I am looking to gain some sort of direction for a project I am working on. We need to chill a 12" diameter steel tube (10" ID) from 400* to around 200*. To do so, we are spraying water onto the steel tube...but within the original machine design have only been able to hit 250* (note: the tube is 10-20' long and moves through my cooling 'tank' at a constant rate). Thus, I am looking for a way to calculate how much water, time, spray, etc we need to cool the steel down to the target temperature.

I understand there are HUGE amounts of variables when attempting a problem like this, but I just want to get somewhat close. any help or direction would be appreciated. I have many more details I can provide.