how long should the pipe be in order to cool the air by this amount?

[hhtguy]

Air of temperature 80 F enters a copper tube with inner diameter of 2 mm. The copper tube is of fixed temperature of -50 F.

Air speed is 8 m/s in order to get the flow rate I want.

How long should the tube be in order to cool the air to at least 0 F when it comes out of the end of the tube?

I'm an electrical engineer so this is not an area I'm familiar with. I don't need an exact answer, a ball park figure will suffice. Thanks

 

[hhtguy]

I tried to use Dittus–Boelter correlation and got a Reynold number of 500,000,000. Prandtl number of 0.75.

Nusselt number =Nu = 0.023 * Re^0.8 * 0.75^.33 = 190,000

Is that even close?

 

[zekeman]

If the tube temperature remains constant, then you get the 1 dimensional energy equation

rho*Pi*D^2/4*cp dT/dt=h*Pi*D*(Tw-T)
or
rho*D/4*Cp/h*dT/dt+T=Tw
rho = gas density
Tw wall temperature

Cp=specific heat
D=diameter
h=film conductance
t= time to reach Temperature

For convenience,let
Q=rho*D/4*Cp/h

The solution

T=Tw+(Ti-Tw)*e^-(t/Q)

For any value of gas temperature T, you solve this for t
Now since
x=vt

x is the distance down the pipe that coincides with the temperature you reach