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CHAPTER 4
HYGROTHERMAL COMFORT INBUILDINGS
4.1 GENERAL ISSUES
Having an enclosed indoor space, in the form
of a building, means more than to be dry. It
includes most basic ideas of comfort, well- being
and security.
An essential function of civil buildings (i. e. of
those buildings whose main users are people)
consists in creating an indoor climate adapted to
human needs, whose global characteristic can bedescribed as comfortable.
In a broad sense, the term comforthas the
meaning of a state of satisfaction expressed by
people with respect to environment.1
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The comfort offered by building indoor
spaces takes into consideration a great number of
agents acting simultaneously on people who usethese spaces; hygrothermal, acoustical, visual,
and olfactory/respiratory agents must be
accounted for in the first place.
Hygrothermal comfort is but a component of
comfort in indoor spaces.
Since it is necessary a certain amount ofenergy
to be consumed in order to achieve hygrothermal
comfort, a very special attention is being given
lately to this component.
Owing to their dual character, objective andsubjective, it is quite difficult to identify the
performance exigencies of indoor spaces related
to hygrothermal exigencies of building users. Thehuman body normal internal temperature of about2
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37o C is obviously an objective matter; on the
other hand each person has his own metabolism,
his own thermo-regulator system, his ownsensitiveness to the action of external stimuli etc,
which are, of course, subjective elements.
It is in thermal performance that the
building enclosure still has its most urgent need
of improvement by far. Earlier the 20th century,
enclosures lightened, windows became larger and
central heating and cooling systems improved.Energy was still cheap and there came a tendency
to under-emphasise enclosures thermal role and
rely on climate services to put things right. Notvery long ago, people became aware of what had
come to be called the energy crisis. Insulation
standards and requirements have risen sharply in
many countries but there are also other things3
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crucial to thermal performance that must be
accounted for.
4.1.2. Scale Influence on Thermal PerformanceIn case of small buildings, the current thermal
concern is to reduce heat loss, with overheating
really becoming a problem only in hot climates.
Passing from small to large buildings, the so-
called scale effect must be emphasised in
connection with thermal performance.
Buildings have metabolic or free heat,produced in proportion to their volume and
indoor activities. Artificial lighting, electrical
machinery, various equipment and, of course,people produce heat. By the scale effect
argument, it follows that large buildings are more
able to keep themselves warm in winter, requiring
less heat input than a scaled-up increase in the4
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needs of small buildings would seem to indicate
(Fig4.1).
Fig. 4.1. Scale Effect on Thermal Performance
The size brings a thermal shift, automaticallymoving large buildings a few degrees up the
temperature scale in comparison with small
buildings and potentially this is a significantbonus.
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4.2. CLIMATE INFLUENCE ON THERMAL
PERFORMANCEGood thermal protection provided by the
enclosure means grater comfort for building users
and, increasingly more important, less energy
consumption in heating and cooling.
Thermal performance has mainly to do with
reducing heat transmission (outwards or
inwards) through the enclosure. Where there is atemperature difference between two places, heat
tends to flow from the higher temperature to the
lower nature always trying to correctimbalances and the transmission can occur in
three ways, namely conduction, convection and
radiation.
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Conduction is encountered when heat passes
through a solid, e. g. a wall. If one of its faces is
heated, the vibrations of the atomic particles onthe surface will intensify, pass their added
excitement to the particles behind them and so on
as a jostling chain-reaction through the wall. The
energy moves but the matter does not.
In convection, the matter does move since it is
heat transmission by the flow of a liquid or gas at
the interface with a solid. Air currents, generatedby local temperature differences, collect heat
from warmer surfaces and impart it to cooler
ones. This is natural convection, as opposed toforced convection by mechanical fans.
Radiation involves no matter at all in the
commonly accepted sense, being energy transfer
by electromagnetic waves. This phenomenon is7
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characteristic to gaseous or liquid environment, as
being the only cases in which energy transfer as
electromagnetic wave is possible.In fig. 4.2. is illustrated, in a suggestive
manner, heat transmission by conduction,
convection and radiation.
Fig. 4.2. Heat Transmission/Loss by Conduction,
Convection and Radiation
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Obviously, heat transmission through building
enclosure varies with the temperature difference
across it, so that the first determinant factor isclimate.
The influence of site location represents a
starting point, especially in case of small
buildings.
