Thermal bridges occur within the building fabric where, because of the geometry or the presence of high conductivity materials, heat flows are two or three dimensional. For many situations simple calculations are no longer sufficient to correctly determine thermal performance and it is necessary to analyse the construction using numerical modelling. A number of software packages are available where these specify the geometry, materials and boundary conditions of the model in 2 or 3 dimensions as appropriate. Typical thermal bridges are as per the adjacent diagram.

A linear thermal bridge is essentially a 2D concept and can be modelled in 2D if possible. However if the plane elements are not uniform in the third dimension - i.e. they contain repeating thermal bridging such as steel studs, then a 3D model must be used. Thermal modelling also allows the minimum internal surface temperature at the thermal bridge to be found and the temperature factor "f" to be calculated. This is necessary in order to check that the thermal bridge does not pose an unacceptable risk of surface condensation and mould growth.

The Ψ (psi) value by definition represents the extra heat flow through the linear thermal bridge over and above that through the adjoining plane elements. From the numerical modelling of a two-dimensional junction, L 2D is the thermal coupling coefficient between the internal and external environments and is calculated from: L 2D=Q / (Ti – Te) (W/mK) where : Q is the total heat flow from the internal to external environment and Ti and Te are the temperatures of the internal and external environments. Hence, the linear thermal transmittance, Ψ, of the two dimensional junction is the residual heat flow from the internal to external environment after subtracting the one-dimensional heat flow through all flanking elements, expressed in W/mK and is determined from: Ψ=L 2D – Σ (U x l) (W/mK) Where; L 2D is the thermal coupling coefficient U is the U-Value in W/m²K of the flanking element l is the length in metres over which U applies.

To account for the heat loss through non-repeating thermal bridges at building junctions, for eg, window, door perimeters, ground & intermediate floor to external wall, party wall, corners, roof to external wall, gable etc.. SAP 2009 (UK) and DEAP in Ireland allows a user defined y-value to be input. The y-value is in effect an additional U Value applied to the sum of all the exposed fabric element areas of the building. It has the same units as the fabric U value of W/m²K. The total heat loss through the non repeating thermal bridges that is added to the heat loss through the exposed building fabric is called the transmission heat transfer coefficient, HTB and is calculated as follows: The sum of the exposed building fabric area ΣAexp is the sum of the roof, walls including windows & doors, and ground floor exposed areas. HTB =y x ΣAexp y=0.04 W/m²K if the ψ values of the lintels, ground-floor/wall and gable/ceiling junctions (Enhanced Construction Details ECD) are limited to 0.07 W/mK and all remaining details are Acceptable Construction details or better. The Energy Savings Trust has prepared ECD’s for different constructions in the UK. y=0.08 W/m²K if all details are Acceptable Construction Details ACDs (or calculated to be the equivalent following numerical modelling). ACD’s for generic construction are prepared by CLG in the UK and DOECLG in Ireland. Target Ψ values for ACD’s are given in Table D1 of TGD Part L in Ireland and part L in the UK. y=0.15 W/m²K if any details are not Acceptable Construction details.

Pictured is a portion of an external corner model of a light steel frame system with the temperature isotherms showing the increased heat flow from internal to external at the junction due to two steel studs at the panel junction at the corner (the red temperature being 20 degrees internal surface boundary condition and the dark purple being 0 degrees external boundary condition modelled).