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Temperature Increase in Pipeline
3

Temperature Increase in Pipeline

Temperature Increase in Pipeline

(OP)
I have a 16 inches (outside diameter)chilled water pipeline (cast iron) that is 80 feet long.  Water is flowing through it with an initial temp of 45 degF.  The line is exposed to an air temperature of 55 degF and I would like to know the temperature at the end of the pipeline.  The flow rate is 1000 gpm.
I'm trying to generate some kind of pipeline heat gain table using the exposed pipe vs the insulated pipe.
Can anybody helps?

RE: Temperature Increase in Pipeline

Here are somme comments for your consideration:

Is the (black) pipe exposed to solar radiation ? If it is, the heat gain during light hours may be markedly larger than by the convection-wise heat transfer from the surrounding air.

Convection HT coefficients for still -indoors- air (natural convection) differ dramatically from those of forced convection (winds).

An estimated value of 0.35 Btu/(h.ft2oF) for still air can increase dramatically for windy conditions.

Besides, what about air humidity ? Could it be that some moisture condenses on the uninsulated pipe, adding some resistance to heat transfer ?

The location of the pipe, whether near ground level or elevated, with or without vertical sections, may also affect heat transfer.

Your comments are appreciated. Thanks.

RE: Temperature Increase in Pipeline

and dont forget the heat gain from the frictional effect although for a 16" dia. pipe w/ a flow of 1000gpm would not be significant and can even be disregarded.

RE: Temperature Increase in Pipeline

Gator,

I have calculated this case and find that the heat transfer values are as follows;

Bare pipe, in shade, no wind
Heat Gain 92.3 W/m of pipe
Heat Gain 72.3 W/m2 of pipe surface
Temp Gain 0.15°C per 100m or 0.08°F/100ft
Temp Gain 0.06°F

Very little heat transfer should be happening under these conditions.

Dennis Kirk Engineering
www.ozemail.com.au/~denniskb

RE: Temperature Increase in Pipeline


To denniskb,

My sources indicate a HTC for free convection of 2.2-2.5 W/(m2*oC) for a horizontal cylinder in air.

Even taking the higher value of 2.5 and a total ΔT of 10/1.8=5.60C, the results show a heat gain of
13.9 W/m2, much lower than the 72.3 W/m2 of your findings.

Where is my error ? Thanks

RE: Temperature Increase in Pipeline

The temperature increase of a fluid moving within a pipe of radius R, length L, at a speed of V m/sec, given a pipe wall temperature of Tp, a heat transfer coefficient to the water of h W/m^2 C, and an initial water temperature of Tw, at a density p, and specific heat C, is given by

Delta T = 2*L*h*(Tp-Tw)/(p*C*V*R)

by my calculation. The heat transfer coefficient to the water can be found from such references as MAdams, Heat Transfer.

I'd be interested if anyone has a reference to confirm my calculation.

corus

RE: Temperature Increase in Pipeline

corus (Mechanical)
Your formula on the right hand side assumes the water temp to remain constant over the length of pipe even if the assumption of pipe wall temp is also constant. The water temp should at least vary.
Start with a differential equation, such as in deriving temp rise in cooling water thru a condenser tube and see a better approximation.
I'm glad to see someone referencing McAdams.  How about references to Jakob?

RE: Temperature Increase in Pipeline

(OP)
Guys...thanks a lot for all the input...it really helps.
Denniskb...what analysis did you use to get the answers...did you use any of the spreadsheets that you have on your website...if you did..please tell me which one.
Have a good day.

RE: Temperature Increase in Pipeline

I re-checked my calc and found I had used an incorrect algorithm for convection so pls consider the following;

Bare pipe, in shade, no wind
Heat Gain 104.4 W/m of pipe
- composed of Convection 12.15 W/m, Radiation 92.25 W/m
- Convective Coeff (internal) 1037 W/m2.K, (external) 1.73 W/m2.K
- Radiative Coeff (external) 13.15 W/m2.K
Heat Gain 81.8 W/m2 of pipe surface
Temp Gain 0.165°C per 100m or 0.091°F/100ft
Temp Gain 0.073°F

25362,
My previuos calc had an error which resulted in 0 W/m2.°K so everything was due to radiation. The algorithms used for both external and internal convection are from Incropera and De Witt and the external one is also used by the 3E Plus software.

corus,
The problem with your formula is that gator1991 does not know the pipewall temperature Tp. My calc puts the outside wall temperature at 7.31°C [45.16 °F].

sailoday28,
Since the temperature change along the pipe length is so small there is no need for a differential equation in this case.