In the extremely unlikely situation of there
being a free choice, and assuming the climate is
temperate so that cold stresses in winter countmore than hot stresses in summer, the site located
half-way up the sun-facing slope of a hill is
advantageous (Fig. 5.3.). It avoids the valleyfloor, where cool dense air tends to collect and
hence hold the temperature several degrees below
the prevailing average. Similarly, it avoids the
wind-prone hill crest, where heat lost by9
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convection increases sharply with the velocity of
the surrounding air stream. There could be around
30 % heat-loss difference between exposed andsheltered locations.
Fig. 5.3. Influence of Site Location on ThermalPerformance
Conversely, in hot climates, the criteria mayreverse, with buildings sited specifically for shade
or for catching whatever cooling breeze is going.
The influence of climate on building shape
is an accepted fact. A buildings heat loss or gain10
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increases with the area of surfaces it exposes to
the air outside. Nature adapts form to climate and
so does tradition in small buildings practice allaround the worl
d, as illustrated
Fig. 4.4. Form Adaptation to Climate
There is an influence of solar radiation on
optimum plan shape and orientation which,
especially in temperate climates, tends to offset
the compactness argument. It would obviously be11
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a good thing if a building could be shaped to
collect as much solar heat as possible in winter,
and yet avoid collecting to much in summer;interestingly, it is possible to obtain such a result.
For instance, in the northern hemisphere,
during the winter most of the suns heating effect
occurs in the middle of the day, since in the
morning and afternoon the sun is low on the
horizon and its effect is weak. So, if the building
is elongated on the east-west axis, thus
presenting a relatively longer southern wall, it
will be exposing a larger collecting surface to
available sun radiation. But what may appear, atfirst, surprising is that this plan shape and
orientation is also one of the best suited for
avoiding excessive summer heat gain. The long
south wall is not so vulnerable then, simply12
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because the summer sun is so much higher in the
sky. This means that the radiation on this wall is
very oblique and, hence, diluted. In summer, thevulnerable times during the day are fairly early
morning and late afternoon, when the sun is lower
in the sky, and thus its rays arrive at an angle
closer to normal to the walls. This is exactly why
the elongated east-west plan behaves favourable
again, because it presents its shorter east and west
elevations to the sun at those times of the day.This situation is illustrated in Fig. 4.5.
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Fig. 4.5. Influence of Solar Radiation on Building
Configuration and Orientation
The effect of window sizingon different
wall elevations is also present in the balancing act
between reducing heat transmission and yet
capturing solar radiation; the overriding influence
is more urgently between providing adequate day-
lighting while satisfying thermal needs as a
whole. Even double glazing has less than half of14
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the insulating value of a good block/brick cavity
wall and is at least 20 times more admissive to
radiation, so thermal questions arise sharply.The extend to which daylighting and thermal
requirement align or conflict depends on climate.
In the hot, dry climate they are convergent, since
the very bright hot conditions favour relatively
small windows. In moderately warm climates, the
windows can be larger, and the southerly oriented
ones may useful add solar gain in winter time. Inthe temperate, cool climate, daylight and thermal
needs tend to conflict. Basically, the windows
should be as small as daylighting needs allow;however, a larger southerly window will have the
merit of allowing solar gain in winter. Of course,
large southern windows increase conductive
losses to the outside air, which may persist even15
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when radiation gain occurs; hence, they are
prime candidates for multiple glazing.
4.3. EXIGENCIES RELATED TO
HYGROTHERMAL INDOOR
MICROCLIMATE
4.3.1. Man-Indoor Space Heat Exchange
The study of hygrothermal comfort and of
the possibilities to achieve it requires, as a first
step, the investigation of human body perceptionand reaction to temperature variations of the
indoor environment.
Due to metabolic processes, there is apermanent heat production inside the human
body, which must be partially eliminated in order
to keep its internal temperature within normal
limits (i.e. around 37o C). A certain amount of16
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heat is received by the human body, through
various specific mechanisms, from its
environment. Theoretically, bodys thermalbalance should equal zero, but actually a relation
of the form (5.1) operates:
Q = Qinternal + Qreceived Qeliminated (5.1)
where:
Q = residual heat (no matter the sign);
Qinternal = amount of heat produced by the humanbody during a given interval of time;
Qreceived , Qeliminated = amount of heat received,
respectively eliminated, by the human bodyduring the same interval of time.
Due to a kind of brain-controlled thermal
regulator system, the human body can
momentarily adapt itself to slightly unfavourable17
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indoor thermal conditions, that is it can take over
a limited amount of residual heat Q. If this
amount becomes significant, a feeling of thermaldiscomfort appears. Building indoor spaces,
which act as environment for their users, must
create conditions for ensuring properly balanced
heat exchanges, thus avoiding overstressing of
human thermal regulator system.
