubes, 100 std. ft/s
Va – Standard Air Face Velocity, std. ft/min
Figure 5. Rating Data for Cold Water Cooling and Dehumidifying Coils
Illustrating performance factors as determined from laboratory tests.
ARI STANDARD 410-2001
34
c N
t
q
1
10
-
- Refrigerant Loading Rate per Tube Circuit, 10-1 Btu /(h × tube circuit)
c N
r w
- Refrigerant Mass Flow Rate per Tube Circuit, lb/(h × tube circuit)
Va – Standard Air Face Velocity, std. ft/min
Figure 6. Rating Data for Volatile Refrigerant Cooling and Dehumidifying Coils
Illustrating performance factors as determined from laboratory tests
ARI STANDARD 410-2001
35
Average Water
Temperature,EF[EC]
Tube Header
32 [0.00] 1.122 0.999
40 [4.44] 1.081 0.999
50 [10.0] 1.038 0.999
60 [15.6] 1.000 1.000
80 [26.7] 0.937 1.005
100 [37.8] 0.889 1.013
120 [48.9] 0.852 1.021
140 [60.0] 0.825 1.033
150 [65.6] 0.814 1.039
160 [71.1] 0.804 1.045
180 [82.2] 0.787 1.061
200 [93.3] 0.774 1.076
220 [104] 0.764 1.094
250 [121] 0.756 1.125
Figure 7. Temperature Correction Factor for Water Pressure Drop
Temperature Correction Factor
NOTE: For Use with Either Hot or Cold Water Coils
with Smooth Tubes
( )
( )
( )
( ) F /? µ
wm t /? µ
F e /L Lt h
wm t e /L Lt h
t F
°
=
°
=
60 2 0.25
2 0.25
60
( )
( )
( )
( ) F 1/?
wm t 1/?
F Lh h
wm t Lh h
h F
°
=
°
=
60 2
2
60
at twm for coil conditions
at twm = 60 °F [15.6 °C]
at twm for coil conditions
at twm = 60 °F [15.6 °C]
0 50 100 150 200 250
[-17.8] [10.0] [37.8] [65.6] [93.3] [121]
1.2
1.1
1.0
0.9
0.8
0.7
twm – Mean Water Temperature, °F [°C]
twm = 0.5 (twl + tw2)
Fh
Ft
ARI STANDARD 410-2001
36
Figure 8. Air-Side Heat Transfer Coefficient Multiplier for Wet Surface
ARI STANDARD 410-2001
37
Coil Characteristic "C" as defined in equation 18, 18a, 18b, for the appropriate fluid.
Figure 9. Surface Temperature Chart for Air Cooling and Dehumidifying Coil
Application
ARI STANDARD 410-2001
38
Figure 10. Efficiency of Annular Fins of Constant Thickness
úû
ù
êë
é ) f Y f k ( / a f w )
f
Y f k ( / a f w 2 6
Nomenclature:
f - Fin efficiency
xb - Fin root radius, in [mm]
xe - Fin tip radius, in [mm]
w - Fin height = xe – xb, in [mm]
Yf - Fin thickness, in [mm]
fa - Film coefficient,
Btu/(h × ft2 × °F) [W/(m2 × °C)]
kf - Fin material thermal conductivity
Btu × ft /(h × ft2 × °F) [W ×mm/(m2 × °C)]
h - Surface effectiveness =
o
p s
A
A A + f
Ao - Total external surface area, ft2 [m2]
Ap - Primary surface area, ft2 [m2]
As - Secondary surface area, ft2 [m2]
