Library / Heat transfer and thermal systems / HTS-38
Heat transfer and thermal systems
Radiosity of an opaque diffuse grey surface
Total radiation leaving an opaque diffuse grey surface per unit area, equal to its emission plus the reflected part of the irradiation G.
- Ref
- HTS-38
- Rev
- v1
- Field
- Heat transfer and thermal systems
- Result
- J [W/m²]
The radiosity J of an opaque diffuse grey surface is the total radiation leaving it per unit area: its own emission εσT⁴ plus the reflected part of the irradiation, (1 − ε)G. Absorptivity is taken equal to emissivity. Radiosity is the variable used in network methods, since it is what other surfaces actually receive from this one.
Total radiation leaving an opaque diffuse grey surface per unit area, equal to its emission plus the reflected part of the irradiation G. Absorptivity is taken equal to emissivity.
Calculator
- Emitted part, εσT⁴367.4 W/m²
- Reflected part, (1 − ε)G100 W/m²
- Net radiation leaving the surface, J − G−32.56 W/m²
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- The surface sends out 467.4 W/m², of which 78.6 % is its own emission and the rest reflected irradiation.
- The net loss J − G is −32.56 W/m²; it equals ε(σT⁴ − G), the surface’s own emission less what it absorbs.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (W/m²) | Local step | Change in result |
|---|---|---|---|---|---|---|
| T Surface temperature | 100 to 2,000 K | 104.5 | 725,900 | 725,800 | +10% | +36.5 % |
| G Irradiation on the surface | 0 to 100,000 W/m² | 367.4 | 20,370 | 20,000 | +10% | +2.14 % |
| ε Emissivity | 0 to 1 | 459.3 | 500 | 40.7 | +10% | −0.697 % |
Sweep of Irradiation on the surface
| Irradiation on the surface (W/m²) | Radiosity (W/m²) |
|---|---|
| 0 | 367.4 |
| 12,500 | 2,867 |
| 25,000 | 5,367 |
| 37,500 | 7,867 |
| 50,000 | 10,370 |
| 62,500 | 12,870 |
| 75,000 | 15,370 |
| 87,500 | 17,870 |
| 100,000 | 20,370 |
Sweep one variable
Variables and how each one contributes
Radiosity
What the equation gives you. Everything else feeds it.
Emissivity
The emissivity of the surface, between 0 and 1. More emissivity swaps reflected irradiation for emission, which raises J when σT⁴ is above G. Raising it by 10 % (to 0.88) moves the result by −0.697 %, from 467.4 to 464.2 W/m².
Surface temperature
The surface temperature, in K. Raises the emission as the fourth power. Raising it by 10 % (to 330) moves the result by +36.5 %, from 467.4 to 638 W/m².
Irradiation on the surface
The irradiation on the surface, in W/m². Raises the reflected part in proportion to 1 − ε. Raising it by 10 % (to 550) moves the result by +2.14 %, from 467.4 to 477.4 W/m².
Worked example with the values above
- Emission: εσT⁴ = 0.8 × 5.67037×10−8 × 300⁴ = 367.44 W/m².
- Reflection: (1 − ε)G = 0.2 × 500 = 100 W/m².
- J = 367.44 + 100 = 467.44 W/m².
Assumptions and limits
- Blackbody or diffuse grey behaviour as stated, in a vacuum or non-participating medium.
- Absolute temperatures and the exact values of σ, h, c and kB given on the page.
Common mistakes
- Using °C in Planck’s law or Wien’s law.
- Mixing per-metre and per-micrometre spectral units.
- Treating a grey surface as if it followed the blackbody spectrum without considering emissivity.
Statistics and uncertainty
The radiation laws for blackbodies are exact, but real-surface emissivity and its variation with wavelength add uncertainty of 10 % or more, and measured view factors depend on exact geometry.
Where it is used
- Infrared sensing, lamps and radiant heaters.
- Setting up radiosity networks and linearised radiation coefficients.
Maths you need
- Planck’s law: spectral emissive power of a blackbody
- Wien’s law: the peak wavelength is inversely proportional to T
- Radiosity: the total radiation leaving a surface per unit area