How can I improve my approach for calculating temperature drop in a quartz pipe?

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Discussion Overview

The discussion revolves around calculating the temperature drop of flue gas in an uninsulated quartz pipe exposed to ambient air. The focus is on the methodology for determining heat transfer coefficients and thermal resistances in a joint conduction/convection scenario.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • David outlines a multi-step approach to calculate temperature drop, including the calculation of Prandtl number, Reynolds number, Nusselt number, and various thermal resistances.
  • Some participants question whether the calculated Reynolds number indicates laminar flow, suggesting that if the flow is not laminar, it could be turbulent or transitional, which may affect the heat transfer calculations.
  • One participant suggests conducting a gas dynamic analysis under the assumption of adiabatic flow, proposing that the temperature drop might be due to the expansion of hot flue gas rather than heat transfer through the pipe wall.
  • David provides specific numerical values for Prandtl number, Reynolds number, heat transfer coefficients, and thermal resistances, expressing concern over the calculated surface temperatures being unexpectedly low compared to the flue gas temperature.
  • David raises a question about the physical expectation of the outside heat transfer coefficient being larger than the inside coefficient in this system.
  • In a later post, David indicates awareness of potential mistakes in the calculations and requests to close the thread.

Areas of Agreement / Disagreement

Participants express differing views on the validity of the flow regime and the implications for heat transfer calculations. The discussion remains unresolved regarding the accuracy of the calculations and the physical expectations of heat transfer coefficients.

Contextual Notes

Participants note potential issues with the assumptions made in the calculations, including the flow regime and the nature of heat transfer in the system. There are indications of missing assumptions and unresolved mathematical steps that could affect the results.

davidgrant23
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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
 
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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.
 
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
 
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)?
 
OP has realized some mistakes, and has asked that this thread be closed.
 

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