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Modeling the comfort effects of short-wave solar radiation indoors
Edward Arens
a
,
*
, Tyler Hoyt
a
, Xin Zhou
a
,
c
, Li Huang
a
,
b
, Hui Zhang
a
, Stefano Schiavon
a
a
Center for the Built Environment, University of California, Berkeley, USA
b
School of Architecture, Tsinghua University, Beijing, China
c
School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai, China
article info
Article history:
Received 21 June 2014
Received in revised form
5 September 2014
Accepted 6 September 2014
Available online 16 September 2014
Keywords:
Solar load
Thermal comfort
Thermal sensation
Shading
MRT
ERF
abstract
Exposure to sunlight indoors produces a substantial effect on an occupant's comfort and on the air
conditioning energy needed to correct for it, yet has in the past not been considered in design or in
thermal comfort standards. A public online model of the effects of solar radiation on human heat gain
and comfort has been developed to make this possible. SolarCal is a whole-body model for ease of use in
early design. Its predictions compare closely (<0.1 PMV mean absolute error) to results of a human
subject test. It can be used to determine the allowable transmittance of fenestration in a perimeter ofce.
©2014 Elsevier Ltd. All rights reserved.
1. Introduction
Windows unshaded from direct solar radiation are common in
commercial buildings. They often introduce signicant problems by
admitting large amounts of solar (aka shortwave) radiation indoors.
Some of the problems are visual, such as glare, but three thermal
ones are also very important.
First, in most buildings the heat gain from solar radiation
absorbed indoors must be removed by energy-intensive air-con-
ditioning. Second, solar gain in the occupied zone is intensely var-
iable and difcult to control: in attempting to keep the temperature
of a sunlit section under control, adjacent spaces are likely to be
overcooled. A third issue is the topic of this paper: solar radiation
landing on occupants directly affects their thermal comfort. The
solar heat absorbed and liberated in clothing and skin must be
offset by cooler air and surface temperatures around the body for
the occupant to remain comfortably in thermal balance (Fig. 1). The
temperature offset may be substantial and beyond the corrective
capacity of conventional cooling systems.
This third issue has received surprisingly little notice in the
design or evaluation of buildings. For example, the relevant indoor
environmental standards ASHRAE Standard 55 Thermal
environmental conditions for human occupancy [2], EN-ISO Standard
7730 [5], and CEN-15251 [6] do not even mention shortwave ra-
diation. Although Fanger published projected area factors for the
human body in 1970 [7], the subject of shortwave gain and comfort
has been almost absent from the research literature until recently.
A few studies [8,9,16,19] have addressed the effect of solar heating
on comfort.
There are no readily available design tools for predicting the
effect of solar radiation falling directly on occupants in buildings.
Potential developers of such tools may have been discouraged by
the complexity of the task: identifying an occupant's position,
determining the position of solar beam radiation on interior room
surfaces, determining the shading and reection from interior
furnishings, and determining the effect of solar altitude and azi-
muth on the occupant's non-cylindrical body shape.
There are complex multi-segment thermal physiology and
comfort models that predict detailed radiative heat exchanges be-
tween the human body and its environment via view factors
[11e13]. These models also predict solar loads on local body parts.
For example, the commercial software RadTherm [20] distributes
solar loads to local body segments in the Fiala thermophysiological
model, from which local skin temperatures are predicted [11]. The
Berkeley Advanced Comfort Model [15] performs the same func-
tions. In both of these, the predicted local skin temperatures are
then converted to local thermal sensation and comfort using the
Zhang et al. [14] comfort model. Multi-segment physiology and
*Corresponding author. 390 Wurster Hall Berkeley, CA 94720.
E-mail address: earens@berkeley.edu (E. Arens).
Contents lists available at ScienceDirect
Building and Environment
journal homepage: www.elsevier.com/locate/buildenv
http://dx.doi.org/10.1016/j.buildenv.2014.09.004
0360-1323/©2014 Elsevier Ltd. All rights reserved.
Building and Environment 88 (2015) 3e9
comfort models are most commonly used in automotive design.
The process is more time-intensive and constrained than typical
building design, in which speed of use is more of an issue. Multi-
segment models may be linked with CFD simulation, and with
advanced fenestration models. WINDOW 6.2 [17] predicts bidirec-
tional scattering for solar radiation impinging on complex window
systems (glass, louvers, and shades). The scattered solar might be
linked to a human manikin in order to distribute solar loads on
different body parts [10]. Solar scattering models have not yet been
linked to thermophysiological and comfort models.
