Heat Transfer of an Exposed Fuel Line

[BenM83]

I am working on a heat transfer problem. In a laboratory we have cold gasoline entering an uninsulated steel tube which runs near the ceiling of the lab. I am trying to determine what the temperature of the fuel will be when it reaches the end of the tube. I know the inlet temperature of the fuel. I also know the temperature of the room that the tube runs in. The equation I am using to solve this problem is q'[sub]s[/sub]A[sub]s[/sub]=m'C[sub]p[/sub](T[sub]e[/sub]-T[sub]i[/sub]). My challenge in solving this problem is that I have two unknowns: the constant heat flux into the pipe from the air in the room (q'[sub]s[/sub]), and the discharge temperature of the fuel at the end of the tube (T[sub]e[/sub]). Does anyone know if there is a way for me to determine the constant heat flux for the tube in the room, without knowing the discharge temperature of the fuel? Or am I missing something is my analysis?

Any help would be greatly appreciated.

 

[MintJulep]

Start with q'[sub]s[/sub] is not a constant.

Because it is a function of the temperature difference from out to in.

https://www.engineeringtoolbox.com/conductive-heat-loss-cylinder-pipe-d_1487.html

And the temperature is increasing as heat flows in.

For sufficiently short sections of pipe both q and Ti can be approximated as constant.

 

[BenM83]

First, thank you for the response. I can see how to apply the equation in the link you provided. A concern I have is that I believe I have a relatively long run of tubing. The tubing is 3/8 inch OD, and it is 150 ft. long.I'm expecting a significant change in temperature. If I used the equation from the link I will end up with a large Q. If I then used that to determine the expected discharge temperature I believe I will end up with an artificially high temperature.

Any thoughts on that? Any additional guidance?

Thank you.

 

[MintJulep]

You do 150 calculations. One for each foot.

The temperature leaving foot 1 is the temperature entering foot 2, etc.

 

[BenM83]

Thanks. Let me give it a shot and see what I come up with. I appreciate your time.

 

[Compositepro]

Why do you care what the temperature of the gasoline is? It will be between cold outside temp. and room temp at the end. I suspect you are focused on something very trivial.

 

[crshears]

Homework?

CR

"As iron sharpens iron, so one person sharpens another." [Proverbs 27:17, NIV]

 

[LittleInch]

Agree with MJ here. But really why don't you just measure it?

Also what is your velocity?

If your exposure time is less than 10 minutes I doubt you're going to see more tham 1 or 2 Deg C. Liquids have so much more heat capacity than gases and if the air isn't being blown at your pipe the heat transfer is going to be very small.

How cold is cold and how hot is your lab?

If your flow stops them it will become the same as ambient unless you can flush out the tubing.

Or just insulate the tubing.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[georgeverghese]

Combined (natural)convective and radiative heat transfer coefficients for bare pipe may be found in Perry Chem Eng Handbook 7th edition in the chapter on Heat and Mass Transfer - see page 5-14 table 5-2. Break up the line into say 3bits of 50ft each if you want a little more accuracy. Ignoring the internal heat transfer resistance would give you quick answers with sufficient accuracy - you'll only have to take this into account if this is a more viscous fuel oil where the internal resistance is similar in magnitude to the external resistance.

 

[BenM83]

LittleInch,
The situation I'm describing hasn't been installed yet, so I cannot measure it. I calculated the velocity to be 0.5 feet/sec. So the gasoline will spend about 5 minutes in the tube which is about 150ft. During the winter the fuel could be well below freezing, and our lab will be about 70F. We have to control gasoline temperature at 86F (30C) for our test. The fuel is circulated within the test setup, where it picks up heat as it is pumped. Typically we only need to cool the fuel, however this past winter we had issues with fuel being too cold. Currently we run fuel lines in an insulated bundle in a trench in our lab. A change in our lab will require us to run exposed, uninsulated fuel lines overhead. What I am trying to do is determine if we need a supplemental heater for this fuel.

I apologize for not responding sooner. I had a mixup in which e-mail received the notification.

I appreciate everyone's comments.

 

[LittleInch]

Well if you need 86 F, your lab is at 70F and your incoming fuel is at say 20F, then you will need a heater as there is not enough heat to get the fuel to your required 86F.

As said, I would not anticipate much heating over about maybe 5 to 10C max for that sort of residence time if the heating is due to natural convection air currents. A 3/8" tube is still fairly big so contains quite a lot of liquid per foot.

Your cold tube would probably attract condensation as well which will mess around with your heat input and drip on your head from time to time, or your notes / tablet / equipment...

I'm sure you can find equations and data to substantiate that, but given the variables and unknowns it could be out by a lot.

I think you will need heater.


Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[MintJulep]

First principles tells you that the fuel cannot get hotter than the air surrounding the pipe.

If the room thermostat is set a 70F then the temperature "overhead" will probably be warmer than that. Probably not as high as 86F, except when it is. For example, when the air conditioning has been off for while.

 

[BenM83]

Thanks for everyone's input. It was a given that the fuel not reach setpoint. The fuel heats up in the test stand, so it does not need to be 86F when it gets to the stand. I was just hoping I could approximate it's temperature when it did get there. However, it seems like doing so will be challenging and require many assumptions that will compromise the result.

Thanks again for everyone's help.

 

[georgeverghese]

Nothing challenging about running this calc - brush up on your Uni heat transfer - the theory is all there.

1/U = 1/(hc+hr) + 1/hi, where hc+hr is the combined external htc mentioned earlier. hi is the internal resistance to heat tranfer, which is given by

Nu = 0.023 (NRe^0.8).(NPr)^0.33

Finally Q = U.A.LMTD

Agreed, if the external tube metal temp is less than water dewpoint temp, the line would be dripping water if it were to be overhead. Look further into your Uni heat transfer text, and you'll see how to estimate the external tube wall temp.

 

[chicopee]

Aside from the heat transfer calculations you will also gain some internal energy from point of supply to point of delivery due to internal friction as the gasoline travel thru that 150'of line.