Thermal transmittance
Encyclopedia
Thermal transmittance, also known as U-value, is the rate of transfer of heat (in watt
s) through one square metre of a structure divided by the difference in temperature across the structure. It is expressed in watts per square metre per kelvin, or W/m²K. Well-insulated parts of abuilding have a low thermal transmittance whereas poorly-insulated parts of a building have a high thermal transmittance.
where Φ is the heat transfer in watts, U is the thermal transmittance, T1 is the temperature
on one side of the structure, T2 is the temperature
on the other side of the structure and A is the area
in square metres.
Thermal transmittancesof most walls and roofs can be calculated using ISO 6946, unless there is metal bridging the insulation in which case it can be calculated using ISO 10211. For most ground floors it can be calculated using ISO 13370. For most window
s the thermal transmittance can be calculated using ISO 10077 or ISO 15099. ISO 9869 describes how to measure the thermal transmittance of a structure experimentally.
Typical thermal transmittance values for common building structures are as follows:
In practice the thermal transmittance is strongly affected by the quality of workmanship and if insulation is fitted poorly, the thermal transmittance can be considerably higher than if insulation is fitted well.
In this example the total resistance is 1.64 K·m²/W. The thermal transmittance of the structure is the reciprocal
of the total thermal resistance. The thermal transmittance of this structure is therefore 0.61 W/m²·K.
(Note that this example is simplified as it does not take into account any metal connectors, air gaps interrupting the insulation or mortar joints between the bricks and concrete blocks.)
It is possible to allow for mortar joints in calculating the thermal transmittance of a wall, as in the following table. Since the mortar joints allow heat to pass more easily than the light concrete blocks the mortar
is said to "bridge" the light concrete blocks.
The average thermal resistance of the "bridged" layer depends upon the fraction of the area taken up by the mortar
in comparison with the fraction of the area taken up by the light concrete blocks. To calculate thermal transmittance when there are "bridging" mortar joints it is necessary to calculate two quantities, known as "Rmax" and "Rmin".
Rmax can be thought of as the total thermal resistance obtained if it is assumed that there is no lateral flow of heat and Rmin can be thought of as the total thermal resistance obtained if it is assumed that there is no resistance to the lateral flow of heat.
The U-value of the above construction is approximately equal to 2 / (Rmax + Rmin)
Further information about how to deal with "bridging" is given in ISO 6946.
ISO 9869 describes how to measure the thermal transmittance of a roof or a wall by using heat flux
meters. These heat flux meters usually consist of thermopiles which provide an electrical signal which is in direct proportion to the heat flux. Typically they might be about 100 mm in diameter and perhaps about 5 mm thick and they need to be fixed firmly to the roof or wall which is under test in order to ensure good thermal contact. When the heat flux is monitored over a sufficiently long time, the thermal transmittance can be calculated by dividing the average heat flux by the average difference in temperature between the inside and outside of the building. For most wall and roof constructions the heat flux meter needs to monitor heat flows (and internal and external temperatures) continuously for periods of around two weeks at least. For ground floors the heat flux meters may need to be left in place for over a year (due to the massive heat storage in the ground).
Generally, thermal transmittance measurements are most accurate when:
Watt
The watt is a derived unit of power in the International System of Units , named after the Scottish engineer James Watt . The unit, defined as one joule per second, measures the rate of energy conversion.-Definition:...
s) through one square metre of a structure divided by the difference in temperature across the structure. It is expressed in watts per square metre per kelvin, or W/m²K. Well-insulated parts of a
- Φ = A × U × (T1 - T2)
where Φ is the heat transfer in watts, U is the thermal transmittance, T1 is the temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...
on one side of the structure, T2 is the temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...
on the other side of the structure and A is the area
Area
Area is a quantity that expresses the extent of a two-dimensional surface or shape in the plane. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat...
in square metres.
Thermal transmittances
Window
A window is a transparent or translucent opening in a wall or door that allows the passage of light and, if not closed or sealed, air and sound. Windows are usually glazed or covered in some other transparent or translucent material like float glass. Windows are held in place by frames, which...
s the thermal transmittance can be calculated using ISO 10077 or ISO 15099. ISO 9869 describes how to measure the thermal transmittance of a structure experimentally.
Typical thermal transmittance values for common building structures are as follows:
- single glazing: 5.7 W/m²K;
- single glazed windows, allowing for frames: 4.5 W/m²·K;
- double glazed windows, allowing for frames: 3.3 W/m²·K;
- double glazed windows with advanced coatings: 2.2 W/m²·K;
- triple glazed windows, allowing for frames: 1.8 W/m²·K;
- well-insulated roofs: 0.15 W/m²·K;
- poorly-insulated roofs: 1.0 W/m²·K;
- well-insulated walls: 0.25 W/m²·K;
- poorly-insulated walls: 1.5 W/m²·K;
- well-insulated floors: 0.2 W/m²·K;
- poorly-insulated floors: 1.0 W/m²·K;
In practice the thermal transmittance is strongly affected by the quality of workmanship and if insulation is fitted poorly, the thermal transmittance can be considerably higher than if insulation is fitted well.