For the foreseeable future, building designers will need a way to
quickly calculate the consequences of different levels of indoor
solar radiation indoors on comfort, peak cooling load, and energy
use. The comfort consequences should be quantied on well-
accepted thermal comfort scales. The peak cooling load and en-
ergy consequences should be quantied by how much the space's
temperature would have to be reduced to offset the solar heat
liberated on the occupant. The solar variables under the designer's
control would be: the presence or absence of sunlight on the per-
son, the extent of the person's body area exposed to direct sun, and
the intensity of solar radiation after ltering through glass and
window furnishings. Evaluating these variables may not require
great geometric precision since occupants' positions in buildings
cannot be very precisely predicted or xed.
This paper describes a solar calculator (SolarCal) that is incor-
porated in the Center for the Built Environment (CBE) web-based
Comfort Tool [18]. The Comfort Tool contains the provisions of
ASHRAE Standard 55 [2] as its core, but it also has optional features
beyond the current requirements of the Standard [21]. SolarCal is
based on a method developed by Arens et al. [1] to evaluate the
effect of solar radiation on comfort outdoors. The SolarCal model is
intentionally simplied so it can be used to quickly estimate the
solar radiation in undetermined environments or in environments
with simple geometries. In this paper, we compare SolarCal simu-
lations against a recent human subject test of solar effects and
comfort, to evaluate the effectiveness of SolarCal's simplied radi-
ation calculations, and its ability to predict comfort in terms of
predicted mean thermal sensation votes (PMV) [7]. We also esti-
mate the level of window shading needed to prevent unacceptable
PMV increases for occupants near windows.
2. Method of calculating solar gain to the body indoors
The SolarCal model is based on the effective radiant eld (ERF), a
measure of the net radiant energy ux to or from the human body.
ERF is used to describe the additional (positive or negative) long-
wave radiation energy at the body surface when surrounding sur-
face temperatures are different from the air temperature. It is in W/
m
2
, where area refers to body surface area. The surrounding surface
temperature of a space is commonly expressed as mean radiant
temperature (MRT). The ERF on the human body from long-wave
exchange with surfaces is related to MRT by:
ERF ¼f
eff
h
r
ðMRT T
a
Þ(1)
where f
eff
is the fraction of the body surface exposed to radiation
from the environment (¼0.696 for a seated person and 0.725 for a
standing person [7]); h
r
is the radiation heat transfer coefcient (W/
m
2
K); and T
a
is the air temperature (
C).
The energy ux actually absorbed by the body is ERF times the
long-wave emissivity/absorptivity
a
LW
, typically equal to 0.95. Solar
radiation absorbed on the body's surface can be equated to an
additional amount of longwave ux, ERF
solar
:
a
LW
ERF
solar
¼a
SW
E
solar
(2)
where E
solar
is the shortwave solar radiant ux on the body surface
(W/m
2
);
a
SW
is short-wave absorptivity, z0.67 for (white) skin and
average clothing.
E
solar
is the sum of three uxes that have been ltered by
fenestration properties and geometry, and are distributed on the
occupant body surface: direct beam solar energy coming directly
from the sun (E
dir
), diffuse solar energy coming from the sky vault
(E
diff
), and solar energy reected upward from the oor (E
re
). These
are dened below.
Diffuse radiation from the sky is assumed to be distributed on
the upper half of the radiatively-exposed portion of the body.
E
diff
¼0:5f
eff
f
svv
T
sol
I
diff
(3)
where f
svv
is the fraction of sky vault in occupant's view (Fig. 2); I
diff
is diffuse sky irradiance received on an upward-facing horizontal
surface (W/m
2
); I
diff
is a standard meteorological parameter
measured in open terrain (Note: in less open terrain, natural and
built surfaces protruding above the horizon block the diffuse sky
radiation behind them. SolarCal assumes that the reduction in I
diff
is
compensated for by the radiation reected from the surfaces. In
clear weather the angular uxes from reected and diffuse sky are
roughly equal); T
sol
is the total solar transmittance, the ratio of
Fig. 1. Occupant exposed to direct solar irradiation (image courtesy of Seattle Times).
Fig. 2. Fraction of sky vault in occupant's view (f
svv
).