Sorry that most of my data is in SI units but the coversions are a pain.

Dennis Kirk Engineering
www.ozemail.com.au/~denniskb

RE: Temperature Increase in Pipeline

sailoday,
You misread my formula. The water doesn't stay constant as the idea was to evaluate the increase in water temperature, ie. the delta T. The value on the right hand side Tw is the initial water temperature as it enters the pipe. The delta T is that increase in water temperature over the pipe length, ie. the outlet temperature will be Tw + delta T.

denniskb, you're correct in that you would need to know the pipe wall temperature for my expression. Presumably with your value inserted into the formula then the outlet water temperature could be found.

corus

RE: Temperature Increase in Pipeline

gator1991,

I performed a heat transfer calculation using 2.5 W/m2/C as suggested by 25362.  My result: a heat flux of 13.8 W/m2 (nearly identical to 25362), or 16.8 W/m (17.5 Btu/hr/ft; 1048 Btu/hr over the 60 foot pipe length).

So, over the length of the 60 ft pipe, there would very little temperature increase in the water (.002 F).

Even with denniskb's calculation with higher heat transfer, the temperature increase is still imperceptibly small.

TREMOLO

RE: Temperature Increase in Pipeline

To Corus, your formula would be right except for the term
(Tp-Tw), which should be LMTD or, at least, the arithmetic average of the temperature differences at both ends of the pipe.

Even in the later case, only when ΔTw is very small ≈ 0, meaning that that the fluid's temperature almost doesn't change, one could use your formula as a good approximation.

Your formula is the result of equating:

V.π R2.ρ.Cp.ΔTw = h. 2π R.L.(LTD)

resulting in:

ΔTw = 2.h.L.(LTD)/(V.R.ρ.Cp)

Do you agree ?

RE: Temperature Increase in Pipeline

25362: You are correct in my derivation although I have no idea what the acronyms mean and, as a cry to the world, would wish that people in general would stop using them, ASAP (joke).

If I read it correctly you are saying that the LTD is the temperature difference between the pipe wall and the mean water temperature in the pipe, rather than the inlet water temperature, as I have used. I agree with this but this puts the unknown outlet water temperature into the right hand side of my equation.

With some manipulation and using the '25362' correction factor, my expression would then become

?Tw = 2.h.L.(Tp-Tw)/(V.R.?.Cp + L.h)

with all values on the right side of the equation being known.

Thanks for the correction.

corus

RE: Temperature Increase in Pipeline

Note that the question marks in the above relate to the delta symbol and the greek rho.
So much for cutting and pasting.

corus

RE: Temperature Increase in Pipeline


Corus, I'm sorry if the acronym disturbs you. But LMTD is a very well known abbreviation for Logarithmic Mean Temperature Difference.

Denniskb, there may again be something wrong with my calculations. The radiation transfer coefficient as well as the radiation heat flux that I found for a pipe in the shade -not exposed to solar radiation- at the given temperatures are much lower than those reported by you, even when using 0.9 for black iron absorptivity. The recommended value for low temperature radiation is only 0.21. Kindly comment.

RE: Temperature Increase in Pipeline

My equation would be an approximation as it assumes that the pipe wall temperature remains constant along the length. As a rough calculation I'd simply assume that the pipe was at 50F, half way between the inlet water temperature and air temperature, presuming there was no additional heating from the sun. In the case of an insulating jacket I'd assume that the pipe was at 45F, the inlet water temperature. That should give a quick and reasonable estimate of the increase in water temperature with the formula I posted and give a comparison between the two cases.

corus

RE: Temperature Increase in Pipeline

gator1991,
The calculation I use is one of my many Excel applications, but no it is not currently available from my website. Sorry but it took way too much time and effort to simply give away.

I am concerned that many of the recent postings are distracting readers from finding a realistic solution to the original problem. The temperature change along the 80 foot length is negligible so simply ignore it. This heat transfer case is, like most real world HT calcs, complicated enough without introducing an additional dimension that is not needed for a solution.

Using typical HT coefficients from texts is useful but often leads to incorrect assumptions about the real world. Look back at my numbers and see that 88% of the heat transfer is via radiation. There is little to be gained from chasing down details of convection coefficients and LMTDs.