fa h - Effective film coefficient,
Btu/(h × ft2 × °F) [W/(m2 × °C)]
( ) ( )
( ) ( )
( ) ( ) ÷ ÷
ø
ö
ç çè
æ
+
-
-
=
b b
b b
b e b U K ß U I
U K ß U I
U / U 1 U 0 1 0
1 1 1
2
2 f
( )
( )
( ) ú
ú
û
ù
ê ê
ë
é
- -
=
1
2
1
6
b e
f f a
b e
f f a
b x / x
Y k / f w
x / x
) Y k /( f w
U
( ) b e b e x / x U U =
( )
( ) e
e
U K
U I
1
1
1 = b
f
f
úû
ù
êë
é ) f Y f k ( / a f w )
f
Y f k ( / a f w 2 6
ARI STANDARD 410-2001
39
Figure 11. Efficiency of Annular Fins of Constant Area for Heat Flow and Spiral Fins
( )
( ) ú
ú
û
ù
ê ê
ë
é
-1 3
2 2
b e
r f a
/x x
Y k / f w
úû ù
êë é
) ( 2 ) 6 ( r Y f k / a f w r Y f k / a f w
úû ù
êë é
) ( 2 ) (6 r Y f k / a f w r Y f k / a f w
( ) ( )
( ) ( )
( ) ( ) ÷ ÷
ø
ö
ç çè
æ
+
+
-
=
b b
b b
b e b U I U I
U ßI U I
U / U U 1/3 - /3 1
2/3 2/3 -
4/3 1 3
4
( ) 1 3
) (6 2
-
=
b e
r f a
b /x x
Y k / f w
U
( ) 2 3 /
b e b e x / x U U =
( ) ( ) e e U I U I ß 3 / 2 3 / 2 / - - =
( ) x x Y Y b r / =
f
f
Nomenclature:
f - Fin efficiency
xb - Fin root radius, in [mm]
xe - Fin tip radius, in [mm]
w - Fin height = xe – xb, in [mm]
Yr - Fin thickness at root, in [mm]
fa - Film coefficient,
Btu /(h × ft2 × °F) [W/(m2 × °C)]
kf - Fin material thermal conductivity,
Btu × ft /(h × ft2 × °F)[W×mm /(m2 × °C)]
h - Surface effectiveness =
o
p s
A
A A + f
Ao - Total external surface area, ft2 [m2]
Ap - Primary surface area, ft2 [m2]
As - Secondary surface area, ft2 [m2]
fah - Effective film coefficient,
Btu /(h × ft2 × °F) [W/(m2 × °C)]
f
ARI STANDARD 410-2001
40
Figure 12.
Determination of RaW, fr and qt
For Fully-Wet Surface Cold Water Coils
Ac
Ac = Ao
Ac = Ao
Ac = Ao
Ac
Ac
b. fr for Form 410-4
c. qt for Form 410-6 and Form 410-9
For Volatile Refrigerant Coils
For Partially Dry and Fully-Wet Surface Cold
Water, Volatile Refrigerant and Cold Aqueous
Ethylene Glycol Solution Coils
a. RaW for Form 410-2
RaW
fr
qt
ARI STANDARD 410-2001
41
Air – Side Unmixed
Tube-Side
Mixed
Also for H2O:
M = Dtw / Dtadb
=
pw w
p aSTD
c w
c Q 4.5
ú úû
ù
ê êë
é
pw w
p aSTD
c w
c Q 1.2
When M > 0 :
M
E
o
c
M ÷ ÷
ø
ö
ç çè
æ -
-
=
-
- e 1
e 1
When M = 0: o c E - - = e 1
(tw1 – t1db), (tg1 – t1db), or (tvlg – t1db) = Initial Air-to-
Fluid Temperature Difference, °F [°C]
Dtw - Water Temperature Difference, °F [°C]
Dtg - Aqueous Ethylene Glycol Solution
Temperature Difference, °F [°C]
Dtadb - Air Dry Bulb Temperature Difference, °F
[°C]
Reference A1.12
Sensible Heat Transfer Exponent = co = Ao / (4.5 cp QaSTD R) =
m t
adb t
?
?
