7th International Thermal Manikin and Modelling Meeting - University of Coimbra, September 2008
INDOOR HEAT EXCHANGES BY RADIATION BETWEEN OCCUPANTS AND
SURROUNDING SURFACES
E. Z. E. Conceição1 and Mª. M. J. R. Lúcio2
1FCMA,
Universidade do Algarve, Campus de Gambelas, 8005-139 Faro, Portugal
email: econcei@ualg.pt
2Agrupamento Vertical Professor Paula Nogueira, R. Comunidade Lusíada, 8700-000 Olhão, Portugal
Summary: In this work a numerical model that allows to simulate the human body thermal and thermoregulatory
systems, the clothing thermal response and the indoor heat exchanges is presented. This program is used in the
calculus of the temperature distribution in the human body and clothing and in the evaluation of the global thermal
comfort conditions, using the PMV index, that two seated occupants are subjected, in a non uniform environment
in Winter conditions, in a desk equipped with two radiant surfaces placed in front and two radiant surfaces placed
behind the human bodies. Special attention is given to the heat exchange by radiation between the human bodies
sections, between different human bodies sections, between the human bodies sections and the surrounding
surfaces, between surrounding surfaces and between the surrounding surfaces and the human bodies sections.
Keywords: Numerical model, Heat exchanges, View factors, Radiosity equations system.
Category: Human thermal physiology and mathematical models
Introduction
Numerical Model
The thermal comfort level, that a occupant feels in a
non uniform environment, depends on the metabolic rate,
the clothing level and the distribution around the body of
the values of the air temperature, air velocity, air relative
humidity, radiant temperature, contact surfaces
temperature and incident solar radiation.
In this study the Predicted Mean Vote (PMV) and
Percentage of People Dissatisfied (PPD) indexes,
presented by Fanger [1], will be used in the evaluation of
the thermal comfort level verified in moderate
environments. These indexes are influenced by the
values of several variables such as air temperature,
velocity and relative humidity around different body
sections, and mean radiant temperature that each body
section is subjected, and also by clothing and activity
levels. In accordance with the main stream of PMV and
PPD indexes, the thermal neutrality of a person is
obtained when the body heat loss is equal to the body
metabolic heat (PMV=0). The standards predict
acceptable fluctuations in the comfort conditions due to
difficulties in obtaining thermal neutrality for all persons
who share the same space at the same time. The
European Standard [2] classifies thermal environments
into three categories of quality (A with PPD<6 %, B with
PPD<10 % and C with PPD<15 %), that allows to select
a priori of one thermal environment according to required
demands.
The influence of the environmental variables around
the body in the human thermal sensation, in this work,
will be evaluated through the multi-nodal simulation of the
human thermo-physiology. More details about this
numerical model can be seen, for example, only for one
occupant in [3] and simultaneously for different
occupants in [4].
The computational model of the human body and
clothing thermal system is based on the energy balance
integral equations for the human body tissue, blood and
clothing as well as mass balance integral equations for
the blood and transpired water in the skin surface and in
the clothing. The human body is divided in 35 or 25
elements and each one could be protected through some
clothing layers.
In the first situation are considered the head, the neck,
the trunk (divided in three), the arms (divided in four), the
hands, the fingers, the legs (divided in four) and the feet,
while in the second situation the fingers are not
considered.
Each element is divided in 4 parts (core, muscle, fat
and skin). In the present study are considered the core
with 1 layer, the muscle with 2 layers, the fat with 2 layers
and the skin with 7 layers.
To control the human body tissue temperature a
thermoregulatory system model was adapted. More
details can be seen, for example, in [5].
Each human body element could be still protected
from the external environment through some clothing
layers. The clothing, which proportionates a micro
environment and is used to promote comfort conditions in
the human body, in this work is simulated through some
cylindrical or spherical clothing layers placed around the
skin layer in some elements. The clothing layers number,
in each element, will be associated to the clothes number
that a person has dressed. In this work are considered
the following clothes: shirt with long sleeves; sweater;
long trousers; socks and shoes.
The model calculates the PMV and PPD indexes to
evaluate the thermal comfort in steady state conditions.
This index is determined through the metabolic rate, the
7th International Thermal Manikin and Modelling Meeting - University of Coimbra, September 2008
clothing level and the different heat fluxes exchanged
between the human body and the environment or
clothing.
