Flow rate?
Lying on the surface or on supports with free flow all around the pipe?
Solar radiation or just air somehow?
Any insulation?
Any painting? Colour?
Wind speed assumed ?( increases the heat input into the pipe if above ground )

If the flow is at least 1-2 m/sec, my best estimate without Solar radiation would be 35 to 40C at the end.

If you're getting Solar radiation as well, then it could be higher than 50C.

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Hi,
To support effectively provide technical information about the piping /insulation/ wind and of course flow rate.
We cannot read your mind.

Steel pipe, DN 8", water Velocity 1.5 m/s, 30 C, air velocity 3m/s,50 C, emissivity pipe 0.8, no insulation > temperature outlet about 36 C
Pierre

Total exposed surface 2760m2, of which say 70% may be used as effective surface for incident solar radiation. Total Solar radiation S is 900w/m2 max in the infra red. Assume pipe surface absorptivity = 0.8, and water velocity = v.
Over an incremental length dL of pipe traversed, heat absorbed per sec dQ = S x 0.8 x .7 x pi x D x dL
Heat absorbed by Mass of water traversing through pipe per sec, dQ = dL/dt . pi. (D2/4). rho. Cp. dT
Equating the 2 expressions and simplifying, D/4 . rho . Cp. dT/dt = S . 0.56, which can be integrated easily for the total traversal time. So for 4000m at 1.5m/sec, t = 4000/1.5 = 2670secs, and T-30 = 5.8degC, for Cp = 4180J/kg/degC. So T = 36degC. You can adjust the traversal time t if your water velocity is not 1.5m/sec.
Natural or forced convection from hot air to pipe is small at low wind velocity in comparison and neglected.

If this was the opposite way round, 50C inside, 30C outside, I would have estimated in 4 km you would lose a few degrees C. It's a fairly large area to volume ratio.

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HI littleInch,
The answer will be about 43 C, all other parameters being the same.
Pierre

Thought it wouldn't be insignificant alright.

So combined should be somewhere between 40 to 45C. Less at night time of course....

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Thanks guys,

I am heading to the site this week to get more information.
I'm assuming the pipe is elevated above ground but it may be a HDPE pipe

HDPE in the Middle East ought to be UV stabilised - carbon black impregnated HDPE. The carbon would have some effect on the assumed solar radiation absorptivity value of 0.8 used in these calcs - adjust parameters in the calc as required.

Would a chiller help to bring down the temperature to 35c?

Yes it would reduce the temp, but only d/s the chiller.

If this is HDPE, watch for both thermal expansion - PE is 10 times that of steel and more importantly the allowable design pressure goes down and shouldn't exceed 50C surface temp.

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Error in my calc.

"Total Solar radiation S is 900w/m2 max in the infra red."

Of the total, only 50% is in the infrared and capable of heating. Remaining is UV and visible light. So, including a 0.5 multiplier on the RHS to S, temp rise would be 2.9degC and not 5.8degC. Exit temp = 33degC. Note the influence of water flowrate on the exit temp ( lower flowrate = higher traversal time = higher exit temp). So the highest temp you'd get is when water flow is at its minimum. Read the calc carefully and adjust where required to suit your conditions.

The entire spectrum is converted to heat, not just IR.

That makes for a long tedious calculation, assuming you can find the spectral absorption

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@Compositepro From what I've read, only IR enables heating when absorbing solar radiation. See the following in the section on infrared light. UV and visible can cause chemical reactions for photosensitive chemicals, but not heating.

https://www.fondriest.com/environmental-measuremen...

From your graph, since reflectance is the complement of emissivity for opaque materials (where transmissivity = 0), we can say, for UV stabilised black HDPE, e = 1-0.1 = 0.9 over the IR wavelength range ( assuming r remains at 0.1 in the far infrared also). And absorptivity is more or less = emissivity for most materials (Kirchoff's Law approximation). And 0.9 inferred from this graph is close enough to the 0.8 value used previously in the calcs.

Quote:

See the following in the section on infrared light. UV and visible can cause chemical reactions for photosensitive chemicals, but not heating.

If the visible reflectance is less than 100%, then visible light is absorbed, and that equates to heat; even white PVC is not 100% reflective in the visible, so it will get heat from visible light

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@IR, thanks for that - agreed, something must happen within the opaque material for any light not reflected.
In the chapter on radiation in Perry, it says for polished metals, emittance in the infra red results from free electron excitation, while bound electron excitation dominates at emission in the shorter wavelengths, including within the visible range of 0.4micron to 0.7micron. And the converse must also be true for absorptance I guess.
So temp rise is 5.8degC at 1.5m/sec water velocity even for UV stabilised HDPE pipe.

Scanning the responses above I did not see any adjustment to the slight increase in internal energy of the water due to friction from the flow in the pipe. The increase in internal energy wont be much but could account for an additional degree or fraction thereof.