Radiation Boundary Condition¶

The Stefan-Boltzmann law models the radiative heat transfer at a boundary: $$ q_n = -\hat{n} \cdot (\kappa \nabla T) = \epsilon \, \sigma \, (T^4 - T_\text{amb}^4). $$

$q_n$ - outward normal heat flux [W/m$^2$]
$\hat{n}$ - outward unit normal
$\kappa$ - thermal conductivity [W/(m K)]
$\epsilon$ - surface emissivity ($0\le\epsilon\le 1$)
$\sigma$ - Stefan-Boltzmann constant = $5.670374419\times10^{-8}$ W/(m$^2$ K$^4$)
$T$ - solid surface temperature [K]
$T_\text{amb}$ - surrounding radiative temperature [K]

Applicability¶

Use the radiation boundary condition when thermal radiation controls the heat transfer between a solid surface and its surroundings. Under this boundary condition, you do not model the surrounding medium. Only the radiative temperature $T_\text{amb}$ represents it.

Typical use cases¶

Furnace and induction-heating workpieces at temperatures where $\epsilon \sigma T^4$ dominates the surface loss.
Spacecraft thermal control — radiative coupling to deep space ($T_\mathrm{amb} \approx 3\,\mathrm{K}$).
Filament / lamp / heating-element studies with bright surfaces.
Combined convection + radiation on hot surfaces — add both conditions on the same marker.

Example¶

condition = RadiationBoundaryCondition(
    name = "My Radiation Boundary Condition",
    marker = my_marker,
    emissivity = 0.8,
    ambient_temperature = 343.0,
)