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close this bookClimate responsive Building (SKAT, 1993)
close this folder2. Fundamentals
View the document(introduction...)
View the document2.1 Climate zones
View the document2.2 Climatic factors.
View the document2.3 Human requirements regarding indoor climate
View the document2.4 Physics

2.4 Physics

2.4.1 Thermal radiation
2.4.2 Heat transmission
2.4.3 Heat storage
2.4.4 Solar heat gain factor
2.4.5 Vapour diffusion

Obviously, indoor climate depends largely on outdoor climate, especially in the case of passive buildings that are neither heated nor cooled. To a certain extent, however, the indoor climate can be influenced with the help of appropriate designs and materials. This influence depends on the physical processes that occur.

General principles
In order to gain a general understanding of the most important processes, the main physical principles are explained. Together with the physical data given in Appendix 5.1 a rough assessment of the characteristics of the most common materials and composite constructions is possible.

The main physical processes that govern the indoor climate are:

· Thermal radiation
· Heat transmission
· Convection
· Heat storage and time lag
· Internal heat sources

Practical recommendations
This chapter explains only the basic physical phenomena. Evaluation and recommendations for particular materials and for a specific situation are given in Chapter 3.

Detailed information
To verify the exact thermal performance of building components is a rather complex task. Detailed information and calculation methods necessary for the study of specific problems can be obtained from various technical books [-8, 11, 127-]

2.4.1 Thermal radiation
(also see Chapter 3.1.4)

Definition
Radiation is the heat transfer from a warmer surface to a cooler surface which are facing each other. This happens in the form of waves and a transmitting media (e.g. air) is thus not required.

Emittance
The warmer surface emits thermal energy in the form of radiant heat always towards a cooler surface. The quantity of emitted energy depends on the temperature difference between the surfaces, and also on the material property (emissivity) of the warmer surface.


Fig 2/27 Emittance e

Absorption and reflectance
Depending on these surface properties the radiation received by the cooler surface can be partly absorbed and partly reflected. These properties are called absorbance-(a) and reflectance-(r).

(a)-+-(r) always equals 1.

Light-colored, smooth and shiny surfaces tend to have a higher reflectance. For the perfect theoretical white surface the reflectance is 1 and the absorbance is 0; for the perfect "black body" absorber the reflectance is 0 and the absorbance is 1.


Fig 2/28 Absorbance a and reflectance r

Geometrical location
The quantity of radiant heat that a body receives depends also on the geometrical location with regard to the heat source.

Surfaces which directly face each other exchange the greatest thermal radiation, whereas surfaces that are turned away from each other exchange less.


Fig 2/29

Balancing effect
As a consequence of this radiation, the warmer surface cools down and the cooler surface heats up.

(Values of emittance and reflectance of the main building materials see Appendix 5.1 )

2.4.2 Heat transmission
(also see Chapter 3.1.4)

Heat always flows from a higher temperature to a lower temperature. The quantity of heat transmitted through a material depends on

· its conductivity;
· the temperature difference between outside and inside;
· the thickness of the material; and
· the surface conductance.

The conductivity k (W/mK)
In conduction, the spread of molecular movement constitutes the flow of heat. The rate of heat flow varies with different materials and depends on its thermal conductivity (k). It is defined as the rate of heat flow through a unit area of unit thickness of the material, by a unit temperature difference between the two sides. The dimension is W/m°C. This value is used to compare the thermal insulation effectiveness of materials that are homogeneous in composition. Its value ranges from 0.03 W/m°C for thermal insulation materials up to 400 W/m°C for metals. The lower the conductivity, the better an insulator is the material.

(k-values of different materials see Appendix 5.1 )

(The k-value corresponds with l in the German system)


Fig 2/30 Conductivity k

Air is a most efficient insulator
Air has an extremely low k-value. The higher the percentage of air enclosed in the material, the better is its insulation value, as long as convection does not occur. To avoid convection, the air enclosures must be fine. The finer the air inclusions, the less convection takes place.

Low weight materials tend to contain more air, thus their conductivity is less. This relationship is generally true for materials of the same kind but of varying densities, and of the same materials with varying moisture content.

Humid materials are poor insulators
Water has a conductivity of 580 W/m°C versus 0.026 W/m°C for still air. Therefore, if the air enclosed in the is replaced by water, the material's conductivity is rapidly increased. For example, an asbestos insulating board in dry conditions has a conductivity four times lower than that of the same board soaked with water.

Resistance R (m²K/W)

The resistance depends on the conductivity and the thickness of a material.

