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Thermal boundary conditions

User-selectable thermal boundary conditions apply only to walls of the solved thermal domain, which can bound fluid or a conducting solid. Fluid walls are already impermeable and no-slip, and their default thermal condition is adiabatic. fixed_temp, heat_flux, and radiative change only that thermal wall behavior. At non-wall fluid boundaries, such as inlets and outlets, thermal behavior is defined by the flow boundary condition and cannot be selected independently.

Fixed temperature

fixed_temp applies temperature as a Dirichlet condition on the selected wall faces. It fixes their temperature; no heat-flux magnitude is prescribed.

Heat flux

heat_flux prescribes heat transfer per unit selected area. Positive flux enters the solved thermal domain and negative flux removes heat from it. A zero value is an explicit adiabatic condition.

The requested flux acts over the meshed patch, so the associated power is

\[ P = q^{\prime\prime} A_{\mathrm{patch}}. \]

Here, \(P\) is the total heat-transfer rate in watts, \(q^{\prime\prime}\) is the API flux in \(\mathrm{W/m^2}\), and \(A_{\mathrm{patch}}\) is the meshed selected area in \(\mathrm{m^2}\).

Use the physical selected area when converting a known power to \(\mathrm{W/m^2}\), and resolve the patch sufficiently for its meshed area to represent the intended surface.

Far-field radiation

radiative exchanges thermal radiation with a far-field environment and optionally absorbs incident irradiation. The calculation uses:

  • surface absolute temperature \(T_{\mathrm{s}}\);
  • far-field absolute temperature \(T_{\mathrm{ambient}}\);
  • API emissivity \(\varepsilon\);
  • API absorptivity \(\alpha\); and
  • API incident_irradiation \(G\).

For these values, the net outward radiative flux is

\[ q_{\mathrm{out}}^{\prime\prime} = \varepsilon \sigma \left(T_{\mathrm{s}}^4 - T_{\mathrm{ambient}}^4\right) - \alpha G, \]

Here, \(\sigma\) is the Stefan–Boltzmann constant, and both \(q_{\mathrm{out}}^{\prime\prime}\) and \(G\) are in \(\mathrm{W/m^2}\). API temperatures are supplied in \({}^\circ\mathrm{C}\) and converted to kelvin internally.

Emission and absorption are independent API inputs. incident_irradiation must already be the irradiation projected onto the face; Vanellus does not calculate source direction, visibility, or shadowing. It also does not model radiation exchange between surfaces inside the domain.

The emitted term is nonlinear. Vanellus linearizes it using the previous iteration’s wall-face temperature and updates the condition as the energy solution changes.

Adiabatic walls and interfaces

An adiabatic wall has zero normal conductive heat flux. Unconfigured exterior walls and interfaces with insulating components use this behavior. Fluid–conducting and conducting–conducting interfaces are not walls and receive no boundary condition: they form one continuous thermal solve.

See also