Pergamon
PII: S0038 – 092X( 01 )00104 – 9
Solar Energy Vol. 72, No. 1, pp. III–V, 2002
Printed in Great Britain
0038-092X / 02 / $ - see front matter
www.elsevier.com / locate / solener
UNITS AND SYMBOLS IN SOLAR ENERGY
Force
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).
The S.I. unit is the newton (N;kg m s 22 ). The
kilogram weight is not acceptable.
Pressure
The S.I. unit is the pascal (Pa;N m 22 ;
k m 21 s 22 ). The unit kg cm 22 should not be used.
It is sometimes practical to use 10 5 Pa51 bar5
0.1 MPa. The atmosphere (1 atm5101.325 kPa)
and the bar, if used, should be in parentheses,
after the unit has been first expressed in pascals,
e.g. 1.23310 6 Pa (12.3 atm). Manometric
pressures in meters or millimeters are acceptable
if one is reporting raw experimental results.
Otherwise they should be convened to Pa.
2
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.
Energy
The S.I. unit is the joule (J ; kg m 2 s 22 ). The
calorie and derivatives, such as the langley (cal
cm 22 ), 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.
Velocity
Velocity is measured in m s 21 . Popular units
such as km h 21 may be in parentheses afterward.
Volume
Volumes are measured in m 3 or litres (1 litre5
10 23 m 3 ). Abbreviations should not be used for
the litre.
Flow
In S.I. units, flow should be expressed in kg s 21 ,
m s 21 , litre s 21 . If non-standard units such as
litre min 21 or kg h 21 must be used, they should
be in parentheses afterward.
3
Power
The S.I. unit is the watt (W;kg m 2 s 23 ;J s 21 ).
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 22 and heat transfer
coefficient as W m 22 K 21 . Energy rate should not
be expressed as J h 21 .
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 kW 3 3600 s 5 4.3 MJ if maintained for 1 h.
It is preferable to say that
Temperature
The S.I. unit is the degree kelvin (K). However,
it is also permissible to express temperatures in
the degree Celsius (8C). 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 21 K 21 .
NOMENCLATURE AND SYMBOLS
Tables 1–5 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
Hourly energy 5 4.3 MJ
rather than
Energy 5 4.3 MJ h 2l .
III
IV
Units and Symbols in Solar Energy
Table 1. Recommended symbols for materials properties
Table 4. Recommended subscripts
Quantity
Quantity
Symbol
Ambient
Black-body
Beam (direct)
Diffuse (scattered)
Horizontal
Incident
Normal
Outside atmosphere
Reflected
Solar
Solar constant
Sunrise (sunset)
Total of global
Thermal
Useful
Spectral
a
b
b
d
h
i
n
o
r
s
sc
sr (ss)
t
t, th
u
l
Symbol
Specific heat
Thermal conductivity
Extinction coefficient 1
Index of refraction
Absorptance
Thermal diffusivity
Specific heat ratio
Emittance
Reflectance
Density
Transmittance
Unit
21
c
k
K
n
a
a
g
e
r
r
t
21
J kg K
W m 21 K 21
m 21
m 2 s 21
kg m 23
1
In meteorology, the extinction coefficient 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
Quantity
Symbol
Range and sign
convention
Altitude
Surface tilt
a
b
Azimuth (of surface)
g
Declination
Incidence (on surface)
Zenith angle
Latitude
Hour angle
d
Q, i
Qz
F
v
0 to 6908
0 to 6908; toward the
equator is 1ive
0 to 3608; clockwise
from North is 1ive
0 to 623.458
0 to 1908
0 to 1908
0 to 6908; North is 1ive
21808 to 11808; solar
noon is 08, afternoon
is 1ive
0 to 1908
Reflection
(from surface)
r
Table 5. Recommended symbols for radiation quantities
Preferred name
(a)
(b)
Table 3. Recommended symbols for miscellaneous quantities
Quantity
Symbol
Unit
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
A
h
m
AM
m2
W m 22 K 21
kg
~
m
Q
Q~
q
T
U
kg s 21
J
W
W m 22
K
W m 22 K 21
h
l
n
s
m
s 21
W m 22 K 24
t, t, Q
s
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 1), the emission, absorption, reflection,
and transmission of radiation by materials have
(c)
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
Symbol
Unit
Q
F
F
E, H
M, J
J
W
W m 22
W m 22
W m 22
Ms, E
Wm
L
W m 22 sr 21
H
J m 22
22
Solar radiation
Global irradiance or solar
flux density
Beam irradiance
Diffuse irradiance
Global irradiation
Beam irradiation
Diffuse irradiation
G
W m 22
Gb
Gd
H
Hb
Hd
W m 22
22
Wm
J m 22
J m 22
J m 22
Atmospheric radiation
Irradiation
Radiosity
Exchange
F↓
F↑
FN
W m 22
W m 22
W m 22
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 ‘ance’ be used for the
following four quantities:
S
Ms
E
emittance e 5 ] or ]
Eb
Msb
f
absorptance a 5 ]
fi
f
reflectance r 5 ]
fi
f
transmittance t 5 ]
fi
D
Units and Symbols in Solar Energy
where E and f is the radiant flux density that is
involved in the particular process. The double use
of a for both absorptance and thermal diffusivity
V
is usual, as is the double use of r for both
reflectance and density. Neither double use should
give much concern in practice.