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I believe it has to do with the calculated radiation heat transfer between surfaces. In non-convex geometry, there will exist (at least) two surfaces which cannot 'see' one another, and thus it is not possible for them to trade/balance radiation heat transfer. In convex geometry, every wall can 'see' every other wall and thus can transfer heat.

An example of non-convex geometry is an L Shape. The right wall of the upper part and the right wall of the lower part cannot 'see' on another to transfer heat. For convex, a box or a pentagon, all of the surfaces can 'see' each of the other surfaces; and no heat balance/transfer problem.