radiation

name	radiation
description	Thermal radiation heat transfer — Stefan-Boltzmann law, emissivity, view factors, radiation networks, blackbody/gray body, combined radiation+convection, radiation shields, solar radiation.
metadata	{"priority":6,"promptSignals":{"phrases":["radiation","thermal radiation","emissivity","view factor","Stefan-Boltzmann","blackbody","radiation heat transfer"],"minScore":4}}

Radiation Heat Transfer — Complete Skill

Fundamentals

Thermal radiation: electromagnetic waves, λ = 0.1-100μm (infrared mainly for engineering) Speed of light: c = 3×10⁸ m/s, c = λν (wavelength × frequency) Does NOT require medium (works in vacuum)

Stefan-Boltzmann Law (blackbody): E_b = σT⁴ [W/m²] σ = 5.67×10⁻⁸ W/(m²·K⁴) [Stefan-Boltzmann constant] Note: T must be in KELVIN always

Planck's Law (spectral distribution): E_bλ = C₁/(λ⁵ × (exp(C₂/λT) - 1)) C₁ = 3.742×10⁸ W·μm⁴/m², C₂ = 1.439×10⁴ μm·K

Wien's Displacement Law (peak wavelength): λ_max × T = 2898 μm·K Sun (5800K): λ_max = 0.5μm (visible — efficient solar) Room temp (293K): λ_max = 9.9μm (far infrared)

Real Surfaces (Gray, Diffuse Approximation)

Emissivity ε: fraction of blackbody emission actually emitted E = ε × σT⁴ (emissive power of real surface) G = irradiation (incident radiation from all directions) α = absorptivity, ρ = reflectivity, τ = transmissivity (α+ρ+τ = 1)

Gray surface assumption: ε = α (absorptivity = emissivity, independent of λ) Diffuse surface: emits/absorbs uniformly in all directions (independent of angle)

Typical emissivities ε:

Surface	ε
Blackbody	1.00
Oxidized steel	0.60-0.80
Polished aluminum	0.04-0.07
Oxidized aluminum	0.10-0.30
Painted surfaces	0.80-0.95
Human skin	0.95
Brick	0.85-0.95
Glass (window)	0.84-0.90
Snow	0.82-0.92
Polished gold	0.01-0.03
Polished copper	0.02-0.05

Radiation Between Two Surfaces — View Factors

F₁₂ = fraction of radiation leaving surface 1 that strikes surface 2

Reciprocity: A₁F₁₂ = A₂F₂₁ Summation rule: ΣF₁j = 1 (for enclosure) Key view factors:

• Infinite parallel plates: F₁₂ = 1
• Small surface in large enclosure: F₁₂ = 1
• Coaxial cylinders (1=inner, 2=outer): F₁₂ = 1, F₂₁ = A₁/A₂
• Infinite concentric cylinders: same as coaxial
• Two small areas, angle θ: F₁₂ = cosθ₁cosθ₂/(πr²)×dA₂

Radiation from disk to disk (coaxial): F₁₂ = 0.5×(S - √(S²-4(r₂/r₁)²)) where S = 1+(1+R₂²)/R₁², R=r/L (From radiation handbooks — lookup for complex geometries)

Net Radiation Exchange (Gray, Diffuse Enclosure)

Radiosity J: total radiation leaving surface (emitted + reflected) J = εσT⁴ + ρG = εσT⁴ + (1-ε)G

Net heat flux from surface: q = (J-G)×A = (E_b - J)/((1-ε)/(εA)) [surface resistance R_surface = (1-ε)/(εA)]

Space resistance (between surfaces): R_space,12 = 1/(A₁F₁₂) [geometric resistance]

Net heat transfer: q₁₂ = (J₁-J₂)/(1/(A₁F₁₂)) = A₁F₁₂(J₁-J₂)

Two Gray Surfaces (Important Cases)

Two infinite parallel plates: q/A = σ(T₁⁴-T₂⁴) / (1/ε₁ + 1/ε₂ - 1)

Small convex object (1) in large enclosure (2): q₁ = ε₁A₁σ(T₁⁴-T₂⁴) [F₁₂=1, A₁<<A₂ → surface resistance of enclosure = 0]

Two large concentric cylinders/spheres: q = A₁σ(T₁⁴-T₂⁴) / (1/ε₁ + (1-ε₂)/ε₂ × A₁/A₂)

General two-surface enclosure: q₁₂ = σ(T₁⁴-T₂⁴) / ((1-ε₁)/(ε₁A₁) + 1/(A₁F₁₂) + (1-ε₂)/(ε₂A₂))

Radiation Shields

Shield between two parallel plates (same area, shield emissivity ε_s): With N shields: q = σ(T₁⁴-T₂⁴) / (1/ε₁ + 1/ε₂ - 1 + N×(2/ε_s - 1)) Low ε_s (polished) → dramatic reduction in q Mylar (aluminized): ε ≈ 0.03 → 1 shield reduces q by ~32× vs. black surfaces

Combined Radiation + Convection

q_total = q_conv + q_rad = h_conv×A×(T_s-T_∞) + ε×σ×A×(T_s⁴-T_surr⁴)

Linearized radiation coefficient: h_rad = εσ(T_s+T_surr)(T_s²+T_surr²) [W/(m²K)] Valid for small ΔT only; use exact form (T⁴ difference) for large ΔT

Solar Radiation

G_solar = 1353 W/m² (solar constant at top of atmosphere) Surface intensity: G_s = G_solar × cos(θ_incidence) × τ_atmosphere τ_atm ≈ 0.7-0.9 (clear sky), 0.3-0.5 (cloudy)

Solar absorptivity α_solar ≠ thermal emissivity ε_thermal (different wavelength ranges) White paint: α_solar = 0.12, ε_thermal = 0.90 (reflects sun, emits IR — good for cooling) Black paint: α_solar = 0.95, ε_thermal = 0.90 (absorbs sun and emits IR) Polished Al: α_solar = 0.10, ε_thermal = 0.05 (reflects sun, poor IR emitter — hot spacecraft surface)

Output

Provide: q [W], view factors F₁₂, radiosity J, h_rad [W/m²K] if linearized, comparison with convection magnitude.