cthe eng pentru studenti

7/29/2019 CTHE Eng Pentru Studenti

1/77

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


2/77

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


3/77

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


4/77

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


5/77

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.

5


6/77

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.

6


7/77

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


8/77

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

8


9/77

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


10/77

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


11/77

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


12/77

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


13/77

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.

13


14/77

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


15/77

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


16/77

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


17/77

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


18/77

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


19/77

- 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

19


20/77

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


21/77

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


22/77

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


23/77

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.

23


24/77

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


25/77

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).

25


26/77

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


27/77

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


28/77

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

28


29/77

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;

29


30/77

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


31/77

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


32/77

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


33/77

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

33


34/77

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


35/77

(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


36/77

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


37/77

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

37


38/77

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

38


39/77

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


40/77

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.

40


41/77

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.

41


42/77

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


43/77

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

43


44/77

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)

44


45/77

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


46/77

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)

46


47/77

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


48/77

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


49/77

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)

49


50/77

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


51/77

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

51


52/77

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

52

input data specified initially


53/77

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


54/77

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


55/77

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

55


56/77

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

56


57/77

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


58/77

Similarly, another map defines 3 macro-zones

from the viewpoint of outdoor air temperature

during a summer conventional day (Fig. 5.27).

58


59/77

Fig.5.26. Winter Climatic Zoning of RomanianTerritory

59


60/77

Fig.5.27. Summer Climatic Zoning of Romanian

Territory

60


61/77

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)

61


62/77

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


63/77

- 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


64/77

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.)

64


65/77

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.

65


66/77

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


67/77

- 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


68/77

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


69/77

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


70/77

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.

70


71/77

Fig.4.35.Conservation of the Density of ThermalConductive Flow in Case of Multy-LayerEnclosure Elements (Non Homogeneous

Structure in x-Direction Only)

71


72/77

Fig, 4.36. Variation of Winter-Time Temperatureinside a Multy-Layer Enclosure Element, in Caseof Stationary Regime

72


73/77

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


74/77

Fig.4.39. Examples of Thermal Non-Homogeneities

(Generating Thermal Bridges) in Enclosure Elements Horizontal Sections Through Exterior Walls

74


75/77

Fig.4.40. Examples of Thermal Non-

Homogeneities (Generating Thermal Bridges ) inEnclosure Elements-Vertical Sections ThroughExterior Walls

75


76/77

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:

76


77/77

cthe eng pentru studenti

Documents