Why an external-dimension Ψ-value can be negative
A negative Ψ-value from an external-dimension calculation does not mean heat travels from outdoors into the building. Ψ is a difference between the heat flow calculated through a junction and the heat flow assigned to the adjoining plane elements. Changing the reference dimensions changes that subtraction, so the residual can change sign while the underlying modelled heat flow stays the same. The conversion below is illustrative, not a measured or published junction result. [1] [2]
- A Ψ-value is a residual: the modelled heat flow through a junction minus the heat flow assigned to its adjoining plane elements under a stated dimension convention. [1] [2]
- In an illustrative conversion, an internal-dimension Ψ-value of 0.060 W/(m·K) becomes −0.020 W/(m·K) when the external reference lengths add 0.080 W/(m·K) of plane-element contribution. [1]
- Internal and external dimension methods use different reference lengths or areas; applied consistently with matching envelope measurements, they should give the same overall fabric heat loss. [1]
What does Ψ measure?
A two-dimensional thermal model calculates heat flow through a junction and its adjoining elements. To obtain the linear thermal transmittance Ψ, the method subtracts the contribution assigned to the flanking plane elements. In the DEEP methods report, the area form is Ψ = (L₂D − Σ(U × a))/l, where L₂D is the thermal coupling coefficient, U is each flanking element’s thermal transmittance, a is its reference area and l is the modelled junction length. Ψ is expressed in W/(m·K). [1]
That subtraction makes Ψ a residual relative to a chosen baseline, rather than a stand-alone measure of heat-flow direction. A negative value means the assigned plane-element contribution exceeds the modelled junction contribution for that convention. It does not, by itself, show the junction’s surface temperature, condensation risk or total heat flow through the building. [1] [2]
How can the same model produce a negative value?
Consider a hypothetical junction with an internal-dimension Ψ of 0.060 W/(m·K). Suppose changing the reference lengths adds 0.25 m for one flanking element with U = 0.20 W/(m²·K), and 0.20 m for another with U = 0.15 W/(m²·K). The conversion is Ψexternal = 0.060 − (0.25 × 0.20) − (0.20 × 0.15) = −0.020 W/(m·K). These assumed inputs illustrate the arithmetic; they are not a thermal simulation or evidence about a real junction. [1]
The negative result is the changed residual after subtracting the larger plane-element baseline. It is not a second physical prediction that heat has reversed direction. The method report explains that internal dimensions are used for one convention and external dimensions for the other, while the calculation method otherwise remains the same. [1]
What should you check before using the value?
Check which dimension convention the Ψ-value uses, then pair it with envelope areas and junction lengths using that same convention. The DEEP report says external Ψ-values tend to be lower in most contexts and that internal and external methods, applied consistently, should give the same fabric heat-loss value. Its findings describe a UK case-study method, not a universal regulatory rule. [1]
For a project calculation, request the model geometry, boundary conditions, plane-element U-values, reference dimension convention and junction lengths. A negative number alone does not establish that a junction is harmless. Assess surface temperature and condensation risk separately using the model’s temperature field and the relevant project conditions. [1] [2]