E. Arens et al. / Building and Environment 88 (2015) 3e94
incident shortwave radiation to the total shortwave radiation
passing through the glass and shades of a window system.
The total outdoor solar radiation on the horizontal (I
TH
)is
ltered by both T
sol
and f
svv
, and multiplied by the reectance (al-
bedo) of the oor and lower furnishings (R
oor
). In addition, the
short-wave reected to the lower half of the body will be accom-
panied by increased long-wave radiation from oor surfaces
warmed by the non-reected portion of the solar. This long-wave
ux may be approximated by increasing the value of R
oor
.
E
refl
¼0:5f
eff
f
svv
T
sol
I
TH
R
floor
(4)
where I
TH
is the total horizontal direct and diffuse irradiance out-
doors (W/m
2
); and R
oor
is the oor reectance (a value might be
(0.2 þ0.3) for short-wave plus long-wave combined).
Direct radiation affects only the projected area A
p
of the body,
and is reduced by any shading of the body provided by the indoor
surroundings:
E
dir
¼A
p
A
D
f
bes
T
sol
I
dir
(5)
where A
p
is the projected area of a standard person exposed to
direct beam sunlight; A
D
is the DuBois surface area of the assumed
person (around 1.8 m
2
); f
bes
is the fraction of body exposed to
sunlight (Fig. 3. Note that this measure does not include the body's
self-shading, only the shading from surroundings); and I
dir
is direct
beam (normal) solar radiation (W/m
2
). The meteorological radia-
tion parameters are related as: I
TH
¼I
dir
sin
b
þI
diff
, where
b
is the
solar altitude.
ERF
solar
can therefore be calculated from the following equation:
ERF
solar
¼0:5f
eff
f
svv
I
diff
þI
TH
R
floor
þA
p
f
bes
I
dir
.A
D
T
sol
ða
SW
=a
LW
Þ(6)
In direct beam sunlight, the projected area of a human body
varies with solar altitude and azimuth. Fanger [7] quantied this
using the empirically determined projected area factor (f
p
):
A
p
¼f
eff
f
p
A
D
(7)
In the CBE Comfort tool, f
p
for seated and standing postures were
taken from the graphs in ASHRAE Standard 55-2013 [2] and t
using a 2-D interpolating spline (Fig. 4).
To obtain ERF
solar
with Equation (6), the inputs are f
svv
,f
p
,T
sol
,
f
bes
,I
diff
,I
TH
,R
oor
,I
dir
,
a
SW
, and
a
LW
along with solar altitude (
b
) and
azimuth. To reduce the climate data input in SolarCal, I
diff
may be
estimated as I
diff
¼0.17 I
dir
sin
b
. Finally, ERF
solar
is added to the
longwave ERF input to determine a new solar-adjusted MRT
(
D
MRT) using Equation (1). This allows a new PMV to be calculated
for an occupant exposed to shortwave radiation.
3. Input data
The following paragraphs suggest methods for obtaining good
estimates for the SolarCal input parameters.
Direct beam solar radiation (I
dir
) values can be found in Typical
Meteorological Year (TMY) weather les [22]. The column labeled
DNI (Direct Normal Intensity) contains a year's worth of repre-
sentative hourly solar intensity data, which can be used to derive a
design condition. For example, the 95th percentile of the daily
maximum DNI may be a reasonable design condition. Should
hourly weather data not be available, Table 1 contains direct solar
beam radiation data for a standard cloudless atmosphere [4] that
can be used in this situation. The best value can be chosen by
considering the latitude of the site and the season of the design
condition. For example, the maximum solar altitude occurring on
the summer solstice in Berkeley, CA is about 75
, corresponding to a
design condition of 915 W/m
2
.
The sky vault view fraction, f
svv
, may be estimated directly or
with a simple equation. It is equal to the angular area of the sky vault
exposed by the window aperture, divided by the total angular area
of the overhead vault, both as seen from the position of the occu-
pant. This value depends mostly on the dimensions of the window
(width w, height h) and the distance between the occupant and the
window (d). With these values we can derive the approximation.
f
svv
z
tan
1
h
2d
tan
1
w
2d
90$180 (8)
where the inverse tangent function returns values in degrees.
When calculating f
svv
for multiple windows, the f
svv
for each may be
calculated and summed to get an approximate total f
svv
. Note that
exterior objects obstructing the sky vault should not be considered,
since they have a similar diffuse reectivity as the sky vault (Fig. 5).
