CHAPTER 5

CHAPTER 4HYGROTHERMAL COMFORT IN BUILDINGS4.1 General issuesHaving 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 be described as comfortable.

In a broad sense, the term comfort has the meaning of a state of satisfaction expressed by people with respect to environment. The comfort offered by building indoor spaces takes into consideration a great number of agents acting simultaneously on people who use these 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 of energy 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 and subjective, it is quite difficult to identify the performance exigencies of indoor spaces related to hygrothermal exigencies of building users. The human body normal internal temperature of about 37o C is obviously an objective matter; on the other hand each person has his own metabolism, his own thermo-regulator system, his own sensitiveness 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. Not very 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 things crucial to thermal performance that must be accounted for.4.1.2. Scale Influence on Thermal Performance

In 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 the needs of small buildings would seem to indicate (Fig4.1).

Fig. 4.1. Scale Effect on Thermal Performance

The size brings a thermal shift, automatically moving large buildings a few degrees up the temperature scale in comparison with small buildings and potentially this is a significant bonus.4.2. Climate Influence on Thermal Performance

Good 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 a temperature difference between two places, heat tends to flow from the higher temperature to the lower nature always trying to correct imbalances and the transmission can occur in three ways, namely conduction, convection and radiation.

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 on the 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, generated by local temperature differences, collect heat from warmer surfaces and impart it to cooler ones. This is natural convection, as opposed to forced convection by mechanical fans.Radiation involves no matter at all in the commonly accepted sense, being energy transfer by electromagnetic waves. This phenomenon is 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

Obviously, heat transmission through building enclosure varies with the temperature difference across it, so that the first determinant factor is climate.

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 count more 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 valley floor, 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 by convection increases sharply with the velocity of the surrounding air stream. There could be around 30 % heat-loss difference between exposed and sheltered locations.

Fig. 5.3. Influence of Site Location on Thermal Performance

Conversely, in hot climates, the criteria may reverse, 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 gain 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 all

around the world, 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 be 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, at first, 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, simply 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, the vulnerable 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. Fig. 4.5. Influence of Solar Radiation on Building Configuration and Orientation The effect of window sizing on 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 of 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. In the 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 even when radiation gain occurs; hence, they are prime candidates for multiple glazing.4.3. Exigencies Related to Hygrothermal Indoor Microclimate4.3.1. 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 perception and reaction to temperature variations of the indoor environment.

Due to metabolic processes, there is a permanent 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 of heat is received by the human body, through various specific mechanisms, from its environment. Theoretically, bodys thermal balance 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 human body during a given interval of time;

Qreceived , Qeliminated = amount of heat received, respectively eliminated, by the human body during the same interval of time.

Due to a kind of brain-controlled thermal regulator system, the human body can momentarily adapt itself to slightly unfavourable indoor thermal conditions, that is it can take over a limited amount of residual heat Q. If this amount becomes significant, a feeling of thermal discomfort 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 and depends 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/h

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/hIf these values are associated to the skin area of human body (1.7...1.8 m2), the resulting densities 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 activityMetabolic Energy

W/m2met

Lying, at rest44...520.75...0.90

Sitting, still52...600.90...1.05

Standing, still56...701.00...1.20

Slow walking100...1301.70...2.25

Fast walking140...2602.40...4.50

Light activities, sitting70...801.20...1.40

Light activities, standing90...1151.55...2.00

Heavy activities280...4004.80...6.90

Heat exchanges that occur in both senses between the human body and its environment are mainly 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), the conclusion 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:

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 the result 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 drawing 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 on Average Indoor Temperature

and Relative Humidity of Indoor Air

In order to ensure proper conditions of thermal comfort, a certain difference between indoor air temperature and average surface temperature of elements enclosing the indoor 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 to the hatched zone in Fig. 5.8.

Fig. 4.8. Dependence of Thermal Comfort on Average Indoor Temperature and Average Velocity of Indoor Air Movement

From the physiological viewpoint, thermal comfort 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 of relative humidity of indoor air between 30 and 70 percent does not have any relevant influence on the quantity of internal heat eliminated by a normally 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).

