# Temperature drop along pipe

1. May 8, 2014

### davidgrant23

Hi there,

I'm trying to find out the temperature drop of flue gas in an uninsulated quartz pipe in ambient air. I am fairly confident with my approach but receive erroneous answers.

I have approached the problem as follows:

1) Calculate the prandtl number
2) Calculate the Re number
3) Calculate the Nu number (for laminar flow in a pipe)
4) Calculate hi (hi = Nu*k/D)
5) Calculate the thermal resistance Rquartz = ln(ro/ri)/(2*pi*k)
6) Calculate the thermal resistance inside convection = 1/(hi*2*pi*ri)
7) Solve for the inside and outside wall temperatures using the following non-linear eqns:
(Tflue-Tinside)/Rinside = (Tinside-Toutside)/Rquartz = 2*pi*ro*(1.32/d^0.25)*(Toutside-Tair)^5/4

The last term comes from the equation for laminar flow to get ho.
8) Calculate ho using ho = 1.32*(Toutside-Tair/D)^0.25
9) Calculate Ro = 1/(ho*2*pi*ro)
10) Calculate U = 1/(Ao*Rtotal)

The problem I have is that the wall temperatures I calculate are odd (inside wall more than 700C different to flue temperature), I would expect them to be very similar. Also, the outside heat transfer coefficient is greater than the inside.

If you could find any faults in my procedure please let me know. Also, if you could suggest the quickest way to get the temperature of the flue gas at the outlet of the pipe from knowing U that would be great.

Thanks,
David

2. May 8, 2014

### SteamKing

Staff Emeritus
You are calculating a bunch of different numbers, but it's not clear there is any understanding going on.

You've calculated a Reynolds number for flow in your pipe. Does the Reynolds No. you obtain indicate that the flow is laminar? If the flow is not laminar, then it's either fully turbulent or perhaps in the transition between laminar and turbulent.

Have you done a simple gas dynamic analysis of a flow in a duct, assuming that the pipe is adiabatic? Your temperature drop may be the result of the hot flue gas expanding as it flows thru the pipe, without transferring scads of heat thru the pipe wall.

3. May 8, 2014

### davidgrant23

Hi Steamking, the reason I calculated the Reynolds number was to determine whether the flow was laminar or turbulent in order to apply the correct Nusselt equation, with the ultimate goal of getting the heat transfer coefficients.

In this case the Re was around 40 due to the very small mass flowrate being dealt with. I am trying to calculate it this way as I am dealing with it as a joint conduction/convection problem, which requires ho and hi.

I would expect a significant temperature drop however as the residence time is quite large.

The numbers I calculated were as follows (to try and give you an idea of the system):

Pr = 1.99
Re = 39.93
RePr(d/L) = 9.15 - this number is needed to determine which Nu relation to apply.
Nu = 4.06
hi = 2.12 W/m2K
Rquartz = 0.0095 (per unit metre)
Rconv1 = 3.26 (per unit metre)

From this point on the results are probably incorrect as the surface temperatures I calculate are strange (around 150C, even though the flue gas is around 1000C!

ho = 12.88 W/m2K
Rconv2 = 0.537 (per unit metre)
Rtot = 3.811 (per unit metre)

U = 4.178 W/mK

If you need any other information then just let me know.

Thanks

4. May 8, 2014

### davidgrant23

I guess another question I should ask is whether ho being larger than hi would be expected physically for such a system (more heat transfer on outside than inside)?

5. May 9, 2014

### Staff: Mentor

OP has realized some mistakes, and has asked that this thread be closed.