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

In summary, the individual is trying to calculate the temperature drop of flue gas in an uninsulated quartz pipe in ambient air. They have approached the problem by calculating the Prandtl number, Reynolds number, Nusselt number, heat transfer coefficients, and thermal resistances. However, they are receiving odd results and are unsure if their approach is correct. They also mention a possible gas dynamic analysis and question whether the heat transfer coefficient on the outside of the pipe would be larger than on the inside.
  • #1
davidgrant23
22
0
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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  • #2
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
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
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
OP has realized some mistakes, and has asked that this thread be closed.
 

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

What causes a temperature drop along a pipe?

The main cause of a temperature drop along a pipe is heat transfer, which occurs as the fluid inside the pipe flows from a higher temperature to a lower temperature. This can also be influenced by factors such as the material and thickness of the pipe, the flow rate of the fluid, and the surrounding environment.

How does the temperature drop affect the flow rate of the fluid?

The temperature drop along a pipe can affect the flow rate of the fluid in a few ways. As the fluid cools down, its viscosity may increase, making it more difficult to flow through the pipe. Additionally, the decrease in temperature can also cause the fluid to contract, resulting in a decrease in volume and therefore a decrease in flow rate.

Can insulation prevent a temperature drop along a pipe?

Yes, insulation can help prevent a temperature drop along a pipe by reducing the amount of heat transfer between the fluid inside the pipe and the surrounding environment. This can help maintain a more consistent temperature throughout the pipe and minimize the effects of the temperature drop on the fluid flow.

What is the significance of the temperature drop along a pipe?

The temperature drop along a pipe is important to consider in various applications, such as in industrial processes, HVAC systems, and plumbing. It can affect the efficiency and effectiveness of the system, as well as the quality of the end product. Understanding and managing the temperature drop can help optimize the performance of these systems.

How can the temperature drop along a pipe be calculated?

The temperature drop along a pipe can be calculated using the heat transfer equation, which takes into account factors such as the material and thickness of the pipe, the flow rate and temperature of the fluid, and the surrounding temperature. Additionally, computer simulations and experiments can also be used to estimate the temperature drop in specific scenarios.

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