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

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

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

(OP)
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

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

(OP)
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?

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

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



 

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