Fig.5.9. Dependence of Thermal Comfort on Average 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 a conventional manner, the so-called Predicted Mean Vote (PMV) indicator is being currently used. It takes into consideration all six parameters 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 thermal comfort 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. Known as Predicted Percentage of Dissatisfaction (PPD), In case of residential buildings, for instance, the following values are required:

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 of any enclosure element to be kept as small as possible. Maximum accepted values for this difference are 4o C for exterior walls and 3o 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;

4.4. Main Phenomena,

Characteristics and Parameters in Hygrothermics of Buildings4.4.1 Heat, Temperature, Thermal Flow, Density of Thermal Flow Heat is a special form of energy, whose presence is detected by the human body which can make the difference between warm and cold.

The quantity of heat held by a body is expressed 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:

T= t + 273(5.4)

Currently, the notation t is used for air temperature, whereas is used for the temperature 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 of quantities 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)

The thermal flow () represents the quantity of heat exchanged

during a time-unit (an hour), measured in watts (W).

The density of thermal flow (q) represents the thermal flow passingthrough 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 represents the 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 common engineering practice to use the so-called technical values of mass heat (given in handbooks tables) expressed in KJ/KgoC. The conversion 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 a difference of 1o C exists between the temperature on its two faces; accordingly, the coefficient of thermal conductivity whose value is determined on experimental basis for any material is measured in W/moC.

The thermal conductivity of a material is mainly 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 having pores filled with water, thermal insulating materials diminish drastically their efficiency (water is 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 factors (e. g. increase of apparent density due to settlement of the material).

A layer of immobile air, 3...5 mm thick, has the 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 other construction materials are given below:

solid brick masonry.......................0.80

cellular concrete block masonry....0.27...0.34

mortar..........................................0.70...0.93

reinforcedconcrete.........................1.62..1.74 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/KgoC]

Current values of a range from 0.0016 m2/h for cellular concrete and gypsum plates to 0.049 m2/h for cellular polystyrene. The thermal absorption (or assimilation) of a material represents its capacity to absorb (to assimilate) heat through the surface in contact with 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 respective surface.5.4.3. Heat Transmission by Conduction

Conduction is the phenomenon of heat transmission (or transfer) inside a solid or between two solid bodies in contact. Conductive heat transmission is carried out from one molecule to another; the energy moves but the matter does not.

In case of building enclosure elements, the conductive 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 with respect to time and the thermal conduction is termed stationary.

If at least one of the temperatures ti or te presents significant variation in time, the conductive heat flow between any two points of the element has variable values with respect to 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 in their immediate vicinity ; interior surface of enclosure elements and surfaces of partitions locatedin their immediate vicinity;In the first case, heat exchange is carried out by conduction, in the second case by convection and in the third case by radiation. This complex phenomenon involving all three elementary types of thermal exchange is schematically illustrated in Fig. 5.11. Fig.5.11. Schematical Representation of Elementary Thermal Exchanges Through Enclosure 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 currents collect 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.

A typical situation is that of vertical elements of the enclosure, i.e. exterior walls. In winter time, the temperature of their outer surface is higher 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 Thermal Exchanges Upon Air Temperature in the Vicinity of an Exterior Wall Surface, if Indoor Temperature is Larger than Out Door Temperature (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 given surface of the enclosure element the outer one in contact with exterior air and the inner one in contact with interior air for practical purposes a complex thermal exchange is considered. A schematically representation of such a convective-radiant thermal exchange is shown in Fig. 4.13, which could be looked upon as a simplified variant of Fig. 4.11.

Fig. 4.13. Schematical Representation of Convective Radiant Thermal Exchanges Through Enclosure Elements, if Indoor Temperature is Larger than Out Door Temperature (ti>te)

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 cannot exceed a limit value known as saturation humidity (s), beyond which water vapours pass into liquid phase. The value of s increases with 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 moment, defines the relative humidity () expressed in percentage.

The temperature at which a volume of air must 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 water vapours it contains will condense on that surface. This phenomenon is called superficial condensation and is accompanied by emanation of 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 entire volume, is termed effective pressure of water vapours (p). If the air is saturated with water vapours, the corresponding pressure value is called 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 Elements4.5.1 General Issues

The special complexity of problems related to achieving correct and efficient hygrothermal layout of buildings strongly requires in the first 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 physical entity (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

The notion of system is intrinsically related to that of model, usually having mathematical features. A mathematical model represents, in mathematical 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 and thermal response, respectively. The basic scheme to solve problems concerning 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 subjected 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 of Systems In case of problems concerning thermal layout 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 pre-established values. Hence, the results of computations should substantiate geometrical and thermophysical characteristics to be requested from the system.

