Solar Energy Vol. 61, No. 1, pp. III-IV, 1997
Elsevier Science Ltd. Printed in Great Britain
Pergamon
UNITS AND SYMBOLS IN SOLAR ENERGY
Pressure
In 1977, a committee of ISES developed a set
of recommended
nomenclature
for papers
appearing in Solar Energy. This is a condensed
and revised version of those recommendations.
The original appeared in Solar Energy 21,61-68
( 1978). Copies of complete recommendations
are available from the editorial offices.
The S.I. unit is the Pascal (Pa = N m-* = kg
m-l s-*). The unit kg cm-* should not be used.
It is sometimes practical to use 10’ Pa= 1 bar=
0.1 MPa. The atmosphere (1 atm = 101.325 kPa)
and the bar, if used, should be in parenthesis,
after the unit has been first expressed in Pascals,
e.g. 1.23 x lo6 Pa (12.3 atm). Manometric pressures in meters or millimeters are acceptable if
one is reporting raw experimental results; otherwise they should be converted to Pa.
1. UNITS
The use of S.I. (Systeme International
d’unites) in Solar Energy papers is mandatory.
The following is a discussion of the various S.I.
units relevant to solar energy applications.
ve/elocity
Velocity is measured in m s-l. Popular units
such as km h-r may be in parentheses afterward.
Energy
Volume
The S.I. unit is the joule (J = kg m* s-*). The
calorie and derivatives, such as the langley
(cal cm-*), are not acceptable. No distinction is
made between different forms of energy in the
S.I. system so that mechanical, electrical, and
heat energy are all measured in joules. Although
the watt-hour is used in many countries for
commercial metering of electrical energy, its use
is discouraged in scientific and technical papers
as it is derived from the hour which is not a
basic S.I. quantity.
Volumes are measured in rnw3 or liters
(1 liter = low3 m3). Abbreviations should not be
used for the liter.
Flow
In S.I. units, flow should be expressed in kg
s-l, m3 s-l, liter s -l. If non-standard units such
as liter min-’ or kg h-’ must be used, they
should be in parentheses afterward.
Temperature
The S.I. unit is the degree Kelvin (K). However, it is also permissible to express temperatures
in the degree Celsius (“C). Temperature differences are best expressed in Kelvin (K).
When compound units involving temperature
are used, they should be expressed in terms of
Kelvin, e.g. specific heat J kg-’ K-‘.
Power
The S.I. unit is the watt (W = kg m*
sm3 = J s-i). The watt will be used to measure
power or energy rate for all forms of energy and
should be used wherever instantaneous values
of energy flow rate are involved. Thus, energy
flux density will be expressed as W m-* and
heat transfer coefficient as W m-* K-‘. Energy
rate should not be expressed as J h-‘.
When power is integrated for a time period,
the result is energy that should be expressed in
joules, e.g. an energy rate of 1.2 kW would
produce 1.2 x 3600=4.3 MJ if maintained for
1 h. It is preferable to say that
2. NOMENCLATURE AND SYMBOLS
Tables l-5 list recommended symbols for
physical quantities. Obviously, historical usage
is of considerable importance in the choice of
names and symbols and attempts have been
made to reflect this fact in the tables. But
conflicts do arise between lists that are derived
from different disciplines. Generally, a firm recommendation has been made for each quantity,
except for radiation where two options are given
in Table 5.
In the recommendations for material properties (see Table l), the emission, absorption,
reflection, and transmission of radiation by
Hourly energy = 4.3 MJ
rather than
Energy=4.3
MJ h-‘.
Force
The S.I. unit is the Newton (N = kg m se*).
The kilogram weight is not acceptable.
III
IV
Units and Symbols in Solar Energy
Table 1. Recommended symbols for materials properties
Quantity
Symbol
Unit
;;
K
J kg-’ K-i
W m-l K-i
m-’
Specific heat
Thermal conductivity
Extinction coefficient’
Index of refraction
Absorptance
Thermal diffusivity
Specific heat ratio
Emittance
Reflectance
Density
Transmittance
n
a
mz s-l
a
Y
E
P
kg rnF3
P
5
+In meteorology the extinction coeficient is the product of
K and the path length, and is thus dimensionless.
Table 2. Recommended symbols and sign convention for
sun and related angles
Table 4. Recommended subscripts
Quantity
Symbol
Ambient
Black-body
Beam (direct)
Diffuse (scattered)
Horizontal
Incident
Normal
Outside atmosphere
Reflected
Solar
Solar constant
Sunrise (sunset)
Total or global
Thermal
Useful
Spectral
a
b
b
d
h
i
n
0
r
S
SC
ST, (SS)
t
t,
th
;
Table 5. Recommended symbols for radiation quantities
Quantity
Range and sign
conversion
Symbol
Altitude
Surface tilt
;
Azimuth (of surface)
y
Declination
Incidence (on surface)
Zenith angle
Latitude
6
5
Hour angle
w
Reflection
(from surface)
r
e, i
0 to +90
0 to f90” ; towards the
equator is +ive
0 to 360”; clockwise
from North is +ive
0 to k23.45”
0 to +90
0 to +90°
0 to k90”; North is
+ ive
- 180” to + 180”; solar
noon is 0, afternoon
is +ive
oto +90
Table 3. Recommended symbols for
miscellaneous quantities
Quantity
Area
Heat transfer coefficient
System mass
Air mass (or air mass factor)
Mass flow rate
Heat
Heat flow rate
Heat flux
Temperature
Overall heat transfer
coefficient
Efficiency
Wavelength
Frequency
Stefan-Boltzmann constant
Time
Symbol
A
h
m
M
;
0
4
T
Unit
m2
W m-2 K-’
kg
Preferred name
(a) Nonsolar radiation
Radiant energy
Radiant flux
Radiant flux density
Irradiance
Radiosity or Radiant
exitance
Radiant emissive power
(radiant self-exitance)
Radiant intensity (radiance)
Irradiation or radiant
exposure
(b) Solar radiation
Global irradiance or solar
flux density
Beam irradiance
Diffuse irradianoe
Global irradiation
Beam irradiation
Diffuse irradiation
(c) Atmospheric radiation
Irradiation
Radiosity
Exchange
kg s-’
J
W
:m-2
u
W rnv2 K-i
1
”
o
r, r, 8
m
S
materials have been described in terms of quantities with suffixes “ance” rather than “ivity,”
which is also sometimes used, depending on the
discipline. It is recommended that the suffix
“ante” be used for the following four quantities:
Unit
P
E. H
J
W
W m-l
Wm-’
M. J
W me2
MS,E
L
W me2
W m-a sr-’
H
J mm2
G
W me2
W m-r
W m-’
J m-r
J me2
J me2
Gb
Gd
H
Hb
Hd
W mm2
W m-*
W m-’
4
absorptance a = -
#i
4
reflectance p = A
SC’
W mm2 Km4
Symbol
transmittance
4
t=i
where E and 4 is the radiant flux density that
is involved in the particular process. The double
use of a for both absorptance and thermal
diffusivity is usual, as is the double use of p for
both reflectance and density. Neither double use
should give much concern in practice.