The metabolic heat produced by human
body is different from one person to another anddepends on the kind of activity performed.
Several average hourly values are given below:
- lying, at rest_____________75...90 Wh/h- sitting, still______________90...105 Wh/h
- standing, still____________95...120 Wh/h
- slow walking (3 km/h) ____175...230 Wh/h18
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- fast walking (8 km/h) _____230...460 Wh/h
- light activities, sitting______120...140 Wh/h
- light activities, standing____150...200 Wh/h- heavy activities___________500...700 Wh/h
If these values are associated to the skin area
of human body (1.7...1.8 m2
), the resultingdensities of internal thermal flow qinternal (W/m2)
are those presented in Table 5.1. This table also
includes values expressed in met, which
represents a reference unit corresponding to a
hourly metabolic heat production of about 58
W/m2 (healthy adult person, sitting, still).Table 5.1. Metabolic Heat Values
Kind of activity Metabolic EnergyW/m2 metLying, at rest 44...52 0.75...0.90Sitting, still 52...60 0.90...1.05
Standing, still 56...70 1.00...1.20Slow walking 100...130 1.70...2.25Fast walking 140...260 2.40...4.50
Light activities, sitting 70...80 1.20...1.40Light activities, standing 90...115 1.55...2.00Heavy activities 280...400 4.80...6.90
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Heat exchanges that occur in both senses
between the human body and its environment aremainly performed by convection, radiation and
evaporation. Thermal conduction operates in a
special manner, through contact between bodys
skin and clothing items; these later convey then
the heat to environment by convection and
radiation.
4.3.2. Global Assessment of Thermal Quality
of Indoor Spaces
Based on comprehensive investigation
carried out on all terms included in eq. (5.1), theconclusion has been reached that the value of
residual heat Q is dependent on six parameters.
Four of them represent thermo-physical
characteristics of indoor spaces. They are:20
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ti= average indoor air temperature;
sm = average surface temperature of all
elements enclosing the respective indoor space,also termed average radiant temperature;
vi= average velocity of indoor air movement;
i= relative humidity of indoor air.
The other two parameters are related to users
characteristics, namely:
M= metabolic energy depending on the kind
of activity carried out;R= thermal resistance of clothing.
Obviously, for given values of M and R, the
feeling of thermal comfort or discomfort is theresult of simultaneous effect produced by the
action of ti, sm,, vi, i . The dependence of thermal
comfort on each of these parameters has been
ascertained on experimental basis by drawing21
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certain relationships sm= f1(ti), vi= f2(ti) i= f3(ti),
as illustrated in Figs. 5.7, 5.8 and 5.9 respectively.
Fig. 4.7. Dependence of Thermal Comfort onAverage Indoor Temperature
and Relative Humidity of Indoor Air
In order to ensure proper conditions ofthermal comfort, a certain difference between
indoor air temperature and average surface
temperature of elements enclosing the indoor22
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space is required. Optimum values of the
difference ti - sm correspond to the so-called
thermal neutrality (the hatched zone in Fig.5.7), meaning that human organism needs no
effort to adapt itself to environment thermal
conditions.
If the velocity of indoor air movement vi
remains below 0.1 m/s (for air temperature
between +16 and +22o C), it does not influence
the amount of internal heat eliminated by
normally dressed people. The optimum range of
thermal comfort in relation to the average
velocity of indoor air movement corresponds tothe hatched zone in Fig. 5.8.
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Fig. 4.8. Dependence of Thermal Comfort on
Average Indoor Temperature andAverage Velocity of Indoor Air
Movement
From the physiological viewpoint, thermalcomfort can be obtained when the relative
humidity on indoor air ranges between 30 and 50
percent. If the average indoor air temperature is
situated between +16 and +22, the variation of24
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relative humidity of indoor air between 30 and 70
percent does not have any relevant influence on
the quantity of internal heat eliminated by anormally dressed person performing a light-type
activity. Significant thermal discomfort appears -
in the form of humid heat exhaustion when
increased air temperature is associated with
increased air relative humidity, a sensation of
sultriness occurs, as shown by the hatched zone in
Fig. 4.9).