It is defined as thickness / k = R

How much heat is prevented from passing through a non-homogenuous section?

The total resistance of a composite construction is the sum of the resistance of its components, thus R1 + R2 + R3....= R total


Fig 2/31 Resistance R

Heat transfer at the surface or surface conductance f (W/m²K)
A thin layer of air film separates the material surface from the surrounding ambient air, and this air film has a specific conductance (f) in relation to the transfer between material and the surrounding air. Surface conductance includes the convection and radiant components of the heat exchange at the surfaces. The resistance of these films is expressed as 1/f.

For internal surfaces this resistance (fi) is around 0.15-m²°C/W, and for external surfaces (fo) it varies between 0.1 and 0.01 m²°C/W depending on wind exposure.

Transmittance U (W/m²K)
(see Appendix 5.1 )
Adding the surface resistance 1/f to R total, the total heat transmission can be calculated:


The reciprocal value is the thermal transmittance U.

(The U-value corresponds with the k-value in the German system)

Quantity of transmitted heat
The U-value represents the total heat transmitted through a composite construction by a temperature difference of 1°C. Multiplying it with the effective temperature difference gives the total heat energy transmitted:

Total heat transmission = U·(ti - to)·(W/m²)

This value, however, is only valid for the theoretical case of stable temperature conditions over a longer period. In reality, the outdoor temperature fluctuates during the course of the day. This is of special relevance in the case of warm climates, where the houses are neither heated nor cooled and the heat flow is thus not unidirectional. Here the time lag, the decrement factor and the thermal capacity play important roles.

2.4.3 Heat storage
(also see Chapter 3.1.4)

Specific heat (Wh/kgK)
This is defined as the amount of energy required for a unit temperature increase in a unit mass of material. The higher the specific heat of a material, the more heat it will absorb for a given increase in temperature. Of all common materials, water has the highest specific heat.

Heat capacity Q (Wh/m² K)
This is defined as the amount of heat energy required for a unit temperature increase in a unit of area.
Thickness x specific mass x specific heat = heat capacity (Q)

Time lag O (h) and decrement factor
The time lag is defined as the time difference between the peak outer surface temperature and the peak inner surface temperature; it is actually the time required for the heat to pass through a material. It is of importance, for instance, in the case where one wants to take advantage in the evening of day time surplus heat energy.


Fig 2/32. Source [ 8 ]

Decrement factor
The decrement factor is the ratio between the temperature fluctuation on the outer and the inner surface. It is the measure of the damping effect. Generally, the higher the thermal capacity or the higher the thermal resistance of a material, the stronger is the damping effect.

The time lag can be controlled by the selection of materials and their thickness. It depends on the thermal capacity Q and the resistance R.

For heavy materials the time lag can be roughly calculated using the formula

time lag O = 1.38 + (Q x R)1/2

For composite constructions, an additional estimated lag should be added to the individual sum of the time lags. It is customary for two layers and light construction walls to add an additional 0.5 hour; for three or more layers, or for very heavy constructions, one additional hour lag is assumed.

(Time lag values of common materials and composite constructions see Appendix 5.1 )

Active heat storage capacity
The heat storage capacity and the time lag of a building structure can be utilized for balancing the indoor temperature. In such a case, however, the so-called active mass only, and not the entire building mass, is taken into account ( see Chapter 3.1.4 ).

2.4.4 Solar heat gain factor

When selecting construction materials in areas with intense solar radiation an important criterion is the solar heat gain factor (SHF). This is defined as the rate of heat flow through the construction due to solar radiation expressed as a percentage of the incident solar radiation. [ 8 ].

SHF (%) = 100 x transmitted solar energy / incident solar energy

As this value can be related to the increase in the inner surface temperature, a performance standard can be established on the basis of experience. Its value should not exceed 4% in warm-humid climates or 3% in hot-dry climates.

A graphic method exists for calculating the SHF. [ 120 ].

For instant practical use a table with the values for common constructions can be found in Appendix 5.1

2.4.5 Vapour diffusion

Water in the form of vapour diffuses through the outer building shell when the outside and inside vapour pressures differ. Vapour usually diffuses from the warmer towards the cooler side of the shell.

This phenomenon requires attention in the case where there is likely to be an area of condensation inside the shell (e.g. "vapour barrier" on the cooler side). This happens when the saturation point is reached, particularly in heated or constantly cooled buildings. In air-conditioned buildings, especially, this aspect requires consideration. However, in naturally climatized buildings such conditions usually do not occur. Hence vapour diffusion is not dealt with in this publication.