# Trying to calculate the length of a tube to heat Ar gas

If one were trying to heat Argon gas from ambient (~20C) through a mild steel tube of some diameter 'd' how long would it need to be? Additional unknown includes flow rate of Ar gas so some general function would be adequate. Unfortunately my thermo-book is limited and does not go into enough detail to solve this problem.

I played around with a few static equations to get a general idea of J/s heat transfer from the steel wall to the Ar gas but this does not account for flow rate however it could likely be converted with some work. Rather than spend too much time on this I was hoping someone could chime in with a heat transfer by convection equation for a laminar flow of Ar in a tube of some radius 'r' and flow-rate 'f' where the tube itself is in a steady state at 800C. It could be assumed that due to the nature of how the tube is heated and the thermal conductivity of steel being 3 orders of magnitude greater than Ar that this temperature will remain constant throughout the process.

I expect the length of the tube of any substantial diameter (greater than 1/4") will likely need to be very long due to the nature of Ar's thermal conductivity. To help aid in heat transfer it would seem reasonable to add steel wool to the inside of the tube in order to create turbulent flow and add a large surface area with minimum 'thickness' of the gas to the thermally conducting steel. To what extent would probably be very difficult to calculate but if a reasonable length tube can be figured for laminar flow then the addition of the steel wool should greatly increase the efficiency of a tube of the same length, hopefully it doesn't work out to something like a mile long :)

• For heat transfer coefficients, you can check the wiki on HTCs, it's got them for laminar and turbulent pipes. Also, if the Reynolds number is too low (less than 2000-4000) you won't be able to sustain turbulence. If it's above 4000, turbulence will form naturally but can be helped along with sharp edges and sudden expansions. – user3823992 Oct 24 '14 at 2:18
• I came up with 4 degree K per meter of 1/4" ID tube with laminar flow. My needs would require 160+ m which is out of the question. Either way, thank you for the suggestions! – eatscrayons Oct 24 '14 at 21:56
• Yeah that doesn't sound quite right... I'll take a stab at the equations in the morning. I doubt that you'd need more than a meter. – user3823992 Oct 25 '14 at 5:51
• I agree, just saw the thermal conductivity for air and it is about the same so 160 m is unreasonably large. I am throwing away the text book formulas and going back to deriving my own. – eatscrayons Oct 25 '14 at 15:11