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Fig.5.9. Dependence of Thermal Comfort onAverage Indoor Temperature
and Relative Humidity of Indoor Air
In order to get a global assessment of the
thermal quality of a given environment, in
relation to an average user dressed in aconventional manner, the so-called Predicted
Mean Vote (PMV) indicator is being currently
used. It takes into consideration all six parameters26
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to determine the value of residual heat Q and
can be calculated by the relation:
PMV= (0.303.e-0.036.M
+ 0.028)Q (5.2)When Q= 0, meaning that the human body
eliminates exactly the internal heat it produces,
PMV= 0 and, theoretically, every person should
feel comfortably. However, it has been
experimentally found that is practically
impossible to build an environment able to
offer simultaneously same degree of thermalcomfort to everybody; even when Q= 0 (and
subsequently PMV= 0), about 5 percent of people
may declare a slight feeling of discomfort. Another indicator, expressing the probable
percentage of declarations of thermal
discomfort has been worked out based on
statistical processing of experimental data.27
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Known as Predicted Percentage of
Dissatisfaction (PPD), In case of residential
buildings, for instance, the following values arerequired:
In winter time:
- average operational temperature of indoor
air, +20o C for most of the rooms;
- average velocity of indoor air, max. 0.15
m/s;
- relative humidity of indoor air, max. 70
percent, with recommended
values 50...60 percent;
- temperature of flooring surfaces, min. +18o
C;
- difference between indoor air temperature ti
and average value of surface temperature
si
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of any enclosure element to be kept as small
as possible. Maximum accepted values for
this difference are 4o
C for exterior walls and3o C for terrace floor.
In summer time:
- average temperature of indoor air, max. +26o
C;
- average velocity of indoor air, max. 0.30
m/s;
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4.4. MAIN PHENOMENA,CHARACTERISTICS AND PARAMETERS
IN HYGROTHERMICS OF BUILDINGS
4.4.1 Heat, Temperature, Thermal Flow,
Density of Thermal Flow
Heat is a special form of energy, whose
presence is detected by the human body whichcan make the difference between warm and
cold.
The quantity of heat held by a body isexpressed by means of its absolute temperature
(T), measured in degrees Kelvin (K). This is
related to the temperature (t or ), measured in
degrees Celsius (o C) by:30
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T= t + 273 (5.4)
Currently, the notation t is used for air
temperature, whereas is used for thetemperature of solid bodies.
In case of two bodies with different
temperatures that are in direct or indirect contact,
heat passes naturally from the warmer to the
cooler body. This thermal exchange, which stops
only when the temperatures of the two bodies
become equal is generally expressed in terms ofquantities of heat, i. e. in quantities of thermal
energy.
The unit for measuring heat quantity is watt-hour [Wh], that has replaced Kilocalorie [Kcal];
however, this later is sometimes still in use. Their
relationship is given by:
1Kcal= 1.16 Wh (5.5)31
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The thermal flow () represents the
quantity of heat exchangedduring a time-unit (an hour), measured in watts
(W).
The density of thermal flow (q) represents
the thermal flow passing
through a unit area ( 1 m2) whose points have the
same temperature; it is measured in W/m2.
4.4.2. Mass Heat, Thermal Conductivity,
Thermal Diffusivity, Thermal Absorption
The mass heat (c) of a material representsthe quantity of heat required by a mass-unit (1 kg)
to increase its temperature by 1o C (or 1 K);
accordingly, the mass heat is measured in
Wh/KgoC. However, there is still a common32
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engineering practice to use the so-called
technical values of mass heat (given in
handbooks tables) expressed in KJ/Kgo
C. Theconversion is based on the relation:
1[Wh/KgoC]= 0.278[KJ/KgoC] (5.6)
The thermal conductivity of a material
expresses its aptitude to transmit heat through its
mass, from one particle to another. This aptitude
is quantified by means of a coefficient of
thermal conductivity (), whose physical
significance is density of thermal flow passing
through a plane element 1 m thick, when adifference of 1o C exists between the temperature
on its two faces; accordingly, the coefficient of
thermal conductivity whose value is determined
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on experimental basis for any material is
measured in W/moC.
The thermal conductivity of a material ismainly dependent on its apparent density, type
and structure of pores, humidity and temperature.
Materials with low apparent density (i. e. with
high porosity) have small thermal conductivity
(due to the air contained by pores, which has very
small value) and are conveniently used for
thermal insulation. When getting wet and havingpores filled with water, thermal insulating
materials diminish drastically their efficiency
(wateris about 25 times greater than air).The design values of for various materials
are conventional values accounting for the
probable humidity under service conditions, as
well as for influence of other unfavourable factors34
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(e. g. increase of apparent density due to
settlement of the material).