This case involves several layers of HT all acting in series and parallel at the same time;
> forced convection in the water flowing in the pipe
> conduction through an inside film layer
> conduction through the pipe wall
> conduction through an external film layer
> natural convection in the air outside the pipe
> radiation transfer between the outer pipe wall and the surroundings

The two keys to solving the HT are 1) determining the HT properties of the various fluids and materials involved and 2) finding the inside and outside surfaces of the pipe. The second of these is the most important and the most difficult.

My application includes a library of environment, materials and fluid properties (temperature sensitive in many cases) as well as a library of convection formulas for both the inner surface and outer surface of the pipe (which provide the Nusselt No values). What the application does is to set up a series of simultaneous equations for the various heat transfer modes and then solves them iteratively by adjusting the surface temperatures until all of the energy flows balance.

The heart of the calculation is the general formula for calculating the thermal resistance of the various layers involved in a pipe.
R = 1/U = 1/(2.Pi.Ri.(hci + hri))+ln(Ro/Ri)/(2.Pi.kio)+1/(2.Pi.Ro.(hco + hro))
U = Overall HT Coefficient
Ri = inside radius
hci = inside convection ceofficient
hri = internal radiation coefficient (= 0)
kio = thermal conductivity of pipe wall

With the application running I can set up and solve simple cases like this one in about 20 minutes and then spend some time checking the sensitivty of the result to various changes in conditions (e.g. wind velocity, surface coefficients, solar radiation levels). For cases where the fluid in pipe temperature changes significantly I simply re-run the calculation for the conditions further along the pipe.

If I had the time I would write out each of the equations used but that may need to wait until retirement?

The point is that this HT case can be reliably solved with an appropriate effort while the simple approach of using typical textbook values can lead to significant errors and a misunderstanding of what is really happening. While many textbooks address the theory I find Incropera and De Witt the most useful.

Sorry to be so long winded but as you can tell I had some real world cases, including personnel safety, to find solutions to and had to go the hard yards on this subject.

Dennis Kirk Engineering
www.ozemail.com.au/~denniskb

RE: Temperature Increase in Pipeline

Corus is right. For this particular case
 
Δtw ≈ 0.1 MTD

where MTD is the mean temperature difference at both ends.

A few iterations assuming, "a grosso modo", water outlet temperatures for logical pipe temperatures, would show the heat-up of water is practically negligible.

RE: Temperature Increase in Pipeline

I'm not sure what objections denniskb has to the advice offered. Although in this case the answer may be negligible it is important for other cases that people may have, like myself. Which solution is incorrect and which is correct and have any measurements been made to validate the calculations?

From all the answers involving heat gain I'm a little surprised that none require the velocity of the water, for instance. Surely for infinite water velocity the increase in water temperature along the length of pipe is zero?

corus

RE: Temperature Increase in Pipeline

corus,

A few temperatures from my simulation may help.

Water         7.22°C     45.00°F
Inside Film   7.25°C     45.05°F
Inside Wall   7.28°C     45.10°F
Outside Wall  7.31°C     45.16°F
Outside Film 10.05°C     50.09°F
Air          12.77°C     50.00°F

The two decimal places does not represent the accuracy but are need to show the small temperature differences.

To use a pipewall temperature of 50°F will produce a wrong result.

The radiative properties I used for the pipe outer wall are;

Background Temperature  12.77°C    50.00°C
Surface Absorptivity     0.80
Surface Emmisivity       0.66
- these figures are for carbon steel with light rust
Background Absorptivity  0.66
Background Emmisivity    1.00

The calculated radiative loads are;

Absorption from background    303.3 W/m2
Emmission from pipe surface  -231.0 W/m2
Radiative heat balance         72.3 W/m2
Radiative Coefficient          13.15 W/m2.°K   2.31 BTU/hr.ft2.°F

I'm not sure where your 0.21 value comes from or what the units are.

Please note how the heat transfer is hugely dominated by the radiative component and how sensitive the result will be to changes in the absorptivity and emmisivity properties.

Of course the convective load will rise quickly if there is wind movement of the air. My calculation indicates that with a wind of 5 m/sec the convective heat load (128.25 W/m) will be 10 times the still air case yet the overall heat load (0.347°C/100 m) will only have doubled. Still a very small change in the water temperature.

Dennis Kirk Engineering
www.ozemail.com.au/~denniskb

RE: Temperature Increase in Pipeline

Thanks dennis but the outside air temperature is 55F and not 50F so I don't know if that will alter your calculation any.

