Looking at the picture above, hose #4 connects through fitting 6 to water pipe circled in green. The other end of hose #4 goes to the bottom of the radiator on the left side. This smaller hose takes hot coolant from the water pipe to the radiator all the time and is not regulated by the thermostat. Its not big enough to cool the entire engine but it helps maintain a constant temperature across the length of the engine.
Put another way, the water pipe is an outlet. It is fed by the block, the small port on the side of the head between cyl 2 and 3, and by hose 22 coming from the heater. When the thermostat is fully closed, this water pipe functions as a small bypass to prevent pressure from building up in the head and block.
So if we plug up the small port between cyl 2 and 3, air would also get trapped in the head and cause that area to overheat.
I think you're telling me i got the direction of flow wrong...
Well i dont think so, please have a look at the direction of flow arrows on the hoses #23 + #22, if water was to be flowing from the block out the green connector we would have a collision of water there.
BMW calls the hoses by these names also:
22 : Water hose outlet (Outlet from the heater core)
23 : Water hose inlet (Inlet to the heater core)
The hose #4 is the circuits connection to the expansion tank, and the system will draw from this resaouir when ever it needs to.
Also have a look at the pump propeller wheel which i added for refrence. The engine would have to be turnng backwards for the water to flow in your suggested direction :-P