Temperature drop in an insulated pipe over 12 hours

In summary, Mark is seeking help with calculating the temperature of engine oil in a pipe after 12 hours, given certain variables. He has derived an equation and calculated the overall heat transfer coefficient, and estimates the final temperature to be 17.83oC. He is asking for confirmation on his approach.
  • #1
Mark Deuchars
1
0
Hello all,

I have been having some problems and would appreciate any help:

I have a length of insulated pipe filled with engine oil at rest, the variables are as follows:

Toil: 40 oC
Tair: 5 oC
h1 (LO): 3600.63 W/m2/K
r1 (pipe inner): 0.1 m
r2 (pipe outer): 0.1095 m
r3 (insulation): 0.1695 m
L (length): 21.5 m
A1 (pipe inner area): 13.50884841 m2
k1 (carbon steel): 50 W/m.K
k2 (mineral wool): 0.0421 W/m.K
h2 (air): 11.6 W/m2/K
A3 (insulation outer area): 22.89749806 m2
Cp (LO): 1928 J/kg.K
Time: 43200 s
Density: 877.8 kg/m3
Volume: 0.68 m3
Mass: 596.904 kg

I am trying to calculate the temperature of the oil in the pipe after a period of 12 hours, assuming that the ambient air temperature remains constant at 5 oC. I have been able to calculate the heat transfer through the pipe and insulation but am having issues calculating the temperature drop over time.

I have derived down to the following equation that gives me the temperature as a function of time: $$T(t)=5+35e^{-\frac{UAt}{mCp}}$$
Where:

U: Overall heat transfer coefficient
A: Surface Area
t: time
m: Mass of oil in pipe
Cp: Specific heat capacity of the oil

I calculated U as 0.3848 using U = 1 / Rt, where Rt is the total thermal resistance of the pipe and insulation.

After plugging in the numbers I get a value of 17.83oC.

If anyone could let me know if I am on the right track and that the formula I have used to calculate the temperature is appropriate that would be great.

Many thanks,

Mark
 
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  • #2
I didn't check the calculation, but the final formula seems correct.
 
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1. What factors affect the temperature drop in an insulated pipe over 12 hours?

The temperature drop in an insulated pipe over 12 hours can be affected by several factors, including the initial temperature of the fluid inside the pipe, the thickness and quality of the insulation, the ambient temperature, and the flow rate of the fluid.

2. How does the type of insulation used affect the temperature drop in an insulated pipe?

The type of insulation used can greatly impact the temperature drop in an insulated pipe. Insulation materials with higher thermal resistance, such as fiberglass or foam, can reduce the rate of heat transfer and result in a smaller temperature drop over time.

3. Can the flow rate of the fluid affect the temperature drop in an insulated pipe?

Yes, the flow rate of the fluid can play a role in the temperature drop in an insulated pipe. A higher flow rate can lead to a greater heat transfer and a larger temperature drop over time, while a lower flow rate can result in less heat transfer and a smaller temperature drop.

4. Is it possible for the temperature to increase in an insulated pipe over time?

No, it is not possible for the temperature to increase in an insulated pipe over time. Insulation is designed to prevent heat transfer, so the temperature of the fluid inside the pipe will gradually decrease as it loses heat to its surroundings.

5. How can I calculate the temperature drop in an insulated pipe over 12 hours?

The temperature drop in an insulated pipe can be calculated using the equation Q = U x A x ΔT x t, where Q is the heat transferred, U is the overall heat transfer coefficient, A is the surface area of the pipe, ΔT is the change in temperature, and t is the time interval. Other factors, such as the thermal conductivity and thickness of the insulation, may also need to be considered when calculating the temperature drop.

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