Exchanges with the Environment
The general philosophy of this model is to consider
that the heat generated inside the human body, by
metabolic reactions, is transported by conduction,
through the tissue, and by blood convection to the skin.
The heat exchanged between the body and the
environment (or clothing layers) is done by: convection,
evaporation, radiation, conduction and respiration.
In the radiation, for example, the human body inside a
space is subjected to the long and short wave radiation:
- Radiative heat exchanges inside the space (long wave
radiation): this term, calculated using the radiosity
equations system, considers the heat exchange by
radiation between the human bodies sections,
between different human bodies sections, between the
human bodies sections and the surrounding surfaces,
between surrounding surfaces and between the
surrounding surfaces and the human bodies sections.
The radiosity equation system, used to evaluate the
heat exchange that each human body section is
subjected, also considers the view factors calculated
between the different surfaces (human bodies and
surrounding surfaces), the surfaces temperature and
the surfaces emissivities;
- Solar radiation (short wave radiation): this term, not
applied in this work, is determined using the incident
solar radiation in each element.
Fig. 1. Grid generation in the occupants, desk, radiant surfaces
and compartment surfaces.
In these methodologies each human body element or
wall surfaces, with inclinations, dimensions and
temperatures equal to the respective body section or
wall, will be divided in infinitesimal areas.
In these calculus are also considered the shading
effects that the body elements and the interior bodies’
surfaces cause in each element.
Space and Human Geometry
In this work a small space, with similar dimensions with
an experimental chamber, of 2.7×2.4×2.4 m3, is
considered. Inside the space two occupants are seated in
a desk equipped with two radiant surfaces: one placed in
front to the occupant and other placed behind the
occupant body (see in Fig. 1). In Fig. 2 is presented in
detail the grid generation around the occupants, desk
and radiant surfaces, while in Fig. 3 is presented the
identification of the different surfaces considered in the
study.
Fig. 1. Grid generation in the occupants, desk and radiant
surfaces.
7th International Thermal Manikin and Modelling Meeting - University of Coimbra, September 2008
In Table 1 are presented the total skin surface
transpired water flux rate per day and the comfort levels,
PMV and PPD, for the right and left occupants.
35
34,5
34
T (ºC)
33,5
33
32,5
32
31,5
Tskin-1
Tskin-2
31
30,5
N
ec
k
U
pp
er Che
A
st
L
b
Ri owe dom
gh
r
t U Ab e n
do
Ri
p
m
gh per
tL
S en
ow hou
ld
er
Ri
Sh er
gh
o
t U uld
e
Ri
p
gh per r
tL
A
ow rm
er
A
Le
R
r
m
i
ft
U ght
Le ppe Ha
n
r
ft
Lo Sho d
we u l
de
r
Le Sho r
ft
ul
U
de
Le ppe r
rA
ft
Lo
r
w m
er
A
Ri
Le rm
gh
t U ft H
a
Ri
p
nd
gh per
tL
Th
o
ig
h
Ri wer
gh
T
t U hig
h
Ri
p
gh per
tL
Le
ow g
er
L
Le Rig eg
h
ft
U tF
Le ppe oot
r
ft
Lo Thi
we gh
rT
Le
ft
hi
U
gh
Le ppe
r
ft
Lo Leg
w
er
Le
g
Le
ft
Fo
ot
H
ea
d
30
Human Body Section
Fig. 4. Skin surface temperature (T) field that the two occupants
are subjected.
1,20E-06
Wskin-1
Wskin-2
1,00E-06
mw (l/s)
8,00E-07
6,00E-07
4,00E-07
Fig. 3. Identification of the surfaces numbers.
2,00E-07
0,00E+00
Human Body Section
Fig. 5. Skin surface transpired water flux rate (mW) field that the
two occupants are subjected.