Calculating thermal transmittance
When calculating a thermal transmittance it is helpful to consider the building's construction in terms of its different layers. For instance a cavity wall might be described as in the following table:| Thickness | Material | Conductivity | Resistance = thickness / conductivity |
|---|---|---|---|
| - | outside surface | - | 0.04 K·m²/W |
| 0.10 m | clay Clay Clay is a general term including many combinations of one or more clay minerals with traces of metal oxides and organic matter. Geologic clay deposits are mostly composed of phyllosilicate minerals containing variable amounts of water trapped in the mineral structure.- Formation :Clay minerals... bricks |
0.77 W/m·K | 0.13 K·m²/W |
| 0.05 m | glasswool | 0.04 W/m·K | 1.25 K·m²/W |
| 0.10 m | concrete Concrete Concrete is a composite construction material, composed of cement and other cementitious materials such as fly ash and slag cement, aggregate , water and chemical admixtures.The word concrete comes from the Latin word... blocks |
1.13 W/m·K | 0.09 K·m²/W |
| - | inside surface | - | 0.13 K·m²/W |
In this example the total resistance is 1.64 K·m²/W. The thermal transmittance of the structure is the reciprocal
Multiplicative inverse
In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction a/b is b/a. For the multiplicative inverse of a real number, divide 1 by the...
of the total thermal resistance. The thermal transmittance of this structure is therefore 0.61 W/m²·K.
(Note that this example is simplified as it does not take into account any metal connectors, air gaps interrupting the insulation or mortar joints between the bricks and concrete blocks.)
It is possible to allow for mortar joints in calculating the thermal transmittance of a wall, as in the following table. Since the mortar joints allow heat to pass more easily than the light concrete blocks the mortar
Mortar (masonry)
Mortar is a workable paste used to bind construction blocks together and fill the gaps between them. The blocks may be stone, brick, cinder blocks, etc. Mortar becomes hard when it sets, resulting in a rigid aggregate structure. Modern mortars are typically made from a mixture of sand, a binder...
is said to "bridge" the light concrete blocks.
| Thickness | Material | Conductivity | Resistance = thickness / conductivity |
|---|---|---|---|
| - | outside surface | - | 0.04 K·m²/W |
| 0.10 m | clay Clay Clay is a general term including many combinations of one or more clay minerals with traces of metal oxides and organic matter. Geologic clay deposits are mostly composed of phyllosilicate minerals containing variable amounts of water trapped in the mineral structure.- Formation :Clay minerals... bricks |
0.77 W/m·K | 0.13 K·m²/W |
| 0.05 m | glasswool | 0.04 W/m·K | 1.25 K·m²/W |
| 0.10 m | light concrete Concrete Concrete is a composite construction material, composed of cement and other cementitious materials such as fly ash and slag cement, aggregate , water and chemical admixtures.The word concrete comes from the Latin word... blocks |
0.30 W/m·K | 0.33 K·m²/W |
| (bridge,7%) | mortar between concrete blocks | 0.88 W/m·K | 0.11 K·m²/W |
| 0.01 m | plaster Plaster Plaster is a building material used for coating walls and ceilings. Plaster starts as a dry powder similar to mortar or cement and like those materials it is mixed with water to form a paste which liberates heat and then hardens. Unlike mortar and cement, plaster remains quite soft after setting,... |
0.57 W/m·K | 0.02 K·m²/W |
| - | inside surface | - | 0.13 K·m²/W |
The average thermal resistance of the "bridged" layer depends upon the fraction of the area taken up by the mortar
Mortar (masonry)
Mortar is a workable paste used to bind construction blocks together and fill the gaps between them. The blocks may be stone, brick, cinder blocks, etc. Mortar becomes hard when it sets, resulting in a rigid aggregate structure. Modern mortars are typically made from a mixture of sand, a binder...
in comparison with the fraction of the area taken up by the light concrete blocks. To calculate thermal transmittance when there are "bridging" mortar joints it is necessary to calculate two quantities, known as "Rmax" and "Rmin".
Rmax can be thought of as the total thermal resistance obtained if it is assumed that there is no lateral flow of heat and Rmin can be thought of as the total thermal resistance obtained if it is assumed that there is no resistance to the lateral flow of heat.
The U-value of the above construction is approximately equal to 2 / (Rmax + Rmin)
Further information about how to deal with "bridging" is given in ISO 6946.
Measuring thermal transmittance
Whilst calculation of thermal transmittance can readily be carried out with the help of software which is compliant with ISO 6946, a thermal transmittance calculation does not fully take workmanship into account and it does not allow for adventitious circulation of air between, through and around sections of insulation. To take the effects of workmanship-related factors fully into account it is necessary to carry out a thermal transmittance measurement.ISO 9869 describes how to measure the thermal transmittance of a roof or a wall by using heat flux
Flux
In the various subfields of physics, there exist two common usages of the term flux, both with rigorous mathematical frameworks.* In the study of transport phenomena , flux is defined as flow per unit area, where flow is the movement of some quantity per time...
meters. These heat flux meters usually consist of thermopiles which provide an electrical signal which is in direct proportion to the heat flux. Typically they might be about 100 mm in diameter and perhaps about 5 mm thick and they need to be fixed firmly to the roof or wall which is under test in order to ensure good thermal contact. When the heat flux is monitored over a sufficiently long time, the thermal transmittance can be calculated by dividing the average heat flux by the average difference in temperature between the inside and outside of the building. For most wall and roof constructions the heat flux meter needs to monitor heat flows (and internal and external temperatures) continuously for periods of around two weeks at least. For ground floors the heat flux meters may need to be left in place for over a year (due to the massive heat storage in the ground).
Generally, thermal transmittance measurements are most accurate when:
- The difference in temperatureTemperatureTemperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...
between the inside and outside of the building is large. - The weather is cloudy rather than sunny (this makes accurate measurement of temperature easier).
- There is good thermal contact between the heat flux meter and the wall or roof being tested.
- The monitoring of heat flow and temperatures is carried out over a long period of time.
- Several spot measurement points are used rather than just one or two.