A layer of immobile air, 3...5 mm thick, hasthe lowest known value of the coefficient of
thermal conductivity (= 0.024 W/moC) among
current materials. Highly efficient thermal
insulating materials (such as cellular polystyrene,
polyurethane, mineral wool et al) exhibit
extremely small values for (0.020...0.050
W/moC). For comparison, for several otherconstruction materials are given below:
- solid brick masonry.......................0.80
- cellular concrete blockmasonry....0.27...0.34
- mortar..........................................0.70...0.93
-
reinforcedconcrete.........................1.62..1.7435
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The thermal diffusivity (a) of a material
expresses its aptitude to spread heat, i. e. to
equalise its temperature. Its value is computed
with the relation:
a=/c [m2/h] (5.7)
where:
= coefficient of thermal conductivity[W/moC]
= apparent density [kg/m3]
c= mass heat [Wh/Kgo
C]
Current values of a range from 0.0016 m2/h
for cellular concrete and gypsum plates to 0.049
m2/h for cellular polystyrene.36
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The thermal absorption (or assimilation) of
a material represents its capacity to absorb (to
assimilate) heat through the surface in contactwith a warmer (solid or fluid) medium. This
capacity is quantified by means of a coefficient
of thermal absorption (s), whose physical
significance is ratio between the variation
amplitude of density of heat flow acting on the
plane surface of a material and the variation
amplitude of temperature on the respectivesurface.
5.4.3. Heat Transmission by Conduction
Conduction is the phenomenon of heattransmission (or transfer) inside a solid or
between two solid bodies in contact. Conductive
heat transmission is carried out from one
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molecule to another; the energy moves but the
matter does not.
In case of building enclosure elements, theconductive thermal transfer is caused by
differences in temperature existing between their
inner and outer faces.
If interior and exterior temperatures of the air
(ti and te, respectively) have negligible variations
in time, the conductive heat flow between any
two points of the element has constant value withrespect to time and the thermal conduction is
termed stationary.
If at least one of the temperatures ti or tepresents significant variation in time, the
conductive heat flow between any two points of
the element has variable values with respect to
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time and the thermal conduction is then termed
non-stationary.
5.4.4. Heat Exchanges by Convection and
Radiation Between Surfaces of Enclosure
Elements and Adjacent Media
The main phenomena related to heat
exchange between interior and exterior
environment that are analysed by the
hygrothermics of buildings take place between:
- interior and exterior surfaces of enclosure
elements;
- surfaces of enclosure elements and the air intheir immediate vicinity ;
- interior surface of enclosure elements and
surfaces of partitions located39
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in their immediate vicinity;
In the first case, heat exchange is carried out
by conduction, in the second case by convectionand in the third case by radiation. This complex
phenomenon involving all three elementary types
of thermal exchange is schematically illustrated in
Fig. 5.11.
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Fig.5.11. Schematical Representation ofElementary Thermal Exchanges ThroughEnclosure Elements, if Indoor Temperature is
Larger than Out Door Temperature (ti>te) Convection is the phenomenon of heat
exchange between the surface of a solid body and
a fluid in direct contact with it.
In case of building enclosure elements,thermal convective exchange occurs on both their
surfaces, the fluid being interior and exterior air,
respectively. Generally speaking, air currentscollect heat from warmer surfaces and impart it to
cooler ones. In fact, it is the local temperature
differences that cause the currents; thus, air
getting warmer expands, becomes less dense and
starts to float upwards over cooler, denser air
flowing in to replace it.
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A typical situation is that of vertical elements
of the enclosure, i.e. exterior walls. In winter
time, the temperature of their outer surface ishigher than that of exterior air; the latter absorbs
heat, gets warmer and moves slightly upwards. At
the same time, the temperature of walls inner
surfaces is lower than that of interior air, which
looses heat, gets cooler and moves slightly
downwards (Fig. 4.12)
Fig. 4.12. Influence of Convective ThermalExchanges Upon Air Temperature in the Vicinity
of an Exterior Wall Surface, if Indoor42
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Temperature is Larger than Out DoorTemperature (ti>te)
Radiation is the phenomenon of heat
exchange between the surfaces of two far apart
bodies, the energy being transferred by
electromagnetic waves.
Since thermal exchanges by convection and
by radiation occur simultaneously on a givensurface of the enclosure element the outer one
in contact with exterior air and the inner one in
contact with interior air for practical purposes acomplex thermal exchange is considered. A
schematically representation of such a
convective-radiant thermal exchange is shown in
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Fig. 4.13, which could be looked upon as a
simplified variant of Fig. 4.11.
