Imagine a rectangular box that is thermally insulated on all sides except for one, where a heat flux is applied.
Now imagine the same box with the same conditions on all sides except that the side with the heat flux is now exposed to open air at a certain temperature and flowing with a certain velocity. The heat flux is still applied only to the surface of the box, but this surface is no longer a boundary of the domain of the overall problem.
As i see it there are two strategies to handle this:
Treat the problem as two separate domains with information passing through the interface between the air and the box.
Convert the surface heat flux (in some way) into an equivalent volumetric source term which applies only to the elements at the interface between the box and the air.
I want to know if there is a canonical strategy for approach #2. How can i convert surface fluxes into internal source terms such that convergence is assured in the limit as the mesh is refined?