= [ Ao / (1.2 cp QaSTD R )]
Figure 13. Crossflow Air-Side Effectiveness
ARI STANDARD 410-2001
42
Sensible Heat Transfer Exponent = co = Ao / (4.5 cp QaSTD R) =
m ?t
adb ?t
= [ Ao /(1.2 cp QaSTD R) ]
Figure 14. Cross-Counterflow Air-Side Effectiveness
When M = 0: o e 1 c E - - =
(tw1 – t1db), (tg1 – t1db), or (tvlg – t1db) =
Initial Air-to-Fluid Temperature Difference, °F [°C]
Air - Side Unmixed
Tube-Side
Mixed
Dtw - Water Temperature Difference, °F [°C]
Dtg - Aqueous Ethylene Glycol Solution Temperature
Difference, °F [°C]
Dtadb - Air Dry-Bulb Temperature Difference, °F [°C]
When M > 0:
( ) ( )
( ) ( ) ( ( ) ( ) ( ) ( ç
ç
è
æ
÷ ÷
ø
ö
ç ç
è
æ
- - + - -
-
- =
- -
2
e 1 sinh
2
e
2
e 1 cosh
e
1
1
2 e 1
/ o c
M
/ o c / o c
M
M
M
E
/ o c
Also for H2O:
M = Dtw / Dtadb
=
pw w
p aSTD
c w
c Q 4.5
ú úû
ù
ê êë
é
pw w
p aSTD
c w
c Q 1.2
Reference A1.17
Air-Side Effectiveness = E = Dtadb / (tw1 – t1db) or ( tv1g – t1db) or (tg1 – t1db)
ARI STANDARD 410-2001
43
Sensible Heat Transfer Exponent = co = Ao / (4.5 cp QaSTD R )=
m t
adb t
?
?
= [ Ao / (1.2 cp QaSTD R )]
Figure 15. Counterflow Air-Side Effectiveness
When M ¹ 1 :
( )
( ) M o c -
M -
M o c
E -
- -
-
=
1
e 1
1
e 1
When M = 1:
1 +
=
o c
o c
E
(tw1 – t1db), (tg1 – t1db), or (tvlg – t1db) = Initial Airto-
Fluid Temperature Difference, °F [°C]
Dtw - Water Temperature Difference, °F [°C]
Dtg - Aqueous Ethylene Glycol Solution
Temperature Difference, °F [°C]
Dtadb - Air Dry-Bulb Temperature Difference,
°F [°C]
Reference A1.12
Also for H2O:
M = Dtw / Dtadb
=
pw w
p aSTD
c w
c Q 4.5
ú úû
ù
ê êë
é
pw w
p aSTD
c w
c Q 1.2
Air-Side Effectiveness = E = Dtadb / (tw1 – t1db) or ( tv1g – t1db) or (tg1 – t1db)
ARI STANDARD 410-2001
44
Figure 16. Aqueous Ethylene Glycol Solution Performance for Smooth Internal Wall Tube Coils
Illustrating performance factors as calculated
ARI STANDARD 410-2001
45
Figure 17. Smooth Internal Tube Wall Heat Transfer Factor for Water
ARI STANDARD 410-2001
46
APPENDIX A. REFERENCES - NORMATIVE
A1 Listed here are all standards, handbooks and other
publications essential to the formation and
implementation of the standard. All references in this
appendix are considered as part of the standard.
A1.1 ANSI/ASHRAE Standard 33-2000, Methods
of Testing Forced Circulation Air Cooling and Air
Heating Coils, 2000, American Society of Heating,
Refrigerating and Air Conditioning Engineers, Inc.,
1791 Tullie Circle, N.E., Atlanta, GA 30329, U.S.A.
A1.2 ARI Guideline E, Fouling Factors: A Survey
of Their Application in Today’s Air-Conditioning
and Refrigeration Industry, 1997, Air Conditioning
and Refrigeration Institute, 4301 North Fairfax
Drive, Suite 425, Arlington, VA 22203, U.S.A.
A1.3 ARI OM-410 Addendum, Certification
Program Operational Manual for Forced-
Circulation Air-Cooling and Air-Heating Coils,
1981, Air-Conditioning and Refrigeration Institute,
4301 North Fairfax Drive, Arlington VA 22203,
U.S.A.
A1.4 ASHRAE Handbook – Fundamentals,
Chapter 6, “Psychrometrics”, Chapter 20,
“Thermophysical Properties of Refrigerants” and
Chapter 21 “Physical Properties of Secondary
Coolants (Brines)”, 2001, American Society of
Heating, Refrigerating and Air-Conditioning
Engineers, Inc., 1791 Tullie Circle, N.E., Atlanta,
GA 30329, U.S.A.
A1.5 ASHRAE Terminology of Heating
Ventilation, Air Conditioning and Refrigeration,
Second Edition, 1991, American Society of Heating,
Refrigerating, and Air-Conditioning Engineers, Inc.,
1791 Tullie Circle, N.E., Atlanta, GA, 30329,
U.S.A.
