Fire heaters : piping

The Material Balance:

"Input = Output + Accumulation."

It is not so much that you want equal flow but that you absolutely do not want to starve one of the tube passes.

You have fire inside that heater and the flame is "impinging" on the tubes. The fluid inside the tube carries away some of the heat by absorbing it as a part of the requirement of the process. If there was no flow in one of the tube passes then that set of tubes would get hotter and hotter and could fail causing a serious fire and possibly the death of one or more workers.