Fig. 4.13. Schematical Representation ofConvective Radiant Thermal Exchanges ThroughEnclosure Elements, if Indoor Temperature is
Larger than Out Door Temperature (ti>te)
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4.4.5. Main Characteristics of the Humid Air
The atmospheric air always contains water
vapours. No matter the temperature, there is a
certain amount of water in vapour form. The
effective humidity is currently termed
absolute humidity (). Its physical
significance is quantity of water in vapour
form contained in a unit volume of air and is
measured in g/m3.
The effective humidity of the air cannotexceed a limit value known as saturation
humidity (s), beyond which water vapours pass
into liquid phase. The value ofs increases with45
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air temperature (Fig. 4.14); in other words, the
warmer the air, the larger is the quantity of water
vapours it can contain.
Fig. 4.14. Relationship Between Saturation
Humidity and Air Temperature
At a given moment, the ratio between the
effective humidity of the air and its saturation
humidity corresponding to air temperature at that
0.891.061.251.521.812.15
4.6
9.410.68
12.1413.66
17.3
15.36
-20-18-16-14-12-10-8-6-4-202468
101214161820
0 2 4 6 8 10 12 14 16 18 20
s(g/m3)
t(o
C)
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moment, defines the relative humidity ()
expressed in percentage.
The temperature at which a volume of airmust be cooled to reach saturation level of
humidity is called dew temperature (d). It
depends on air temperature and air relative
humidity (Table4.3).
If a mass of air having the dew temperature d
has contact with a cold surface whose
temperature s is smaller than d, part of the watervapours it contains will condense on that surface.
This phenomenon is called superficial
condensation and is accompanied by emanationof heat (0.7 Wh/g).
The partial pressure of water vapours
contained in a certain volume of air, representing
their pressure should vapours occupy the entire47
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volume, is termed effective pressure of water
vapours (p). If the air is saturated with water
vapours, the corresponding pressure value iscalled saturation pressure of water vapours (ps).
Both values are measured in pascals [Pa].
As in case of saturation humidity (s), the
value of ps increases with air temperature (Fig.
4.15); in other words, the warmer the air, the
grater is the saturation pressure of water vapours
it contains.
4.5. MODELLING THERMAL BEHAVIOUR
OF ENCLOSURE ELEMENTS
4.5.1 General Issues
The special complexity of problems related
to achieving correct and efficient hygrothermallayout of buildings strongly requires in the first48
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place to set up a systemic framework for analysis.
As it is well known, the simplest scheme of a
functional system is represented like a physicalentity (of the black box type) which transforms
an input function into an output function (Fig.
4.16). In general, the input consists in external
actions that generate perturbations of state of the
system frequently of random character thus
triggering its running. The output represents
results or effects of input actions.
Fig.
4.16. Schematical Representation ("Black Box"Type) of a System
)(cause) SYSTEM
OUTPUT y ()
(effect)
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The notion ofsystem is intrinsically related to
that of model, usually having mathematical
features. A mathematical model represents, inmathematical terms, the running of a system and
hence offers the possibility to predict qualitative
and quantitative evolution of its output (response)
to various inputs (external actions).
In case of problems concerning thermal
dynamics of the systems, input and output
functions are essentially thermal excitation andthermal response, respectively.
The basic scheme to solve problemsconcerning thermal analysis of the systems can
be represented as in Fig. 4.17. According to this
scheme, the relevant characteristics are specified
for both thermal excitation and system subjected50
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to investigation. The scope of this analysis
consists in assessing systems thermal response
to variation of thermal excitation.
Fig. 4.17. Basic Scheme of Thermal Analysis ofSystems
In case of problems concerning thermallayout of the systems, the basic scheme is
illustrated in Fig. 4.18, where initially specified
input data are those characterising both thermal
excitation and thermal response. The scope of
thermal layout of a system consists in designing
it so that its response to a given thermal
excitation (real or conventional) ranges between
THERMALEXCITATION SYSTEM
input data specified initiallyoutput data tobe computed
THERMALRESPONSE
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pre-established values. Hence, the results of
computations should substantiate geometrical and
thermophysical characteristics to be requestedfrom the system.