32
31
T (ºC)
30
29
28
27
Tclothing-1(1)
Tclothing-2(1)
26
N
ec
k
U
pp
er Che
Lo Ab st
d
w
o
Ri
gh er A me
tU
bd n
p
Ri
om
gh per
tL
S en
ow hou
ld
e
Ri r Sh er
gh
o
t U uld
er
p
Ri
gh per
tL
A
ow rm
er
A
Le
Ri
rm
ft
U ght
Le ppe Han
r
ft
d
Lo Sho
ul
w
er
de
Le Sho r
ft
ul
de
U
Le ppe r
r
ft
Lo Arm
w
er
A
Ri
Le rm
gh
ft
tU
H
an
Ri
p
d
gh per
tL
Th
o
ig
h
Ri wer
gh
Th
tU
ig
h
p
Ri
gh per
tL
L
ow eg
er
L
Le Rig eg
h
ft
U t Fo
ot
Le ppe
r
ft
Lo Thi
gh
w
Le e r T
ft
hi
gh
U
Le ppe
r
ft
Lo Leg
w
er
Le
g
Le
ft
Fo
ot
H
ea
d
25
Human Body Section
Fig. 6. Clothing temperature (T) field, in the first layers, that the
two occupants are subjected.
32
Tclothing-1(2)
Tclothing-2(2)
31
T (ºC)
30
29
28
27
26
N
ec
k
U
pp
er Che
Lo Ab st
d
w
o
Ri
gh er A me
tU
bd n
p
Ri
om
gh per
tL
S en
ow hou
ld
e
Ri r Sh er
gh
o
t U uld
er
p
Ri
gh per
tL
A
ow rm
er
A
Le
Ri
rm
ft
U ght
Le ppe Han
r
ft
d
Lo Sho
ul
w
er
de
Le Sho r
ft
ul
de
U
Le ppe r
r
ft
Lo Arm
w
er
A
Ri
Le rm
gh
ft
tU
H
an
Ri
p
d
gh per
tL
Th
o
ig
h
Ri wer
gh
Th
tU
ig
h
p
Ri
gh per
tL
L
ow eg
er
L
Le Rig eg
h
ft
U t Fo
ot
Le ppe
r
ft
Lo Thi
gh
w
Le e r T
ft
hi
gh
U
Le ppe
r
ft
Lo Leg
w
er
Le
g
Le
ft
Fo
ot
ea
d
25
H
This program is used in the calculus of the
temperature distribution in the human body and clothing
and to evaluate global thermal comfort conditions, using
the PMV index, that two seated occupants are subjected,
in a non uniform environment in Winter conditions, in a
desk equipped with two radiant surfaces placed in front
and two radiant surfaces placed behind the human
bodies.
In this work 1.2 Met. of activity level and 1 Clo. of
clothing level (shirt with long sleeves, sweater, long
trousers, socks and shoes) are used, while the air
temperature value (equal to the spaces surfaces and
desk) is 17 ºC, the air relative humidity is 70 % and the
radiant surface temperature is 50 ºC. The air velocity
value and the inlet solar radiation are neglectable.
The radiosity equations system uses, step by step, the
human body and spaces surfaces temperatures,
calculated in each iteration, and the pre-calculated view
factors.
In Fig. 4 is shown the skin surface temperature field
that the two occupants are subjected, while in Fig. 5 is
presented the skin surface transpired water flux rate field,
that the two occupants are subjected. The clothing
temperature fields, in the first and second layers, that the
two occupants are subjected are presented in Fig. 6 and
7, respectively.
The first clothing layers are associated to the shirt with
long sleeves (in the trunk and superior members), long
trousers (in the inferior members) and socks (in the
inferior area of the inferior members and in the feet),
while the second layers are associated to the sweater (in
the trunk and superior members), in the long trousers
(only above the socks) and in the shoes (in the feet).
H
ea
d
N
ec
U
k
pp
er Ch
L
Ri ow Abd est
gh er om
t
Ri Up Ab en
d
gh pe o
t L r S me
ow ho n
Ri er S uld
gh h er
o
t
Ri Up uld
gh pe e r
tL rA
ow rm
er
Le
ft Ri Ar
U g
Le pp ht m
ft er Ha
Lo Sh nd
w ou
e
Le r Sh lder
ft
o
U u
Le pp lde
ft er r
Lo A
w rm
er
Ri
gh Le Arm
f
t
Ri Up t H
gh pe an
tL rT d
Ri owe hig
gh r T h
t
Ri Up hig
gh pe h
tL rL
ow eg
e
Le Ri r Le
ft gh g
U t
Le pp Fo
ft er ot
Lo T
h
Le wer igh
ft
T
U h
Le pp igh
ft er
Lo L
w eg
er
Le Leg
ft
Fo
ot
Results and Discussion
Human Body Section
Fig. 7. Clothing temperature (T) field, in the second layers, that
the two occupants are subjected.