The solar transmittance T
sol
is most easily obtained from the
International Glazing Database, containing data from many glazing
manufacturers [23]. The database is included in the WINDOW
software developed by LBNL [24].
Transmittance is sometimes specied in terms of shading coef-
cient (SC). SC is by denition referenced to the radiation passing
through clear glass with a T
sol
of 0.87. Similarly, center-of-glass Solar
Heat Gain Coefcient (SHGC) provides an approximation of T
sol
.
These metrics differ from T
sol
in that they include the inward long-
wave ux resulting from shortwave radiation absorbed in the glass.
This additional ux does not arrive at the occupant in the collimated
beam of direct shortwave radiation. Using SC and SHGC, the model
will tend to overpredict solar gain on the occupant when glass
absorptance is high, or the occupant is further from the window.
In SolarCal, the solar altitude/azimuth parameters only deter-
mine the radiation incident on the occupant. Transmission through
the building's fenestration also depends on the angle of the sun
relative to the glazing, but the SolarCal model does not extend to
including the glazing orientation. It is the designer's responsibility
to adjust T
sol
for transmission reductions caused by non-normal
solar incidence angles on the window.
The shortwave absorptivity
a
SW
of the occupant may range widely
dependingon the color of the occupant's skin, as well as the colorand
Fig. 3. Fraction of body exposed to sun (f
bes
).
E. Arens et al. / Building and Environment 88 (2015) 3e95
amount of clothing covering the body. In the SolarCal web tool, we
choose 0.67 as a reasonable estimate for this value. If the user has
specic assumptions about the clothing or skin color of the occu-
pants, a more accurate estimate can be calculated using Table 2 [3].
4. Comparing model predictions to a human subject test
Hodder and Parsons (H/P) used an automobile mockup (Fig. 6)
with moveable heat lamps to emulate four levels of solar radiation
impinging on human subjects [8]. Air temperature was between
22.8 and 24.0
C, metabolic rate 1.2 met, and clothing resistance
0.7 clo. Fig. 7 shows the input variables for modeling the test, as
represented in the SolarCal interface.
Table 3 rst shows solar loads on the subject (W/m
2
) predicted
by SolarCal's A
p
method and by BCM's detailed 5000 polygon
manikin; SolarCal is 7% low. The
D
MRT from SolarCal is then
compared to
D
MRT calculated from H/P's globe thermometer
readings. The two
D
MRT values were then used to calculate PMV.
The experiment found that 200 W/m
2
solar gain produced an in-
crease of roughly one PMV scale unit. The SolarCal PMV prediction
agrees well with the experiment's actual thermal sensation votes
(<0.1 PMV mean absolute error), which use the identical scale as
PMV. The discrepancies are less than 0.15 scale unit except with
zero radiation.
5. Calculation examples
In this section we will develop two example SolarCal
calculations.
Fig. 4. Projected area of body exposed to sun (A
p
) as a function of altitude and azimuth, in standing posture (left) and seated posture (right). Azimuth zero represents the sun in
front of the occupant.
Table 1
Typical direct beam solar radiation values for a standard cloudless atmosphere
depending on the solar altitude angle.
Solar altitude angle [
] 5 10 20 30 40 50 60 70 80 90
Direct beam solar
radiation [W/m
2
]
210 390 620 740 810 860 890 910 920 925
Fig. 5. From the moving walkway, the altitude angle to the top of the window is
approximately 60. Since the width of the window is very large, we have a f
svv
value of
about 1/3.
Table 2
Shortwave absorptivity (
a
SW
) values for common clothing and skin types.
White
clothing
Khaki
clothing
Black
clothing
White
skin
Brown
skin
Black
skin
a
SW
0.2 0.57 0.88 0.57 0.65 0.84
Note: because SolarCal is a whole-body model, it cannot differentiate between local
body parts (such as check, back, hand etc.), or between body parts with or without
clothing. Comfort effects stemming from such differences must be modeled with
multiple-segment comfort models as described in the Introduction above [15,20].
Fig. 6. Automotive test chamber.
E. Arens et al. / Building and Environment 88 (2015) 3e96
1) Should skylights admit solar radiation onto the occupant from
overhead, SolarCal can be used to assess the resulting comfort
impact. The designer must determine a time in the year when
direct solar radiation strikes the occupant, and obtain T
sol
for
that time, accounting for the incidence angle of the solar beam
on the skylight glazing.