Fig. 4.18. Basic scheme for Designing ThermalLayout of Systems
THERMALEXCITATION SYSTEM
THERMALRESPONSE
Output data
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input data specified initially
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4.5.2. Problems of Defining Enclosure Systemand Its Physical- Geometrical Model
For reasons aimed to simplify the design
process, in the current practice both modelling
and analysis are performed on enclosure elements
and sub-ensembles. In most situations, thermal
exchanges occur through building elements of
wall-type (mainly, exterior walls) and of floorslab-type;
Any enclosure element is physically and
functionally connected to other elements of samekind situated in its plane, as well as to different
other elements situated, as a rule, in planes
orthogonal to its own.53
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The thermal response of an exterior wall,
taken as a whole, is obviously influenced by itsconnections to other building elements that
introduce more or less significant thermal
effects. A rigorous assessment of its thermal
response should, therefore, be based on 3-
dimensional models with adequate coverage of
connection zones (Fig. 4.19).
Fig.4.19. 3D-Model for Thermal Analysis of an
Exterior Wall54
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4.5.3. Problems of Defining Thermal
Excitation The enclosure of a building can be
considered as interface between two
environments, having different thermal
characteristics which are inherently variable in
time. Consequently, any enclosure element acts
like a filter performing heat exchanges between
two environments of different temperatures.
Fig.4.25.Schematical Representation of Thermal Actions
Exerted on Enclosure simplified representation ofan equivalent thermal convective exchange
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each of the two environments separated by
enclosure elements can be characterised by anunique parameter of temperature-type. In
general, these temperatures exhibit time-
variations, each governed by its own laws, but
having close correlation.
As long as the difference ti te, is not 0,
there is a heat exchange between indoor and
outdoor environment through the enclosure, thisphenomenon being strongly influenced by its
geometrical and thermophysical characteristics,
and by the exterior conditions.In general, these data represent hourly
average temperatures recorded during a
significant period in winter (or summer) time
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and extended over relatively many successive
years.
In case of common-type buildings, thecurrent design practice takes into consideration,
instead of a conventional variation of te during the
day (24 hours), just its average value. For
example, the parameter te,conv used for establishing
the required characteristics of heating
installations represents the average value of
outdoor air temperature corresponding to a winterconventional day; for Bucharest this average
value is equal to 15.3o C.
Present Romanian technical regulationsprovide a map of the territory, defining a number
of 4 macro-zones from the viewpoint of the
outdoor air temperature during a winter
conventional day, as shown in Fig. 5.26.57
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Similarly, another map defines 3 macro-zones
from the viewpoint of outdoor air temperature
during a summer conventional day (Fig. 5.27).
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Fig.5.26. Winter Climatic Zoning of RomanianTerritory
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Fig.5.27. Summer Climatic Zoning of Romanian
Territory
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4.6. BASIC ISSUES RELATED TO
THERMAL RESPONSE OF ENCLOSURE
ELEMENTS In case ofsingle-layer elements (with
homogenous structure in all directions), the
differential equation of thermal conduction takes
for a stationary unidirectional thermal regime
the simple form (Fig. 4.31):
d2/dx2= 0 (4.16)
whose integration gives the solution:
(x)= C1x+C2 (4.17)
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Fig. 4.31. Convention for the Reference Systema) in winter time; b) in summer time
The two constants are obtained by means of limit
conditions, i.e.:
- for winter conditions
(0)= si and (d)= se
- for summer conditions
(0)= sse and (d)= si
The solution results as follows:62
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- for winter conditions:
(x)= -(si se)x/d + si (4.18)
- for summer conditions:(x)= -( se - si)x/d + se (4.19)
Since the values of si and se are not known,the relations (4.18) and (4.19) are not
operational. In order to get these values, one
should make use of the limit conditions stating
that, in case of stationary thermal regime, the
density of thermal conductive-radiant flow
that penetrates one of the elements surface
is conserved during its passage and also
when getting out through the opposite
surface. This is expressed by (Fig. 5.32):
qiC-R
= qk
= qeC-R
(5.20)63
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Fig. 5.32. Conservation of the Density of Thermal
Flow in Case of StationaryRegime
For instance, under winter condition, one can
write:qiC-R= (ti-si)/Rsi (5.21)
qk = (si-se)/R (5.22)
qeC-R= (se-te)/Rse (5.23)
Hence, eqs. (5.20) can be written as follows:
(ti-si)/Rsi= (si-se)/R= (se-te)/ Rse= (ti-te)/RT
(5.24.)
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where:
Rsi and Rse represent resistance to surface
thermal exchange (for inner and outer surface,respectively)
R= d/ represents resistance to thermal
conductive transfer through elements thickness
d, for a material with coefficient of conductivity
. This also termed resistance to thermal
permeability.
