A radiation heat-transfer coefficient is a convenient way to express radiative exchange in a form resembling Newton’s cooling law. Unlike a fixed material constant, its value depends on surface emissivity and the absolute temperatures of the surface and its surroundings. A coefficient copied from an old material table can therefore be meaningless without the temperature range, surface condition, geometry, and assumptions behind it.
Calculate an effective coefficient for the stated conditions
For a gray surface exchanging radiation with a large black enclosure, the net radiative heat flux can be written as q/A = εσ(Ts⁴ – Tsur⁴). Factoring the fourth-power difference gives an equivalent coefficient: hr = εσ(Ts + Tsur)(Ts² + Tsur²). Temperatures must be absolute (kelvin in the SI form), and the Stefan-Boltzmann constant is 5.670374419 × 10⁻⁸ W/(m²·K⁴), per NIST’s 2022 CODATA value.
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The examples assume emissivity 0.90 and surroundings at 293 K. They are calculated comparison points, not published material properties. The assumed emissivity is not a recommendation for a real surface: oxidation, coating, finish, wavelength, temperature, and contamination can change emissivity. The NASA technical report presents the same linearized form and also distinguishes a one-gray-surface/black-surroundings case from exchange between two gray surfaces.
What the coefficient does and does not mean
The effective coefficient converts a radiative temperature difference into an equivalent heat-flux relationship for the stated temperature pair. If Ts and Tsur are close, it can simplify a local calculation. If temperatures vary substantially, the coefficient changes with them; do not treat one value as constant over a large operating range without checking the resulting error.
Emissivity describes how a real surface emits radiation relative to an ideal blackbody under specified conditions. It is not determined by the bulk material name alone. A polished metal, an oxidized surface, and the same metal with a high-emissivity coating can behave very differently. Surface condition can also change over time through scale, dust, moisture, wear, or chemical exposure. Use measured or authoritative emissivity data for the actual surface, temperature, and spectral context.
The table’s black-enclosure assumption is also important. Two facing gray surfaces require an effective emissivity and a view factor based on their geometry. Partial view, shields, openings, and surrounding objects can alter net exchange. Radiation does not replace convection or conduction; a complete thermal balance may need all three modes, plus transient storage and external heating.
Use the equation carefully
Keep consistent units and absolute temperature. In SI, use kelvin, watts, square metres, and the NIST value of σ. For a one-gray-surface/black-surroundings model, enter the surface emissivity once. For two real surfaces, do not simply multiply two emissivities; use the appropriate effective-emissivity expression and view factor for the enclosure configuration. State each assumption so another engineer can reproduce the calculation.
For an engineering design, document surface identification, emissivity source, temperature bounds, geometry, view factor, and whether convection and conduction are included. Run a sensitivity check for uncertain emissivity and temperature. Safety-critical thermal design should be reviewed against the applicable validated method and test data; these example coefficients are not design approval.
As a quick reasonableness check, the effective coefficient should rise when either absolute temperature rises under the stated assumptions, because the factored temperature term increases. It should also scale linearly with emissivity in this simplified expression. If a spreadsheet produces a negative coefficient for a positive emissivity, or changes when Celsius is substituted for kelvin, revisit the equation and units before relying on the result.
- Use absolute temperature in the fourth-power law.
- State emissivity and surrounding-surface assumptions.
- Account for view factors when both surfaces are gray.
- Recalculate when temperature or surface condition changes.
Browse the reference chart collection, explore workshop tool guides, and see infrared heater equipment for a separate application of thermal energy.
References
NIST publishes the CODATA Stefan-Boltzmann constant. NASA’s thermal radiation appendix derives the linearized coefficient and discusses effective emissivity for two gray surfaces.