Assume the occupant is seated and a horizontal skylight with
dimensions 2 m 2 m is 4 m is directly above the occupant. The site
is Miami, FL, where the solar altitude angle in summer is high
enough to admit direct solar through this skylight onto the occu-
pant. For a maximum solar altitude angle of 87
, use Table 1 to
determine a direct solar beam intensity of 925 W/m
2
. The skylight
glass has a rated T
sol
of 0.2, which will remain about the same for
this near-normal solar incidence angle.
Only the occupant's lower legs will be shaded by the desk under
this overhead sun angle, so the f
bes
is 0.9. We will assume shortwave
absorptivity of 0.7. The oor is covered with a dark carpet with
reectivity of 0.2. We will assume the longwave from the absorbed
solar gain in the carpet adds another 0.3 to the oor reectance, for
a total of 0.5. The f
svv
is approximated from Equation (8):
f
svv
z
tan
1
2
8
tan
1
2
8
90 180 ¼0:01 (9)
These conditions result in an MRT delta of 3.9
C, and an ERF of
16.5 W/m
2
. We will discuss the signicance of this later.
Notice that if this modest skylight is enlarged to a size often seen
in glazed atria (f
svv
~ 0.5) the MRT delta increases to an MRT delta of
8.2
C and an ERF of 34.2 W/m
2
.
2) Here we analyze a shading design for an occupant placed near a
window, as in Fig. 1. The solar altitude is 75
with a direct solar
intensity of 910 W/m
2
. The vertical glass has a rated T
sol
of 0.5,
which the designer determines to be 0.3 for the sun angle under
consideration. The occupant is seated facing the 3 m 3m
window at a distance of 1 m, yielding a f
svv
of 0.32. In this case
we will assume that half of the body is shaded by the furniture
of the occupant, and that the absorptivity is 0.7. A light beige-
colored oor has a total SW þLW reectivity of 0.6. Under
these conditions, the
D
MRT is 8.0
C. The results of this are
plotted in Fig. 8. In both cases, the air temperature (25
C) and
relative humidity (50%) are represented by the red dot, airspeed
is 0.1 m/s, clothing is a typical summer ensemble (0.5 CLO), and
the metabolic rate is 1.2 MET. On the left hand side, the MRT is
25
C. On the right, the MRT is 33
C, after the 8.0
C adjustment.
The blue area represents the comfort zone on the chart for the
respective conditions, where the PMV is between 0.5 and 0.5.
The solar increase to MRT clearly produces an unmanageable
shift in the occupant's comfort zone, moving the occupant well
outside its boundaries with a high PMV. The designer can use the
model to evaluate solar control options that reduce this heat gain.
Fig. 7. Input for modeling the test.
Table 3
Comparison of modeled and experimental results.
Solar radiation level (W/m
2
) 600 400 200 0
Air temperature (
C) 24.0 23.4 23.4 22.8
Solar
load
(W/m
2
)
BCM with 5000 polygon manikin 103.4 68.9 34.5 0
SolarCal model 96.7 64.4 32.2 0
D
MRT H/P test using Globe T 20.0 18.4 14.3 1.4
SolarCal model 23.1 15.4 7.7 0
PMV H/P results using computed MRT 2.8 2.3 1.9 0.2
SolarCal model 3.1 1.9 0.9 0.1
Actual mean thermal sensation vote in H/P
experiment
3.1 1.9 1.1 0.2
Fig. 8. The psychrometric chart with comfort zone representing the range of 0.5 to 0.5 PMV before (L) and after (R) an 8.0 C
D
MRT has been applied to a typical comfort model
input condition. The tool is available online http://smap.cbe.berkeley.edu/comforttool.
E. Arens et al. / Building and Environment 88 (2015) 3e97
6. Application to shading
The PMV increase caused by short-wave solar radiation can be
used to determine a practical maximum for allowable T
sol
in
architectural interiors.
It seems reasonable to assume that solar gain in a typical
conditioned ofce should not increase the occupant's PMV more
than one-half a scale unit (e.g., from 0 to þ0.5, starting at the
neutral temperature and increasing to the upper boundary of the
comfort zone).
