Radiation Boundary Condition¶

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

$q_n$ - 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¶

The radiation boundary condition is applied when heat transfer between a solid surface and its surroundings is dominated by thermal radiation. Under this boundary condition, the surrounding medium is not modeled explicitly; its influence is represented solely by the radiative temperature $T_\text{amb}$.

Typical use cases¶

High-temperature heat transfer where radiation is significant
Surfaces exposed to open environment or large enclosures
Thermal problems in vacuum (no convection)
Combined convection–radiation boundary modeling

Example¶

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