In eqs. (4.24), the notation: RT= Rsi+R+Rse hasbeen introduced, RT having the significance of
resistance to thermal transfer(or, for the sake of
simplicity, just thermal resistance) and beingmeasured in [m2 oC/W].
The inverse value: U= 1/RT, [W/m2 oC] is
currently termed thermal transmittance.
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By operating conventional transformations,
eqs. (5.24) will yield to the following relations:
si= ti-Rsi(ti-te)/RT (4.25)
se= te+Rse(ti-te)/RT (4.26)
corresponding to winter conditions.
In a similar manner, the following relations
are established for summer conditions:
si= ti+Rsi(te-ti)/RT (4.27)
se= te-Rse(te-ti)/RT (4.28)
Getting back to eqs. (4.18) and (4.19), and
introducing the expression of si and se from eqs.(4.25)...(4.28), one can write the following
relations:
- for winter conditions
(x)= ti-(Rsi+x/)(ti-te)/RT (4.29)66
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- for summer conditions
(x)= te-(Rse+x/)(te-ti)/RT (4.30)
which can be further transformed to:
(x)= [-(ti-te)/RT]x+[ti-Rsi(ti-te)/RT] (4.31)
and
(x)= [-(te-ti)/RT]x+[te-Rse(te-ti)/RT] (4.32)
for winter and for summer conditions,
respectively.
A graphical representation of these linear
functions of temperature field is shown in Fig.
4.33. Obviously, their gradient is inverselyproportional to the value for , hence illustrating
the fact that temperature fall increases along
with the increase of thermal insulating67
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characteristics of the material the element is made
of.
Fig. 4.33.Variation of the Function "TemperatureField" Inside Enclosure
Elements a) in winter time; b) in
summer time
Any of the diagrams in Fig. 4.33 can be
completed to account for temperature variation
occurring in the air layers adjacent to elementssurfaces (Fig. 4.34). The temperature fall ti-
si, as well as se-te can be interpreted as the
effect of resistance to thermal permeability68
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presented through the convection-radiation
phenomenon between air and the solid element.
Fig. 4.34. Variation of the Function "TemperatureField" For Enclosure Elements, Accounting forTemperature Variation in the Air Layers Adjacent
to Element's Surfaces (Winter Time)
In case ofmulti-layer elements (with non
homogenous structure on x axis only) one
should make use of limit condition imposing69
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conservation of the density of thermal
conductive flow when passing from one layer to
another. This is expressed by (Fig.4.35):
qiC-R= q1k= q2k=...= qnk= qeC-R (4.33)
With the notations previously used in case of
single-layer elements eqs. (5.33) can be put in the
form:
(ti-si)/Rsi = (si-1)/R1= (1-2)/R2=...=(n-1-se)/Rn=
(se-te)/Rse= (ti-te)/RT (5.34)where:
RT= Rsi+(R1+ R2+... Rn)+Rse= Rsi+R+Rse
R=jdj/j represents resistance to thermalconductivity transfer (or, resistance to thermal
permeability) of a multi-layer element.
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Fig.4.35.Conservation of the Density of ThermalConductive Flow in Case of Multy-LayerEnclosure Elements (Non Homogeneous
Structure in x-Direction Only)
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Fig, 4.36. Variation of Winter-Time Temperatureinside a Multy-Layer Enclosure Element, in Caseof Stationary Regime
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Within the large picture of thermal bridges,
the most common are those created by linear
(vertical or horizontal) inclusions of materialswith high thermal conductivity. Another category
is represented by joining and connecting zones of
enclosure elements; very frequently, in these
zones are also present highly thermal conductive
materials. From another viewpoint, thermal
bridges can be categorised into: current-field
bridges (partially penetrating into or completelybreaking through the element), intersection (or
corner) bridges, complex-type bridges (typically
encountered at the joints of prefabricated largepanels used for exterior walls).
Some typical examples of thermal bridges in
building enclosure elements are illustrated in
Figs. 4.39 and 4.40.73
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Fig.4.39. Examples of Thermal Non-Homogeneities
(Generating Thermal Bridges) in Enclosure Elements Horizontal Sections Through Exterior Walls
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Fig.4.40. Examples of Thermal Non-
Homogeneities (Generating Thermal Bridges ) inEnclosure Elements-Vertical Sections ThroughExterior Walls
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4.7.2. Temperature Variation Around Thermal
Bridges
In order to analyse the characteristics of thermalfield associated to a thermal bridge zone in an
enclosure element, one of the simplest case
(already considered as classic) is in the fig.below:
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