The value of 0.21 you refer to was quoted by 25362 and they are referring to the value of emissivity which has no units.

I'm a little surprised that radiation is so dominant as from my experience radiation only becomes dominant in free surfaces to air when the surface temperature is into the hundreds of degrees celsius, whatever that is in F. However, are you then using that amount of heat flow from the outer surface you have calculated into a similar equation I derived that involves the water flow rate?

corus

RE: Temperature Increase in Pipeline

Corus,

Sorry my mistake, the last line of temperatures should read

Air          12.77°C     55.00°F

Also I meant to put the 0.21 query to 25362 and when I re-read his post you are right that it is unit free. He actually stated this as absorptivity rather than emissivity.

My calculation could always be wrong though I have tested it against various text book examples and been able to match the results. The texbooks, however, do not usually provide much for combined HT cases.

25362,

If you provide me with some alternative numbers for absorptivity and emissivity I would be happy to re-run the calculation with different values.

I am always looking for additional data to add into the application library and so improve the calculations, though I always try to collect the source reference for each new piece of data. Likewise I can provide much of the data in my library to those interested.

I have been looking for a way to make a pdf printout of the calculation available via Eng-Tips but this does not appear to be possible. I will try to add a new download section to my website this weekend where these things can be accessed.

Dennis Kirk Engineering
www.ozemail.com.au/~denniskb

RE: Temperature Increase in Pipeline

Denniskb

Holman's table 8.3  compares absorptivities of various surfaces to solar and low-temperature(~25oC) radiation. A striking difference is given for cast iron: 0.94 and 0.21, respectively.

My estimates are based on a 50 year-old nomograph. This one gives a value for hr = 0.8 in british units, based on the given temperatures and ε = 0.9 for the pipe, to be used in the formula for heat flux:

qr = hr*Δt

According to this graph, qr = 0.8*10 = 8 Btu/(h*ft2) => 8*3.155 ≈ 25 W/m2.

As I said, it is a very old source, and it may be totally wrong.

RE: Temperature Increase in Pipeline

25362,

The surface finish of the cast iron (like many other materials) can have a dramatic impact on its radiative properties.

For steel I have;
              Absorp-Solar   Absorp-Ambient   Emissivity
Clean             0.45            0.2            0.55
Light Rust        0.8             0.8            0.55
Heavy Rust        0.95            0.95           0.87

There is lots of data about on emissivity (due to the proliferation of hand held IR thermometers) and for Cast Iron the values again vary widely with surface finish.

New (polished?)   100°C     0.05
New unoxidised    100°C     0.21
Oxidised          100°C     0.74
Heavily Oxidised  104°C     0.95

The 0.21 absorptivity number looks likely to be for new clean material (as was much of the older data collected from laboratory tests rather than the condition likely in the field).

Further it is essential that both the absorptivity and emissivity values are taken from the same sample as the two act closely in determining the radiant transfer. I tried the clean steel data above on this pipe and the pipe was a nett rejector of heat rather than an absorber?

I have added a pdf file of my calculation to my website (look for miscellaneous downloads) so you can have a look.

Dennis Kirk Engineering
www.ozemail.com.au/~denniskb

RE: Temperature Increase in Pipeline


Dennis, how can I reach miscellaneous downloads from your main page ? Thanks.

RE: Temperature Increase in Pipeline

Go to "Design Calculations"

Fill out the form and "submit" from bottom of page

Last item on page click "here"

Select the file for download.


Dennis Kirk Engineering
www.ozemail.com.au/~denniskb

RE: Temperature Increase in Pipeline

Yes, it is free and it has some very useful data attached to it. It is however targeted at marketing insulation products and providing comparisons between alternative insulations.

While the application is quite clever in some ways it provides very limited control over the inputs and methods used. It does not deal with solar heating at all. Overall it does not provide a thorough solution which is quite disappointing considering the effort that has gone into it.

I tried this case using 3E Plus with the following results;
Method 1     48.69 W/m
Method 2     43.35 W/m
My Software 104.38 W/m

Dennis Kirk Engineering
www.ozemail.com.au/~denniskb

RE: Temperature Increase in Pipeline

Dennis,

What formulas have you used to perform the calculation.  I would like to calculate the 'black steel' temperature of a pipe that is exposed to sunlight.

Any assistance would be appreciated.

