Radiation Exchange Simulator: Thermal Radiation Between Surfaces

simulator advanced ~12 min
Loading simulation...
q = 24,300 W/m² — net radiation from hot to cold surface

A 1000 K surface with ε = 0.85 radiating toward a 400 K surface through view factor 0.5 transfers about 24,300 W/m² — the T⁴ dependence makes radiation extremely powerful at high temperatures.

Formula

E = ε × σ × T⁴ (Stefan-Boltzmann law for grey body)
q_net = ε₁ × σ × F₁₂ × (T₁⁴ − T₂⁴)
λ_max = 2898 / T (Wien’s displacement law)

The Fourth-Power Law

Thermal radiation obeys the Stefan-Boltzmann law: emissive power scales as the fourth power of absolute temperature. This means a surface at 2000 K radiates 16 times more energy than one at 1000 K. At room temperature, radiation is a minor player compared to convection, but in furnaces, rocket nozzles, and stellar atmospheres, it utterly dominates. The simulation animates photon streams whose intensity scales with T⁴, making this nonlinear relationship viscerally clear.

View Factors and Geometry

Not all radiation leaving a surface reaches the target. The view factor F₁₂ captures the geometric fraction — determined by surface size, distance, and orientation. Two large parallel plates close together approach F = 1, while small distant surfaces have F near 0. Computing view factors analytically involves double-area integrals, but standard charts and formulas cover common configurations. The simulator lets you adjust F₁₂ and immediately see its impact on net heat exchange.

Emissivity and Real Surfaces

A perfect blackbody has emissivity ε = 1, but real surfaces range from polished metals (ε ≈ 0.03–0.1) to oxidized metals and ceramics (ε ≈ 0.7–0.95). Emissivity depends on wavelength, temperature, and surface finish. Engineers exploit low-emissivity coatings for radiation shields (spacecraft MLI blankets) and high-emissivity coatings for efficient radiators (satellite thermal panels). This simulation shows how even small emissivity changes cascade through the T⁴ law.

Industrial and Space Applications

In steel mills, radiant furnaces transfer megawatts purely through radiation. In space, with no convective medium, radiation is the only way to reject waste heat — the International Space Station uses large radiator panels. Infrared cameras exploit thermal radiation for non-contact temperature measurement. Understanding radiative exchange is essential for thermal design in these extreme environments, and this simulator provides the interactive foundation.

FAQ

What is the Stefan-Boltzmann law?

The Stefan-Boltzmann law states that the total emissive power of a blackbody is proportional to the fourth power of its absolute temperature: E = σT⁴, where σ = 5.67 × 10⁻⁸ W/(m²·K⁴). For real surfaces, emissivity ε scales this: E = εσT⁴. The T⁴ dependence means radiation becomes dominant at high temperatures.

What is a view factor?

The view factor F₁₂ is the fraction of radiation leaving surface 1 that directly reaches surface 2. It depends purely on geometry: the size, shape, and relative orientation of the surfaces. View factors obey the reciprocity rule (A₁F₁₂ = A₂F₂₁) and the summation rule (all view factors from a surface sum to 1).

What is Wien's displacement law?

Wien's law states that the peak wavelength of blackbody radiation is inversely proportional to temperature: λ_max = 2898/T μm. At 300 K (room temperature), the peak is at ~10 μm (infrared). At 5800 K (Sun), the peak is at ~0.5 μm (visible light).

How do radiation shields work?

Radiation shields are thin, low-emissivity surfaces placed between hot and cold surfaces. Each shield adds thermal resistance, reducing net radiative transfer. N shields with emissivity ε reduce heat transfer by approximately a factor of (N+1). This principle is used in spacecraft insulation and cryogenic Dewar flasks.

Sources

Embed

<iframe src="https://homo-deus.com/lab/heat-transfer/radiation-exchange/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub