When does a thermal bridge need a 3D calculation?
A repeated two-dimensional section works for a thermal bridge that continues with the same cross-section along a line. It cannot fully represent an isolated point penetration, such as an anchor or bearing, where heat flow spreads around the element in three dimensions. The Passive House Institute’s criteria distinguish continuous connections calculated as 2D Ψ-values from point elements assessed through 3D heat-flow simulation and χ-values. For repeated point bridges, the calculation must also account for their number per square metre. Model choice follows the geometry and repetition pattern. [2]
- Continuous connections can be represented as 2D Ψ-values; point elements such as dowels, anchors and bearings are treated as 3D heat-flow simulations with χ-values. [2]
- EN ISO 10211:2017 provides four validation test cases: two 2D and two 3D. COMSOL reports passing all four and details its implementation of 3D case 3. [1]
- For a repeating field of point bridges, PHI’s certification criteria for renovation systems express the U-value surcharge ΔU in relation to the number of elements per square metre of external area. [2]
- In COMSOL’s ISO 10211:2017 case 3, computed heat flows differed from reference values by 0.22% to 0.25%, and minimum surface temperatures by no more than 0.01 °C. [1]
What does a 2D section assume?
A 2D model represents a section of a connection that continues along a line. The Passive House Institute’s renovation-system criteria classify connection details as two-dimensional Ψ-values, while distinguishing point elements such as dowels, anchors and bearings for three-dimensional heat-flow simulation. A section through one discrete object does not capture the full heat spreading around its sides and ends. [2]
What does a 3D benchmark establish?
A benchmark checks whether calculation software can reproduce a defined reference problem. COMSOL’s implementation of EN ISO 10211:2017 test case 3 models a conductive horizontal block crossing an external wall between two floors. The exterior surface is at 0 °C and the interior at 20 °C. Computed heat flows differed from the standard’s expected values by 0.22% to 0.25%; minimum surface temperatures differed by less than or equal to 0.01 °C. These results meet the stated limits for that test case. They do not establish the result for an anchor, bracket or other assembly with different geometry and materials. EN ISO 10211:2017 defines four validation cases, two 2D and two 3D; COMSOL says its method passes all four and presents case 3 here. [1]
How does repeat density enter the calculation?
A point thermal transmittance χ describes the heat transfer of one point bridge in W/K. PHI’s certification criteria for renovation systems (version 1.0, 29.07.2024) require point bridges to be included in the U-value calculation as a ΔU surcharge based on the number of elements per square metre of external area. In dimensional terms, ΔU (W/(m²K)) = χ (W/K) × density (elements/m²), when the repeated elements are represented by the same χ-value. For an illustrative square layout with 600 mm spacing in both directions, density is 1 ÷ (0.6 m × 0.6 m), or about 2.78 elements/m². This is an arithmetic example, not benchmark data or a recommended spacing. If the element count varies, PHI’s certification criteria call for an average U-value based on the reference building model. For ETICS systems using EPS insulation with simple façade anchors, PHI permits the tabulated values in Appendix A of its Protokollband Nr. 35 where the design is comparable; otherwise the χ-value must be calculated with 3D finite-element software in accordance with ISO 10211. The PHI document assigns this calculation to PHI for certification. The heat-flow contribution associated with ΔU then depends on the temperature difference across the assembly. [2]
Which model should answer the question?
Use a 2D calculation for a continuous connection represented by its linear Ψ-value. Use 3D analysis for a point element or penetration whose heat flow spreads in three dimensions; PHI’s criteria also identify cases where a point bridge within a 2D connection must be modelled in 3D and included in the linear heat-loss value. For a real assembly, document its geometry, material properties, boundary conditions, model extent and, for repeated penetrations, actual count per square metre. A solver’s performance on a benchmark supports confidence in the calculation method, but only a model of the assembly in question answers its heat-loss question. [1] [2]