How to use this calculator
Pick a geometry and enter its dimensions, the emissivities and the temperatures. For geometries that don’t enclose each other, the rest of what each surface sees is treated as black surroundings at the temperature you enter.
Formulas
Worked example
Long concentric cylinders: r₁ = 0.1 m at 800 K (ε = 0.8) inside r₂ = 0.2 m at 400 K (ε = 0.6), per meter
- F₁₂ = 1, A₁ = 0.628 m², A₂ = 1.257 m².
- Resistances: (1 − 0.8)/(0.8 × 0.628) = 0.398, 1/0.628 = 1.592, (1 − 0.6)/(0.6 × 1.257) = 0.531 m⁻².
- σ(800⁴ − 400⁴) = 21 773 W/m².
- Q = 21 773/2.521 = 8.64 kW per meter of length.
Frequently asked questions
What is a view factor?
The fraction of the radiation leaving surface 1 that strikes surface 2 directly. It depends only on geometry.
Why is there a surface resistance?
A gray surface emits less than a blackbody and reflects part of what hits it. (1 − ε)/(εA) is the resistance between its blackbody emissive power and its radiosity; it vanishes for a black surface.
What is a reradiating surface?
An insulated surface with zero net radiation: it absorbs and re-emits everything. Its node floats in the network with no connection to Eb.