How to Calculate a ψ-Value per EN ISO 10211
From a 2D construction detail to the linear thermal transmittance Ψ, step by step in ThermX.
What a ψ-Value Is
The linear thermal transmittance Ψ (psi-value, W/(m·K)) quantifies the extra heat loss caused by a thermal bridge — a junction, slab edge, lintel or balcony — beyond what the plain 1D U-values of the adjoining building elements already account for. It is the number you need for heat-loss calculations (e.g. EN ISO 13789/52016) and for energy certificates in most European countries.
EN ISO 10211 defines how to compute it from a 2D numerical model:
Ψ = L2D − Σ (Uj · lj)
where L2D is the thermal coupling coefficient from the 2D calculation (total heat flow per metre of junction divided by the temperature difference), Uj is the 1D U-value of each flanking element, and lj is the length over which that U-value applies in the model.
Step 1 — Model the Geometry
Draw the junction cross-section with the polygon and rectangle tools (or import it — ThermX reads DXF, DWG and THMX files). Follow the EN ISO 10211 rules for the model extent:
- Place cut-off planes at least 1 m from the central (disturbing) element, or at a plane of symmetry if one is closer.
- Include the full build-up of each flanking element (all layers).
- Model dimensions consistently — decide on internal or external dimensions up front; the resulting Ψ (ψi vs ψe) only makes sense together with the dimension convention used in the whole-building calculation.
Step 2 — Assign Materials
Assign a material to every region. The built-in library uses design thermal conductivities from EN ISO 10456 (concrete, brick, mineral wool, EPS/XPS, steel, timber…). For products with declared λ values from a datasheet, create a custom material.
Step 3 — Set Boundary Conditions
Apply convective boundary conditions to the internal and external surfaces and adiabatic conditions to the cut-off planes:
- Internal: e.g. 20 °C with surface resistance Rsi = 0.13 m²·K/W (the CEN preset in the Boundary Conditions panel).
- External: e.g. 0 °C with Rse = 0.04 m²·K/W.
- Cut-off planes: adiabatic (no heat flow) — this is what EN ISO 10211 prescribes for section planes.
Because steady-state conduction is linear, the Ψ result does not depend on the particular temperature pair — only on geometry, conductivities and surface resistances.
Step 4 — Mesh and Solve
Open the Meshing panel and generate the mesh — ThermX uses Delaunay triangulation with Ruppert refinement and quality controls. Then solve (the GPU solver is picked automatically when available). To demonstrate mesh independence as EN ISO 10211 requires, refine the mesh and re-solve: the total heat flow should change by well under 1–2% between refinements.
Step 5 — Define Flanking Components and Read Ψ
Open Results → PSI. ThermX already knows L2D from the solution; in the Component Editor you add each flanking element with its 1D U-value and its length in the model, and Ψ is computed automatically.
Say the solver reports L2D = 0.95 W/(m·K) for a wall–floor junction, the wall has U = 0.30 W/(m²·K) over l = 1.00 m and the floor U = 0.25 W/(m²·K) over l = 1.00 m. Then Ψ = 0.95 − (0.30·1.00 + 0.25·1.00) = 0.40 W/(m·K). (Numbers chosen for arithmetic clarity, not as a benchmark.)
The 1D U-values of the flanking elements can be calculated per EN ISO 6946 (layer-by-layer thermal resistances plus Rsi/Rse) — or by solving each flanking build-up alone in ThermX as a quick cross-check.
Sanity Checks
- Ψ should usually be positive for geometric and material thermal bridges; small negative values are legitimate when using external dimensions at corners.
- Verify the solver against the built-in EN ISO 10211 Annex A cases (A.1, A.2) from the Validation panel if you need documented evidence.
- State the dimension convention (internal/external) next to every reported ψ-value.
ThermX costs €10 one-time and runs on Windows, macOS, Linux — and in your browser. Download ThermX or open it in your browser and compute your first ψ-value on a built-in example in minutes.