plumberet
You need to think about the purpose of the bridge wall. It is there to force the flue gas flow in a particular path and concurrently generate a pressure drop which affects the draft through the furnace as a whole. It is like designing a piping system but it's not tubular. You have to understand the flows through the furnace, where the radiant loads and convective flows have to be. Then you choose to put the wall where it does the most good for your design concept and size it accordingly.