Calculating Temperature Drop with Heat Loss from Pipe - David

[davidgrant23]

Hi there, I am dealing with a pipe that is surrounded by air and trying to calculate the temperature drop. The inlet temperature is 1273K and the ambient air is 293K.

In my quest to do so I have calculated the overall heat transfer coefficient to be around 10 W/m2K, which I believe for a gas hot fluid/gas cold fluid situation like I have here is a fairly reasonable number. However, the problem arises when I try to calculate the temperature drop along the pipe.

The heat content of the stream at the inlet is Qin=m*cp*Tin= 113W, which is quite low as the mass flowrate is 10^-5 kg/s magnitude.

However, I thought I could calculate the temperature drop by doing Qout = Qin-Qloss, where Qloss = U*A*logmeanT. The area is 2*pi*r*l = 0.063m2 and logmeanT=579K. This gives a Qloss of 365W, which is greater than the inlet stream!

How can the Qloss be greater than Qin. This obviously gives a negative outlet temperature which cannot be true. Can you suggest what I am doing wrong?

Thanks,
David

 

[Q_Goest]

Hi davidgrant. Are you performing the heat transfer analysis along the entire length of pipe all at once or are you breaking it up into sections (short lengths). The temperature differential at any section shuld be decreasing so heat flux is decreasing as that happens as well. Breaking it up like this and making what is essentially a 1 dimensional FEA type analysis should clear up any inaccuracies.

 

[256bits]

Your calculation of LMTD is going to have problems since it is in ambient air.

For a pipe within a pipe, the LMTD can assume there is an average temperature of each fluid at ends A and B.
For the flue gas, this would be the case.

For the ambient air this would not be the case.

If your pipe is horizontal, you have a type of cross flow heat exchanger. Convection means that as the air flows around the pipe upwards it has an increase in temperature. The air though, is not at one particular temperature for the whole circumference of the pipe, and there could be a great disparity, hot spots at places and not others, especially nearer the hot end.

If your pipe is vertical, then you have either a type of parallel flow or counter flow heat echanger, depending upon whether your gas in moving downwards or upwards. The air would by convection flow upwards, and again, since it is not in an enclosed space, its temperature could not be considered even as there will be some mixing with air that has already been heated with that still at ambient.

You might have to tweek your analysis to take this into account. Perhaps you could determine the Pr and all those numbers at the hot end versus the cool end for ambient air flowing over a cylinder and see how much of a difference that makes to the U, and ho.

Perhaps the area of the pipe has a correction factor to be taken into account for such a high temperature. ( ie hot spots )

I am listing what could be the problem with the LMTD or surface area of heat transfer, but you will have to investigate further, perhaps due some research on whether some general rules do apply. Surely something such as this has been done before.

 

[davidgrant23]

Hi davidgrant. Are you performing the heat transfer analysis along the entire length of pipe all at once or are you breaking it up into sections (short lengths). The temperature differential at any section shuld be decreasing so heat flux is decreasing as that happens as well. Breaking it up like this and making what is essentially a 1 dimensional FEA type analysis should clear up any inaccuracies.

Thanks for the suggestion, it helped, but no enough to make the answer seem plausible. Spliting the pipe up into 5cm segments resulted in a outlet temperature of about 100C. Better, but still not likely in truth. Further divisions don't seem to make much of a difference.

I believe now that the solution would involve taking into account the heating of the air in the pipes vicinity, as well as other factors such as hotspots that the other person mentioned. This seems like a problem that is difficult to quantify theoretically, but I am open to any suggestions that people have.

 

[Q_Goest]

I have a program that might work for this. I could try it and see what happens. At least that way you have some other analysis to compare yours to.
What fluid is it?
What diameter pipe and schedule? What length? What material?
Any insulation on the pipe?
Any other information I need to know to do this analysis?
Assuming inlet temperature is 1273K, pipe in atmospheric air, mass flow 0.00001 kg/s.