Thermal bridges: the temperature factor fRsi

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We continue our series of articles on the topic of thermal bridges: this time, we illustrate the fRsi value, which describes the thermal ”strength” of a node under the point of view of internal surface temperatures.

As we have explained in a previous article, the PSI value describes a higher or lower heat flow caused by a discontinuity in the thermal envelope - a thermal bridge. On the other hand, the fRsi factor is of primary importance for health and comfort considerations.

To guarantee a comfortable environment, the thermal envelope needs to be as homogeneous as possible, so that the temperatures can be even over the internal surfaces. This principle is valid for new constructions as well as for energy retrofits, regardless of the overall energy efficiency level of the building. To achieve this, the thermal bridges of the building need to be designed and calculated not only under the point of view of the heat flow (PSI), but also to address the internal surface temperatures (fRsi).

A thermal bridge caused by the geometry of the structure, that generates a discontinuity in the thermal envelope.
A thermal bridge caused by the geometry of the structure, that generates a discontinuity in the thermal envelope.

THE TEMPERATURE FACTOR fRsi

In winter, the “average” room temperature is guaranteed by the combination of the thermal envelope and the heating system. The same happens in summer time, if the building is provided with a cooling system. However, this does not mean that the internal temperatures are even over the internal surfaces. Because of discontinuities of the envelope (thermal bridges), the internal temperature is lower than the “average”. In summer , temperatures at thermal bridges are higher, depending on the dynamic behaviour of the structure under the changing external conditions.

Raising the average temperature of the whole house by a few degrees does not help, because the surface temperature in the “weakest” spots remains lower. This phenomenon is caused by the fRsi temperature factor of the thermal bridge.

The fRsi factor is given by the difference between the internal temperature in the “weak” spot minus the external temperature, divided by the average temperature difference between inside and outside:

fRsi = ( Tmin - Te ) / ( Ti - Te )

Tmin: internal surface temperature at the thermal bridge;

Ti: internal room temperature;

Te: external temperature.

The difference between the internal room temperature and the external temperature is relatively easy to find. Design room temperature is usually 20 °C (68 °F), while the external temperature depends on the climate you are designing for. The minimum internal temperature at the thermal bridge (Tmin), however, requires a finite element calculation accordingto ISO 13788, based on the geometry of the node, and on the materials used in the construction. Please notice that the fRsi factor cannot be calculated from the internal temperature obtained from an ISO 10211 calculation, because the two norms assume different values as far as internal and external surface resistances.

The fRsi factor is an dimensionless number, ranging from 1 to 0.

fRsi = 1: the internal surface temperature at the thermal bridge is exactly the same as in the rest of the house. It is the best result you could ever get, and it is physically impossible to obtain;

fRsi = 0: the temperature at the thermal bridge is identical to the outside one, with a terrible outcome in terms of comfort. This result is also physically impossible.

If it is impossible to achieve a fRsi value of 1 where a thermal bridge is located, on the other hand you should always try and get values as close to 1 as possible.

TEMPERATURE FACTOR AND COMFORT

A surface temperature that is lower than the “average” room temperature has several negative effects on comfort and overall healthyness of the building.

From the point of view of thermal comfort, this temperature asymmetry makes us feel that a room is “cold”, even though the average temperature may be higher than normal room temperature. Under the same principle, the same room feels “warmer” in summer.

The combination of localised lower temperatures and high humidity (caused by lack of ventilation), fosters the appearance of mold and/or condensation exactly where the fRsi factor is at its lowest.

Mold inside a bathroom, caused by low surface temperatures and lack of ventilation. - photo by Damiano Chiarini.
Mold inside a bathroom, caused by low surface temperatures and lack of ventilation. - photo by Damiano Chiarini.

To avoid mold disasters, any work done on the thermal envelope should include a thorough analysis of the fRsi factors.

COMPARING fRsi FACTORS

When you design how to go about a specific thermal bridge, you can compare the “strength” of different solutions from a comfort point of view by comparing their fRsi values.

Calculation of the fRsi factor for the thermal bridge of a concrete column in a masonry wall, with an unmitigated solution (left) and a mitigated one (right).
Calculation of the fRsi factor for the thermal bridge of a concrete column in a masonry wall, with an unmitigated solution (left) and a mitigated one (right).

As shown in the graph, the unmitigated solution A (left) is going to foster mold growth even with mild outside temperatures, in spring and autumn.

CONCLUSIONS

To guarantee a comfortable and healthy indoor environment, the “weak” points of the thermal envelope (thermal bridges), need to be properly addressed.

Whether or not you are building/refurbishing to meet the Passive House standard, health needs to be a priority. The design of the thermal envelope should include the calculation of the fRsi factors of the thermal bridges, to obtain internal surface temperatures high enough to avoid the risk of mold and condensation.

The fRsi factor, as described in this article, can be used to compare different options to mitigate a thermal bridge, and to find out which one can guarantee the best comfort.