1997 Hyundai Tiburon heater core

That is not something any mechanic has ever wondered about. If you really want to know which is in and which is out, get a copy of the manufacturer's service manual. They usually have a "Theory of Operation" section that shows a diagram of coolant and oil circulation.

First, you'd be smart to not remove any hose from the heater core. They get stuck on and should be cut off when you're replacing the hoses. If you twist and tug on them, you can break the solder bond when brass tubes are used. A lot of newer heater cores have plastic pipes that can crack easily. Remove one of the hoses from the engine instead, then run water from a garden hose into that hose, then into the nipple it came from. Let the water run out of the radiator cap, then force water into the radiator too to push it out the other way. Remove the lower radiator hose to let the water drain out. We don't like to open radiator petcocks because that takes too long to drain, and a lot of them break apart inside and will have a constant drip about once every five seconds. The only way to solve that is replace the radiator.

Nope. Pick the hose that's easiest to remove. When you push water into the hose from a garden hose, the water will go through the heater core one way. If it comes out the radiator instead of the nipple on the engine, just hold the palm of your hand over the radiator's opening.

Push water into the nipple, and if necessary, hold your hand on the radiator, then the water will go through the heater core the other way and come out the hose you have removed.