Net radiation exchange and gray surfaces
Emission and absorption must both enter a net radiative heat balance.
Key knowledge
A diffuse opaque gray surface has emissivity ε and thermal absorptivity ε in the gray thermal model. In a uniform black enclosure, its net outward rate is Q̇_out=εσA(T_s⁴−T_e⁴). For two infinite parallel diffuse gray surfaces viewing only one another, the net flux from surface 1 to 2 is σ(T₁⁴−T₂⁴)/(1/ε₁+1/ε₂−1). The second relation includes repeated reflections, so an arbitrary gray environment cannot always be replaced by the black-enclosure formula.
Values and equations
Q̇_out=εσA(T_s⁴−T_e⁴); q_1→2=σ(T₁⁴−T₂⁴)/(1/ε₁+1/ε₂−1)
- Q̇_out
- Net outward radiant heat-transfer rate to the black enclosure W
- q_1→2
- Net radiant flux from parallel surface 1 to surface 2 W m⁻²
- ε,ε₁,ε₂
- Gray emissivities and, in this thermal model, absorptivities 1
- σ
- Stefan–Boltzmann constant W m⁻² K⁻⁴
- A
- Radiating area m²
- T_s,T_e,T₁,T₂
- Absolute surface, enclosure and two-plane temperatures K
Conditions and scope
- The enclosure relation assumes black thermal irradiation filling the surface’s outward hemisphere, an isothermal surface, no participating medium, and gray diffuse optical properties over the relevant thermal wavelengths.
- The parallel-plane relation assumes uniform temperatures, opaque diffuse gray surfaces, no edge losses or participating medium, and 0<ε₁,ε₂≤1.
- Use absolute temperatures; the enclosure formula allows 0≤ε≤1. These models do not infer thermal infrared emissivity from visible colour.
Sources · 2
References
Sources retain their recorded scope. A source link alone does not establish verification of every statement.
Evidence and review
Gray-surface radiation exchange with a black isothermal enclosure and two large parallel gray planes under the stated geometric conditions.
2026-10-10 · Independent Chemistry, Biology and Earth/Cosmos editor (AI editorial review). Source checks and independent AI editorial review of compact reference claims, equations, units, conditions and conceptual mappings. This is not human specialist certification, laboratory accreditation, whole-book verification, or a claim that all possible foundational knowledge is present.
Foundational review
2026-10-10 · Independent AI editorial inspection of this new compact reference entry, its equations, applicability, sources and knowledge connections.
Sources from other places
Scope or convention differs
Diffuse opaque gray-surface networks account for reflection and give εσA(Ts⁴−Te⁴) against a large black enclosure.
The parallel-plane expression follows by specializing the two-surface network to equal areas and unit view factor; it is not printed separately here.
Indian Institute of Science · NPTEL
- Heat and Mass Transfer · Radiation module IndiaEnglish
Radiation exchange networks and large enclosure, PDF pp20–24
- Heat and Mass Transfer · Radiation module
Entry details
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- foundation-physics-gray-radiative-exchange
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