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How sensitive is a Ψ-value to material conductivity?

Passivebase Editorial Desk

A calculated Ψ-value can respond strongly or weakly to uncertain material conductivity; there is no universal percentage change. The result depends on where the material sits in the junction and how changing its conductivity affects both the calculated heat flow and the reference heat flow through adjoining elements. To test one detail, rerun the same model with justified design values for that material while keeping the other inputs fixed. The resulting spread is a model sensitivity range, not measurement uncertainty or a guarantee of built performance. [1] [2] [3] [4]

What does a Ψ-value include?

A linear thermal transmittance Ψ describes the junction heat flow that remains after accounting for the heat flow through the adjoining plane elements. The Sustainable Energy Authority of Ireland defines Ψ as heat loss per degree and per unit junction length that is not accounted for in those elements’ U-values. ISO 10211:2017 sets out 2D and 3D models for calculating heat flows and deriving linear and point thermal transmittances. This accounting means a conductivity change can affect the modelled junction flow and, where the material is also part of a reference element, that element’s U-value contribution. The net change in Ψ therefore need not track the percentage change in conductivity. [1] [2]

Which conductivity values should you vary?

Use values justified for the specific material and the conditions expected in the building element. ISO 10456 describes procedures for determining declared and design thermal values and converting values between conditions, including temperature and moisture conversions. Check which edition of ISO 10456 your project requires before using its procedures. A nominal value from a product page is not automatically the right design value for a particular junction. Record the product or material, the source and status of each value, and the assumptions used to derive any design value. [3]

How do you isolate conductivity’s effect?

First select a documented range of design conductivity values for the material under study. Then rerun the same junction model for each value, changing only that input. Keep geometry, boundary conditions, dimensional convention, other material properties and the reference component calculations fixed. ISO 10211 specifies the model geometry, boundary conditions and thermal values used in thermal-bridge calculations; it assumes physical properties are independent of temperature and that there are no heat sources within the building element. Those assumptions define the scope of this simplified sensitivity check. [1]

Record each input and its resulting Ψ in W/(m·K). Report the lowest and highest results and their difference; if you report a percentage change, name the baseline used. Retain the model inputs and software settings so the comparison can be reproduced. This is a recommended way to isolate one input’s effect, not a claim that the cited standard prescribes this reporting format. [1]

What does the spread tell you?

The spread answers a narrow question: how much does this model’s Ψ change across the selected conductivity values when the other inputs stay fixed? It does not quantify uncertainty in the full calculation. Geometry, boundary conditions, other material properties, numerical discretisation and how closely the model represents the built junction remain outside a one-input test. [1] [4]

The National Physical Laboratory’s Measurement Good Practice Guide No. 11 describes identifying sources of measurement uncertainty, estimating their contributions and combining them under appropriate assumptions. It concerns measurement uncertainty, so it does not provide an uncertainty budget for a simulated Ψ-value. A conductivity sweep is a sensitivity check, not a confidence interval for the real junction. To judge a specific detail, request its geometry, material records, boundary conditions, dimensional convention and model outputs alongside the conductivity values used. [4] [1] [3]

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