Convection Boundary Condition¶

The convection boundary condition models heat transfer between a solid surface and a surrounding fluid through convection. The convective heat flux at the boundary is described by Newton’s law of cooling: $$ q_n = -\hat{n} \cdot (\kappa \nabla T) = h (T - T_\text{amb}). $$

$q_n$ - outward normal heat flux [W/m$^2$]
$\hat{n}$ - outward unit normal
$\kappa$ - thermal conductivity [W/(m K)]
$h$ - convective heat transfer coefficient [W/(m$^2$ K)]
$T$ - solid surface temperature [K]
$T_\text{amb}$ - ambient fluid temperature [K]

Applicability¶

This boundary condition is applicable when heat transfer between the solid and the surrounding fluid is dominated by convection and the detailed fluid dynamics are not explicitly modeled. The influence of the fluid is represented solely by the coefficient $h$ and the reference temperature $T_\text{amb}$.

Typical use cases¶

Motor / transformer housings cooled by ambient air or forced airflow — $h$ taken from correlations or CFD pre-studies.
Power-electronics heat sinks with air or liquid coolant.
Quench / cool-down studies in induction heating where the workpiece is plunged into a coolant after the heating cycle.
Pipe / duct walls in heat exchangers when the fluid side is not explicitly modelled.

Example¶

condition = ConvectionBoundaryCondition(
    name = "My Convection Boundary Condition",
    marker = my_marker,
    convection_efficiency = 7.0,
    temperature_medium = 343.0,
)