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Suppose a hot body is surrounded by a coil of very good thermally conducting pipe with cold water flowing inside which comes at a certain fixed low temperature in the pipe and leaves at some higher temperature after absorbing the heat. Will the rate of the hot body’s cooling down increase or decrease with increase in the water flow rate?

I think the rate of cooling will increase. But this is also in opposition to the intuition that the water will have less time to take away heat from the hot body, hence decreasing the cooling rate. I doubt that this is wrong since though the water is moving faster, water behind with lower temperature is following immediately after.

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  • $\begingroup$ How is the heat exchange between the body and the coil? Is there a gap, air and heat transfer through the air or a coil fits tightly to the body and heat transfer is through contact? $\endgroup$
    – Alex Trounev
    Aug 10, 2019 at 9:13
  • $\begingroup$ @AlexTrounev Through contact $\endgroup$
    – Atom
    Aug 10, 2019 at 9:14
  • $\begingroup$ Perhaps you have experimental data showing a decrease in heat transfer with an increase in flow rate. In numerical calculations, I noticed this effect. It is observed in transient viscous flows. $\endgroup$
    – Alex Trounev
    Aug 13, 2019 at 3:06

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The cooling rate will increase as the flow rate is increased.

The water in the pipe will heat up as it absorbs heat from the hot body, setting up a temperature distribution in the water within the pipe. Near the inlet it will have the temperature you pump it in with, and the temperature near the outlet will depend on how much heat it has absorbed from the hot body. The greater the flow rate, the less time water will have to absorb heat until it exits the pipe, and the colder it will be near the outlet.

According to Newton's law of cooling, the heat transfer rate to the water along a given piece of the pipe is proportional to the temperature difference between the hot body and the water. Since the water within the pipe is cooler on average when the flow rate is higher, this temperature difference is also higher on average, and so is the cooling rate.

The problem with your intuition is that although a given mass of water does have less time to absorb heat when water is being pumped in faster, now more water is being pumped in, by the same factor. The difference is that this mass of water does not get as hot by the time it leaves the pipe, so it is capable of absorbing more heat from the pipe per unit time as it flows.

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  • $\begingroup$ You did not give references to either experimental data or numerical calculations. Do we just have to believe you? $\endgroup$
    – Alex Trounev
    Aug 13, 2019 at 3:07
  • $\begingroup$ If you have doubts about any of my arguments, you could have pointed it out in your comment instead of the absurd and unnecessarily confrontational comment you left. I gave arguments that I believe are clear for most people to follow, referring to Newton's law of cooling, which is a successful model of interfacial heat conduction in many cases. I also pointed out the flaw in the reasoning that Atom was unsure about. If you don't believe me, I can live with that. If you would like to refute my claim or post a better answer, you are also free to do so. $\endgroup$
    – Puk
    Aug 13, 2019 at 6:38
  • $\begingroup$ There is nothing personal about my question. This is a scientific forum, so the arguments must be scientific. How did you get the idea that in such a heat exchanger in the form of a wound tube with water inside, with an increase in the flow rate, cooling rate will increase? Give experimental data or results of numerical calculations confirming this hypothesis. $\endgroup$
    – Alex Trounev
    Aug 13, 2019 at 7:56
  • $\begingroup$ Perhaps you haven't read my answer. If you did, you would see that it follows from the arguments I make that increasing the flow rate increases the cooling rate. The expectation that every answer on this website be supported by experimental data or numerical calculations is frankly ridiculous. The macroscopic theory of heat conduction is well established and reasoning based on such a theory, without doing math, is surely sufficient to answer this question, which is seeking a qualitative answer. $\endgroup$
    – Puk
    Aug 13, 2019 at 8:14
  • $\begingroup$ OK! Just add these links: sciencedirect.com/science/article/abs/pii/0017931063901005 $\endgroup$
    – Alex Trounev
    Aug 13, 2019 at 9:33

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