Convection Boundary Condition¶

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

$q_n$ - 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¶

Use this boundary condition when convection controls the heat transfer between the solid and the fluid. You do not model the detailed fluid dynamics. Only the coefficient $h$ and the reference temperature $T_\text{amb}$ represent the fluid.

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,
)