7th International Thermal Manikin and Modelling Meeting - University of Coimbra, September 2008
Table. 1. Transpiration water flow rate (mW) and comfort levels
(PMV and PPD).
mW (l/day)
PMV
PPD (%)
Right
Occupant
0,70
-0.85
20.4
Left
Occupant
0,69
-0.73
16.4
In accord to the obtained results, is possible to
conclude that:
− In the skin temperature field is possible to verify that
the surrounding occupant, due to the radiative heat
exchanges between the two occupants, increase
lightly the temperature value mainly in the upper and
lower member located between the two occupants.
This conclusion is more clear in the results presented
in the clothing temperature field;
− The water transpiration, for both occupants, are
around 0.7 l/day;
− In Winter conditions, when the radiant surface is off
and only is considered one occupant, the predicted
mean vote is -0.91, while the percentage of dissatisfied
people is 22.25 %;
− The comfort level, that the two occupants are
subjected, when the radiant surface is on, increase in
relation to the previous situation. The predicted mean
vote is -0.85 and -0.73, while the percentage of
dissatisfied people are 20.4 % and 16.4 % for the
occupant seated, respectively, in the right and left side;
− In fact the obtained comfort values are not in accord to
the comfort limits recommendation. Nevertheless, the
values are near the comfort limits recommendation;
− The light difference verified in the comfort levels that
the two occupants are subjected are associated to
some errors in the view factors determinations. These
differences can be reduced if the grid generation had
increased, nevertheless, this procedure increases the
computational time calculation;
− To increase the comfort level, that the occupants are
subjected, is recommended, in future works, to
increase the radiant panel dimension or to decrease
the distance between the radiant panel and the human
body sections. The radiant panel temperature increase
is other possibility, nevertheless this procedure can
represent danger for the occupants.
Conclusions
In this work a numerical model, that allows to simulate
the human body thermal and thermoregulatory systems,
was used to evaluate the thermal comfort level that two
seated occupants are subjected, in a non uniform
environment in Winter conditions, in a desk equipped
with two radiant surfaces placed in front and two radiant
surfaces placed behind the human bodies
It was verified that the radiative heat exchanges,
calculated by the radiosity model, is very important in a
correct and detailed evaluation in the heat exchanges by
radiation verified between the occupants sections,
between the different occupants sections and between
the occupants and the surrounding bodies.
In accordance with the results obtained is possible to
conclude that the developed radiant panels increase the
thermal comfort level, nevertheless is suggested to
increase the panels dimensions or to reduce the distance
between the panels and the occupants, in order to obtain
acceptable thermal comfort conditions in accordance with
the actual standards.
The differences obtained in the thermal comfort level
by the occupants are associated to the view factors
approximations. To reduce these differences is
suggested to reduce the grid space around the people
and surrounding surfaces.
Acknowledgement
This research activity is being developed inside a
project approved and financed by the Portuguese
Foundation for Science and Technology and POCI 2010,
sponsored by the European Comunitary Fund FEDER.
References
[1] Fanger P.O. Thermal Comfort. Copenhagen: Danish
Technical Press (1970).
[2] ISO 7730. Ergonomics of the Thermal Environments –
Analytical Determination and Interpretation of Thermal
Comfort using Calculation of the PMV and PPD Indices
and Local Thermal Comfort Criteria. International
Standard. Switzerland (2005).
[3] E. Z. E. Conceição, Mª M. J. R. Lúcio, T. L. Capela
and A. I. P. V. Brito. Evaluation of Thermal Comfort in
Slightly Warm Ventilated Spaces in Non-Uniform
Environments. Int. Journal on Heating Air Conditioning
and Refrigerating Research. Vol. 12. Nº 3. July (2006).
451-458.
[4] E. Z. E. Conceição and Mª. M. J. R. Lúcio. Evaluation
of Thermal Comfort Conditions in a Classroom Equipped
with Radiant Systems. Healthy Buildings 2006. Lisbon.
Portugal. 4-8 June 2006.
[5] J. A. J. Stolwijk. Mathematical Model of
Thermoregulation. In J. D. Hardy, A. P. Gagge and J. A.
J.
Stolwijk.
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Behavioral
Thermoregulation. (1970). 703-721. Springfield.