The total T
sol
required to limit occupant overheating is shown in
Table 4 for the geometry of a simulated perimeter zone cubicle
shown in Fig. 9.I
dir
¼900 W/m
2
, solar altitude ¼65
,f
svv
¼0.3,
f
bes
¼0.5, and R
oor
¼0.5. The indoor environment is: air
speed ¼0.1 m/s, relative humidity ¼50%; and occupant
clothing ¼0.57 clo. The sun is from the side at 90
azimuth, and
activity is 1.1 met.
However, if a building were being maintained at the cool
boundary of the comfort zone, solar gain might usefully increase
the occupant's PMV by as much as one scale unit. (For energy
reasons, this strategy should only be allowed in the heating sea-
son!). Fig. 10 uses the above cubicle example to show the boundary
of allowable T
sol
for a range of indoor ambient temperature con-
ditions. It is the red line representing the PMV ¼0.5 contour. The
blue and black lines in the gure are the PMV ¼0 and PMV ¼0.5
contours, respectively. An ambient temperature deviation of 1.5
C
from neutral corresponds to a 0.5 PMV scale change, as does a 0.15
change in T
sol
.
In the absence of solar gain, lowering 1.5
C from neutral causes
thermal sensation to drop from PMV ¼0to0.5. Adding solar
radiation 15% T
sol
brings thermal sensation up 0.5 PMV units, back
to neutral. To reach the upper threshold (PMV ¼0.5) from this
lower temperature, T
sol
can be as high as 30% before PMV exceeds
0.5. However, above neutral ambient temperatures (the right side
of the gure), the allowable T
sol
must be below 0.15, reaching zero
at 1.5
C above neutral.
7. Conclusions
The direct warming effect of solar radiation on occupants may
cause discomfort, and require a large amount of correction by
the cooling system. It should be accounted for in architectural
and engineering design, preferably early in the process. This
paper describes SolarCal, a new public online web-based tool for
predicting solar effects on comfort.
The SolarCal model computes an increase in MRT equivalent to
shortwave gains from direct, diffuse, and indoor-reected radi-
ation on a person. This is then used to compute PMV using the
method prescribed in ASHRAE Standard 55-2013.
Comparison of results from SolarCal, the advanced multi-
segment Berkeley Comfort Model, and a physical experiment
shows SolarCal giving reasonable predictions of solar effects on
MRT, and on comfort expressed as PMV.
Low solar transmittance is needed to prevent excessive increase
in occupants' thermal sensation indoors. The transmission of
glass plus shades together probably should not exceed 15% if the
sun will be shining on an occupant indoors.
Nomenclature
MRT mean radiant temperature
C
ERF effective radiant eld W/m
2
f
eff
fraction of body exposed to sun -
h
r
radiation heat transfer coefcient W/m
2
K
T
a
Air temperature
C
a
LW
longwave radiation absorptivity e
a
SW
shortwave radiation absorptivity e
ERF
solar
effective radiant eld solar component W/m
2
E
solar
total shortwave solar radiant ux W/m
2
E
dir
direct beam component of shortwave solar radiant ux
W/m
2
E
diff
diffuse component of shortwave solar radiant ux W/m
2
Table 4
Solar transmission (T
sol
) that limits an occupant's PMV increase to one-half scale
unit.
Metabolic rate (met) Azimuth
30
90
120
1 12.2% 13.5% 14.1%
1.1 13.5% 14.9% 15.5%
1.2 15.2% 16.7% 17.5%
1.3 16.4% 18.1% 18.9%
Fig. 9. Ofce cubicle geometry.
Fig. 10. T
sol
boundary predicted by the SolarCal model.
E. Arens et al. / Building and Environment 88 (2015) 3e98
E
re
reected component of shortwave solar radiant ux
W/m
2
f
svv
fraction of sky vault exposed to body e
T
sol
glazing solar transmittance e
I
dir
direct solar beam intensity W/m
2
I
diff
diffuse solar beam intensity W/m
2
I
TH
Total horizontal solar beam intensity W/m
2
R
oor
oor reectivity e
A
p
projected area m
2
f
bes
fraction of body exposed to sun e
b
solar altitude angle deg
References
[1] Arens E, Gonzalez R, Berglund L. Thermal comfort under an extended range of
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E. Arens et al. / Building and Environment 88 (2015) 3e99
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... The model SolarCal (ARENS et al., 2015) is also applied to MRT by adding the solar radiation effect on human body heat gain and comfort. It is a simplified model that intends a quick estimation of solar radiation and is recommended by ASHRAE Standard 55 (AMERICAN…, 2017). ...
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