How the calculators are checked

1. Direct numerical integration

The automated tests integrate the defining integral of the configuration factor, cos θ₁ cos θ₂ / (π r²), numerically over the emitter. They do this for parallel rectangles centred on and offset from the receiver, and for perpendicular rectangles with and without a wing wall. The closed-form expressions used by the calculators agree to better than 2 × 10⁻⁵.

2. Physical limits

An infinite parallel plane gives φ = 1. A half-space seen from the corner of a perpendicular wall gives φ = 0.5, so the flux at the corner is half the emitted flux. An emitter seen edge-on gives φ = 0.

3. Worked cases from completed projects

Results stored in independently built spreadsheet calculators from completed boundary-opening and fire-severity assessments are reproduced to at least nine significant figures. Those spreadsheets use σ = 5.68 × 10⁻⁸ W/m²K⁴ and T + 273, so these cases use the IFEG constants.

Defaults that differ from common spreadsheets

The calculators default to σ = 5.670 × 10⁻⁸ W/m²K⁴ and T + 273.15. Many spreadsheets use the IFEG 2005 values, 5.68 × 10⁻⁸ and T + 273, and you can choose either. At 860 °C with ε = 0.9 the emitted flux is 84.14 kW/m² with the first set and 84.24 kW/m² with the second. Lengths such as the solid return wall are solved exactly and then rounded up. Some spreadsheets step along a 0.05 m grid instead, which gives 1.05 m where the exact value is 1.00 m.

Found a case that disagrees with your own calculation? Email tin@cavies.studio and it will be checked and added here.