Fig. 4.18. Basic scheme for Designing Thermal Layout of Systems4.5.2. Problems of Defining Enclosure System and 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 floor slab-type; Any enclosure element is physically and functionally connected to other elements of same kind situated in its plane, as well as to different other elements situated, as a rule, in planes orthogonal to its own. The thermal response of an exterior wall, taken as a whole, is obviously influenced by its connections 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 Wall4.5.3. 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 of an equivalent thermal convective exchangeeach of the two environments separated by enclosure elements can be characterised by an unique 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, this phenomenon 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 and extended over relatively many successive years. In case of common-type buildings, the current 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 winter conventional day; for Bucharest this average value is equal to 15.3o C.

Present Romanian technical regulations provide 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. Similarly, another map defines 3 macro-zones from the viewpoint of outdoor air temperature during a summer conventional day (Fig. 5.27).

Fig.5.26. Winter Climatic Zoning of Romanian Territory

Fig.5.27. Summer Climatic Zoning of Romanian Territory4.6. BASIC ISSUES RELATED TO THERMAL RESPONSE OF ENCLOSURE

ELEMENTS In case of single-layer elements (withhomogenous 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)

Fig. 4.31. Convention for the Reference System a) 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:

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)

Fig. 5.32. Conservation of the Density of Thermal Flow in Case of Stationary

RegimeFor 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.)

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 has been introduced, RT having the significance of resistance to thermal transfer (or, for the sake of simplicity, just thermal resistance) and being measured in [m2 oC/W].

The inverse value: U= 1/RT, [W/m2 oC] is currently termed thermal transmittance.

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)

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 inversely proportional to the value for , hence illustrating the fact that temperature fall increases along with the increase of thermal insulating characteristics of the material the element is made of.

Fig. 4.33.Variation of the Function "Temperature Field" 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 elements surfaces (Fig. 4.34). The temperature fall ti-si, as well as se-te can be interpreted as the effect of resistance to thermal permeability presented through the convection-radiation phenomenon between air and the solid element.

Fig. 4.34. Variation of the Function "Temperature Field" For Enclosure Elements, Accounting for Temperature Variation in the Air Layers Adjacent to Element's Surfaces (Winter Time) In case of multi-layer elements (with nonhomogenous structure on x axis only) one should make use of limit condition imposing 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 thermal conductivity transfer (or, resistance to thermal permeability) of a multi-layer element.

Fig.4.35.Conservation of the Density of Thermal Conductive Flow in Case of Multy-Layer Enclosure Elements (Non Homogeneous Structure in x-Direction Only)

Fig, 4.36. Variation of Winter-Time Temperature inside a Multy-Layer Enclosure Element, in Case of Stationary Regime Within the large picture of thermal bridges, the most common are those created by linear (vertical or horizontal) inclusions of materials with 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 completely breaking through the element), intersection (or corner) bridges, complex-type bridges (typically encountered at the joints of prefabricated large panels used for exterior walls).

Some typical examples of thermal bridges in building enclosure elements are illustrated in Figs. 4.39 and 4.40.

Fig.4.39. Examples of Thermal Non-Homogeneities (Generating Thermal Bridges) in Enclosure Elements Horizontal Sections Through Exterior Walls Fig.4.40. Examples of Thermal Non-Homogeneities (Generating Thermal Bridges ) in Enclosure Elements-Vertical Sections Through Exterior Walls4.7.2. Temperature Variation Around Thermal Bridges

In order to analyse the characteristics of thermal

field associated to a thermal bridge zone in an enclosure element, one of the simplest case (already considered as classic) is in the fig.below:

Fig. 4.50. Layout of an Exterior Structural Wall Made of Brick Masonry With Additional Thermal ProtectionINPUT x ()

(cause)

SYSTEM

OUTPUT y ()

(effect)

THERMAL

EXCITATION

SYSTEM

input data specified initially

output data to be computed

THERMALRESPONSE

THERMALRESPONSE

SYSTEM

THERMAL

EXCITATION

input data specified initially

Output data

0.89

1.06

1.25

1.52

1.81

2.15

4.6

9.4

10.68

12.14

13.66

17.3

15.36

-20

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

14

16

18

20

0

2

4

6

8

10

12

14

16

18

20

s

(g/m

3

)

t (

o

C)

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