A1.6 Blast Coil Manufacturers Institute, Proposed
Commercial Standard for Rating and Testing Air
Cooling Coils Using Non-Volatile Refrigerant, 1945,
BCMI Code TS-4044.
A1.7 Brown, Gosta, Theory of Moist Air Heat
Exchangers, 1954, Trans. Royal Institute of
Technology, Stockholm, Sweden, Pages 12-15, Nr
77.
A1.8 Carrier, W.H. & Anderson S.W., The
Resistance to Heat Flow Through Finned Tubing,
1944, ASHVE Transactions, Pages 117-152, Vol.
50, American Society of Heating, Refrigeration, and
Air-Conditioning Engineers, Inc., 1791 Tullie
Circle, N.E., Atlanta, GA, 30329, U.S.A.
A1.9 Copper Development Association, Inc.,
Standards Handbook, Part 2-Alloy Data, 1985, 260
Madison Ave., New York, NY 10016, U.S.A.
A1.10 Gardner, K.A., Efficiency of Extended
Surface, 1945, ASME Transactions, Pages 621-631,
Vol. 67, American Society of Mechanical Engineers,
Three Park Ave., New York, NY 10016, U.S.A.
A1.11 International Nickel Co. Inc., Properties of
Some Metals and Alloys, 1982, Suffern, NY 10901,
U.S.A.
A1.12 Kays, W.M., London, A.L., & Johnson
D.W., Gas Turbine Plant Heat Exchangers, 1951,
American Society of Mechanical Engineers, Three
Park Ave., New York, NY 10016, U.S.A.
A1.13 Keenan, J.H., Keyes, F.G., Hill, P.G., &
Moore, J.G., Thermodynamic Properties of Water
Including Vapor, Liquid, and Solid Phases, 1969 I-P
version, John Wiley & Sons, Inc.
A1.14 Keenan, J.H., Keyes, F.G., Hill, P.G., &
Moore, J.G., Thermodynamic Properties of Water
Including Vapor, Liquid, and Solid Phases, 1978 SI
version, John Wiley & Sons, Inc.
A1.15 McElgin, John & Wiley, D.C., Calculation
of Coil Surface Areas for Air Cooling and
Dehumidification, March 1940, Heating, Piping and
Air Conditioning, Pages 195-201.
A1.16 Rich, D.G., The Efficiency and Thermal
Resistance of Annular Fins, 1966, Proceedings of the
Third International Heat Transfer Conference, Vol.
III, Pages 281-289, American Institute of Chemical
Engineers, 345 East 47th Street, New York, NY
10017, U.S.A.
A1.17 Stevens, R.A., Fernandez, J., & Woolf, J.R.,
Mean Temperature Difference in One, Two and
Three-Pass Crossflow Heat Exchangers, 1957,
ASME Transactions, Pages 287-297, Vol. 79,
American Society of Mechanical Engineers, Three
Park Ave., New York, NY 10016, U.S.A.
A1.18 Ware, C.D. & Hacha, T.H., Heat Transfer
From Humid Air to Fin and Tube Extended Surface
Cooling Coils, 1960, ASME Paper No. 60-HT-17,
American Society of Mechanical Engineers, Three
Park Ave., New York, NY 10016, U.S.A.
ARI STANDARD 410-2001
47
APPENDIX B. REFERENCES - INFORMATIVE
B1 Listed here are standards, handbooks and other
publications which may provide useful information
and background, but are not considered essential.
References in this appendix are not considered part of
the standard.
B1.1 Goodman, W., Performance of Coils for
Dehumidifying Air, 1938 & 1939, Heating, Piping
and Air Conditioning, Vol. 10 (Nov.-Dec. 1938),
Vol. 11 (Jan.-May 1939).
B1.2 Wile, D.D., Air Cooling Coil Performance,
July 1953, Refrigerating Engineering, Pages 727-
732, 794, 796, Vol. 61. American Society of
Heating, Refrigeration, and Air-Conditioning
Engineers, Inc., 1791 Tullie Circle, N.E., Atlanta,
GA, 30329, U.S.A.