Multiple convective boundary conditions on the same selection

This section describes how the thermal solver calculates convective heat flow and post-processing outputs when multiple convective boundary conditions are applied on the same geometric selection.

The total convective heat flow on an element, denoted as i, is the sum of contributions from various boundary conditions (BC), labeled as b. Each BC may have multiple fluid elements, j, connected to i through convective conductances Gij:

where Ti and Tj are temperatures for the solid element i and fluid element j, respectively.

The convective heat flow contribution from each BC can also be expressed as:

where:

  • h is the input heat transfer coefficient (HTC) of the BC.
  • A is the area of the BC.
  • C is the area correction factor.
  • Ti(fb) is the fluid temperature for element i from BC b.

To align with the first equation, the following relationships are established:

In post-processing for a single BC, the output convection coefficient is given by:

and the area corrected convection coefficient is:

When dealing with multiple BCs, the objective is to average h, A, and C such that:

The averaged values are used in post-processing outputs, with hi as the convective flux output, hi Ci as the area corrected convective flux output, and Ci as the area correction factor. The averaged fluid temperature is calculated as:

So that, the convective heat flow for element i is:

The averaged area Ai is defined as:

This indicates that the area corrected HTC is the sum of the area corrected HTCs from the contributing BCs:

The averaged area correction factor is then defined as:

Which leads to the HTC being the sum of the HTCs from the contributing boundary conditions.