Thermal Bridge Heat Transfer & Vapour Diffusion Simulation Program AnTherm Version 6.115 - 10.137 [ ← ] [ ↑ ] [ → ] [ToC]

### Temperature factor fRsi (f*Rsi)

Thermal bridges cause additional heat losses on one hand and on the other they cause low interior surface temperatures. Accordingly, to characterize the effect of thermal bridges, two different, independent parameters are needed - f*Rsi and thermal coupling coefficient (Leitwert, thermal conductance). For the case of many spaces connected via the thermal bridge these are the weighting factors g0 , ... , gn and the thermal conductance matrix of thermal coupling coefficients Lij .

To estimate the risk of a possible condensation or mould growth, the surface temperature of the interior space must be known. It is not reasonable to declare this temperature in degrees of Celsius, as this would only be valid for some defined boundary conditions mix, i.e. some specific temperature set for indoor air space and exterior air. Instead the temperature factor  f*Rsi , as defined in EN ISO 10211, shall be used (in the bibliography is is also known as temperature difference quotient Θ ).

It is a constant, construction specific value, that is independent of any temperature difference between indoor and outdoor climate. This factor can be calculated only with two- and three dimensional heat transport simulation software.

Thanks to the super-refinement AnTherm evaluates temperature factors f*Rsi directly out of base solutions (the weighting factors) and independently of the dimensionality of thermal bridge (2D or 3D).

The temperature factor f*Rsi is calculated and output in the results report for the coldest point of any respective space - in addition to the weighting factors. For the case of only two space it is nothing else but 1 − gSe (i.e. within results report the row of weighting factors for the exterior space shall be subtracted from 1).

Important: The temperature factor f*Rsi is defines for only two spaces connected to the thermal bridge. When three or more spaces are considered the temperature factors g0 , ... , gn must be used for the evaluation!

### Definition

The temperature factor f*Rsi (fRsi) : the difference between the interior surface temperature θsi of a component and exterior air temperature θe, related to (defided by) the difference of temperatures between interior air θi and exterior air θe. The surface temperature is to be determined with some well defined surface resistance Rsi :

Θ = f*Rsi = (θsi - θe) / (θi - θe)

where

θsi [°C] interior surface temperature
θe [°C] exterior air temperature
θi [°C] interior air temperature

The calculation of the interior surface temperature °C can be then derived from following equation:

θsi = f*Rsi • (θi − θe) + θe

When one dimensional case is considered, e.g. to asses regular layer structure of external wall, the f*Rsi might be calculated from

f*Rsi = 1 − U / αsi

or

f*Rsi = 1 − U * Rsi

where

U [W/(m·K)] thermal conductance of the wall
αsi [W/(m2·K)] thermal surface conductance of the interior surface
Rsi [m2·K/W] thermal resistance of the interior surface.

Taking the definition formula of f*Rsi and replacing the terms with the formula used within AnTherm θsi = θi*gSi + θe*gSe (valid for the two space case only!), one shell obtain as intermediate result:

f*Rsi = ((θi*gSi+ θe*gSe) - θe) / (θi - θe)

Considering simultaneously, that for the two space case also gSi + gSe = 1 is valid, thus gSe = 1 - gSi holds too, one receives short equation:

f*Rsi = 1 - gSi

or

f*Rsi = gSe

Thanks to the super-refinement AnTherm evaluates temperature factors f*Rsi directly and precisely out of base solutions (the weighting factors) and independently of the dimensionality of thermal bridge (2D or 3D).

### Space corners in three dimensions

At corners of spaces there are three two dimensional thermal bridges crossing over which consequently results in three dimensional distribution of temperatures. At such corners lower interior temperatures result when compared to those of two dimensional thermal bridges (edges). Therefore significantly higher risk of mould growth or vapour condensation is located here.

Thanks to the super-refinement AnTherm evaluates temperature factors f3DRsi directly and precisely out of base solutions (the weighting factors) and independently of the dimensionality of thermal bridge (2D or 3D).

### Minimum requirements (design factors)

To reduce the mould growth risk by applying design measures several requirements shall be fulfilled.

For example, for all structural, geometrical and material thermal bridges deviating from  DIN 4108 Beiblatt 2, the temperature factor f*Rsi at the worst location must suffice the requirement of f*Rsi ≥ 0,70 .

The respective design factors are specified in local regulations of the assessment of condensation or mould growth risk and vary strongly from country to country.