Regards

Andrew Lindsay

RE: Temperature Increase in Pipeline

(OP)
Andrew I got the formulas from this website
http://sti.srs.gov/fulltext/fulltext-1998.htm

The name of the document was Heat Transfer Model of Above and Underground Insulated Piping Systems
I look for it but I couldn't find it you will probably have to ask them about it.

Good luck

RE: Temperature Increase in Pipeline

Gator1991,

I've had a look at the paper (managed to find it by typing the title into google).

I want to calculate the temperature of a pipe that is exposed to sun light.  Where do I put the heat loading into the equations?

hb (equation 5) appears to be a boltzmann type equation, but I am not sure how to use this.  Say I have a 350 W/m2 solar radiation hitting the pipe at 90°.  How do I calculate the actual surface temperature of the pipe.  I am actually interested in the stagnant case, where there is no flow in the pipe, and could simply assume that the pipe is a solid steel rod.

Any ideas would be appreciated.

best regards

Andrew

RE: Temperature Increase in Pipeline


Andrew

Holman's Heat Transfer has a worked exercise (example 8-10) on a similar subject on solar radiation.
I suggest you have a look at this example. Good luck.

RE: Temperature Increase in Pipeline

Andrew

The temperature of the plate will reach around 50 - 60°C.

The Solar absorption will be around 330 W/m2
The Bacground absorption will be around 300 W/m2

The Surface emmissions will be around 550 W/m2
The Convection loss will be the balance.

I have posted to my website a pdf output from my software for this case Solar_PipeHT_Dev.pdf.

I have also posted an Excel solution which will allow you to solve for other conditions. The solution comes from Incropera and DeWitt Example 12.11.

Enter the pipe length and diameter.
Enter the solar radiation level - range 0 > 1000 W/m2
Enter the sky temperature - range -43 > 0°C
Enter the ambient air temperature
Provide absorptivity for solar - range 0.45 > 0.95 for steel
Provide absorptivity for ambient - range 0.2 > 0.95 for steel
Provide emissivity - range 0.55 > 0.87 for steel

Enter the surface temperature and increase this until the overall heat transfer = 0 (equilibrium)

You can force the convective load to 0 in the blue cell for the case where no air movement is present (e.g. ambient = steel temperature)

The "Heat Transfer Model ...." paper has some useful information but does not deal with either solar heating or radiant heat transfer with the sky. As you can see above these have a major impact on the calculations.

Try running a case with the sky temperature down at -35°C to see how much this matters. (This is the temperature you often see displayed in an aeroplane in flight and on a clear day is quite visible to a pipe on the ground. This is also what make water freeze at night in the desert)

In the center of Australia on a very clear day it is not unusual to have 1000 W/m2 Solar radiation and -43°C sky temperature at the same time. Pipe temperatures in excess of 90°C can be experienced.

Be careful with the absorptivity and emmissivity numbers from the text books as a small layer of dust can significantly affect the real value.

Dennis Kirk Engineering
www.ozemail.com.au/~denniskb

RE: Temperature Increase in Pipeline

Dennis,

I've looked at your site, but can't seem to find the documents you have described.

Regards

Andrew

RE: Temperature Increase in Pipeline

Surely the temperature of the sky is -273C approximately?

corus

RE: Temperature Increase in Pipeline

The sky temperature seems to be a great discussion subject. Atmospheric resistances and reflections may be the reason why -273C can not be used. I would be curious to hear what values on the sky temperature has been shown to give reliable results (assume clear sky, and cloudy respectively)?

RE: Temperature Increase in Pipeline

The mechanism of heat transfer from Warm Air to Cold Pipe changes drastically with the Dew Point temperature of the air...and a slight breeze will tend to decrease the corresponding heat gain rather than increase it.

The condensing effect may not be dominant for a 45 deg. F. Pipe in 55 Deg F. Air but will almost certainly be dominant with 65 deg air.  For slow moving fluid in a large pipe having considerable potential for radiant gain, there will develop a sharp line of dry surface(top side of horizontal pipe) to wet surface (bottom) which means the actual rate depends on time of day and also means a North-South pipe tranfers heat differently than an East West...

This a phase change, gravity driven mechanism and very dependent on the pipe orientation, for a vertical pipe will actually invert the interior natural convection effect in a still pipe full of cool water.

The overall result remains the same: the heat gain is negligible from a temperature or nominally from the energy standpoint but the destructive and contaminatory effects of the condensation and drippage, even on CI pipe, is usually cause for minimal insulation anyways....unless, of course, the 55 deg air ondition and movement makes condensation impossible.


 

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