Well... I agree with ya rolf that the surface area of the tube is greater than that of the element, but here's my thinking..
Lets talk about temperature transfer effectiveness or "influence" on the air.
Say... the surface area of the small tube is 30x the area of the heater.
Per cubic centimeter of area, the element has a much greater influence on the air passing through than the air that contacts the walls of the tube.
I don't know physics. I'm not even the best at math... So I cant write down how it works..
All that I know is, I don't have to really worry about the tube temp.
Why?
#1. Well... first of all... You're hair dryer takes 30 seconds to get to its max temp? Well this thing blows air HOTTER than target within 3 seconds of operation.
#2 Since it can do that, then all is needed is a simple proportional control to not let it go over during the initial start up and keep it near target.. It is obvious that the element will be working a little harder at the beginning when the tube is at RT to get the target temp... but the power delivered to the element is calculated by the circuit and the target temp is held.
As the tube gets a little warmer with periodic operation, of course the target temp will be reached with less work required by the element, that amount of work again is determined by the controller.
So without really understanding the physics of it... I have witnessed, first hand, that it is totally possible to achieve what I am talking about here.
Ohh and the air flow is produced by a box (computer type) fan.
Volume or air and rate of flow? I have no ****ing clue...
Like I said... physics isn't my thing.... But I am a specialist at ghetto improvisation.
I hope you get it working to your liking. Keep us posted, I'll like to hear about your progress, I don't mind being proved wrong, that is part of learning. Much of my physics education is by osmoses because my school learning was mostly forgotten many decades ago.