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Heat Flux Boundary Condition

The heat flux boundary condition prescribes the normal heat flux across a boundary (Neumann condition): $$ q_n = -\hat{n} \cdot (\kappa \nabla T). $$

  • \(q_n\) - prescribed outward normal heat flux [W/m\(^2\)]
  • \(\hat{n}\) - outward unit normal
  • \(\kappa\) - thermal conductivity [W/(m K)]
  • \(T\) - solid temperature [K]

A positive value of \(q_n\) corresponds to heat leaving the solid, while a negative value corresponds to heat entering the solid.

Applicability

This boundary condition is applicable when the heat exchange at a boundary is known a priori, for example from experimental data or simplified models, and does not depend on the local surface temperature.

Typical use cases

  • Applied surface heat load or cooling rate
  • Specified heat transfer from external sources (e.g. heaters, lasers)

Example

condition = HeatFluxBoundaryCondition.Constant(
    name = "My Heat Flux Boundary Condition",
    marker = my_marker,
    normal_heat_flux = 1000,
)

cff_normal_heat_flux = CffConstantScalar(value=1000)

condition = HeatFluxBoundaryCondition(
    name = "My Heat Flux Boundary Condition",
    marker = my_marker,
    normal_heat_flux = cff_normal_heat_flux,
)