All you need is someone who has been educated in heat transfer to do the calculation for you, and a reasonable estimate of the range of external conditions. Will this be exposed to rain? Is there a problem with over-cooling it?

If you're worried about how cold it could get, then if it rains or snows outside, that will set your shellside (tube exterior) conditions for the heat transfer calc. For snow, set the tube exterior to a uniform temperature of 0 C...heat transfer will be controlled by the tubeside film coefficient entirely.

If it is indoors, you need only the ambient temperature and an estimate of the free convection heat transfer coefficient for the tubeside. Estimates good enough for what you're doing can be found in a table- you don't need to calculate it in detail using correlations. It then becomes a straightforward single tube heat exchanger calculation, a model for which you can find in any heat transfer textbook. The thermal conductivity of the tube metal is unlikely to matter, as both your tubeside and shellside convection film coefficients will be poor relative to the conductivity of a thin piece of just about any metal. But the model you find in a heat transfer text will take the metal into account, just in case. If your calculation shows that the tube metal is a significant fraction of the resistance, you've done something wrong.

What pressure / velocity are you running at?

For 15m of pipe (unless you meant 585 feet) it might be very low if your velocity is high.

How accurate do you have to be?

A pipe at 660F (350C) is a major safety hazard so I would imagine you need to insulate for personnel protection purposes regardless and really - how much does 15m of insulation for a 1/2" pipe cost??

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Sorry, the length was meant to be 585 feet long. The goal was to have the process gas end within a range of 140-250F. I figured the calculation would be more intensive than anticipated and I need to dig out my old heat transfer textbook.

OK, makes more sense, but the issue of v hot pipes and people plus minimal cost of insulation makes me wonder why you're bothering?

If you're actually trying to cool it then you're in a lot more difficulty, especially if this pipe is outside somewhere. you'll probably need to break the pipe into a lot of different sections as simple equations don't like big changes in temperature from one end to the other.

What's the gas velocity?

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Given that the flow rate is 40scfh, the velocity should be 200 in/s or 28800 ft/s if my math is correct.

40 scfh through 585 ft. of 1/2" tubing? The outlet temperature will be ambient temperature. If you are concerned about condensation you will need to heat trace. If you only care about the outlet temperature and not transit temp., put a heater at the end of the line.

All depends on the pressure.

Your maths and units don't match....

If the gas is basically at atmospheric pressure and temperature then you're looking at about 100"/sec or 8 feet a second. I suppose at 600F you might be double that?

So your gas would take 73 seconds to transit the pipe section. Or at a high temperature say 40 seconds. It might loose less heat than you think.

But if you are at say 1barg or 2 barg then it all changes rather a lot.

Also if you're changing gas temp by several hundred degrees F then your gas density is going to change as well adding even more complication to your calculation.

But wind, rain, snow, if outside all has a big impact.

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Also: If you get a response it's polite to respond to it.

Read up natural convection and radiation losses from bare pipes to find the heat loss for zero to low windspeeds. If you have a higher cross windspeed, convection losses would be somewhat higher. These correlations for (hc + hr) would all be in your Uni text on heat transfer.

Agree that if it's 585 ft long and the gas flow is only 40 scf per HOUR, the gas will exit at ambient temperature. Compositepro has given you absolutely the right advice about what to do about it also. Tracing a line that long to keep that tiny amount of gas warm is foolish unless condensation will cause problems.