ISO 10077-2:2012 Test case D.3 - PVC frame section with steel reinforcement and insulation panel

QuickField simulation example

QuickField simulation of the test case "D.3. PVC frame section with steel reinforcement and insulation panel" presented in ISO 10077-2:2012*

Problem Type
Plane-parallel problem of heat transfer.

Geometry

total width b = 110 mm

Given
Thermal conductivity of PVC, λ1 = 0.17 W/K-m.
Thermal conductivity of EPDM, λ2 = 0.25 W/K-m.
Thermal conductivity of insulation panel, λ3 = 0.035 W/K-m.
Thermal conductivity of steel λ4 = 50 W/K-m.

Task
Calculate two-dimensional thermal conductance L^2D in accordance with ISO 10077-2:2012*.
(Reference thermal conductance L^2D = 0.424 W/(m*K) )

Solution
Air contact surface thermal resistance R_s is caused by convention mechanism of heat transfer (contrary to conductivity mechanism in case of two solid bodies in contact).
The convection coefficient value is reciprocal to the surface resistance value:
α₂₀ = 1/0.13 W/(K·m²),
α₀ = 1/0.04 W/(K·m²).

Thermal conductivities of air gaps are adjusted to include the convection and radiation heat transfers in real situation, and correlated with the actual temperatures on the gap contours according to the recommendation of ISO 10077-2:2012. Equivalent air gap conductivity calculations are automated in the accompanying Excel spreadsheet.

Results
Heat flux and temperature distribution in frame section profile:

Two-dimensional thermal conductance L^2D = Heat flux per meter depth / Temperature difference = 8.58 / 20 = 0.429 W/(m*K).
Difference between the calculated and reference values is less than 3%. This simulation accuracy complies with the requirements of ISO 10077-2:2012.

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* ISO 10077-2:2012 Thermal performance of windows, doors and shutters -- Calculation of thermal transmittance -- Part 2: Numerical method for frames.