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Is this a trick question?

Yes, the statement is correct. Weird edge cases aside, increasing the flowrate increases the heat transfer coefficient, which increases the heat flux.

Wow, this got a lot more engagement than I expected, I guess it was an interesting problem. I didn't go though all the math, but it looks like the conclusion people have arrived at is that in most normal situations, increasing the flow rate does indeed lead to increased heat transfer, falling off asymptotically as the limits of the heat transfer rate of the container walls is reached. Thus it looks like the market should resolve to YES. Anyone disagree?

@IsaacKing yeah, what u said

The fastest way to get a good answer on the internet is to bet lots of ᛗ on the wrong answer

@IsaacKing well, it was interesting to remember the old days, and solve some good "vague physics question". Props to @citrinitas he was the one who took effort to correct me

So, it turns out that some systems (maybe a majority of them) use flow control, to control heat transfer rate. However, they all have a limit at which they can transfer heat, it is not like you can just pump as much as you need

@Catnee I'd argue that going beyond a system's designed limit would be an abnormal situation

This is how my (closed loop, forced water, radiator) heater works. I can open a valve, which increases the flow rate and lets more hot water into the radiator. The radiator then emits more heat into my cold room.

The hotter the fluid is when it comes into contact with the cold area, the faster heat will flow. The colder the fluid is when it comes into contact with the hot area, the faster heat will flow.

A radiator is a very normal setup for this

@LudwigBald That is not a closed loop, you are not transferring heat using water, you are just receiving it. The water that comes into your radiator has a constant temperature, no matter how high your flow rate

@Catnee of course I'm transferring heat. It starts out at the heated end and then goes into the cold room. It's a closed loop, but not a closed system overall of course. But that wasn't specified (and doesn't matter here).

Okay, here's a decent "normal situation"

Look at the radiator of a car. The engine has a maximum efficiency temperature, and the coolant circuit includes a thermostat designed to keep the engine at that temperature. The thermostat controls the flow rate of coolant to the radiator. If the coolant is too fast, the radiator will dissipate too much heat and bring the engine below its optimal point. Too slow and the engine overheats.

Source https://en.wikipedia.org//wiki/Radiator_(engine_cooling) scroll to "temperature control"

@citrinitas damn, yeah, using this type of control makes sense in a car, where you don't have access to a water pond 😭

Here's another "normal situation", empirically tested: CPU cooling loops

https://www.youtube.com/watch?v=MFoWyYGqBxE (go to 9:50)

Bonus abnormal situation: https://www.youtube.com/watch?v=m7Pn7_a37W8

@citrinitas The video is a very cool demonstration of the theory: The difference between normal and high is indeed much less than the difference between low and normal!

lmao

https://www.eng-tips.com/viewthread.cfm?qid=432703

In the real applications, it would expect "Hot area" to be not the straight pipe, but some complex shape component, which means a lot of turbulence, which as my intuition says: a lot more drag and dead zones if you try to pump more liquid around it and as a result -> less heat transfer. But someone might prove me wrong!

oh boy, it took me much longer to write down the solution in somewhat-understandable form than just to solve it myself. I've made a model in which liquid is separated into small batches that do not transfer heat between eachother, only from Hot and Cool areas. Also, each batch has a uniform temperature throughout it's volume. There are no friction, no heat loss, flow is liminar, almost like we have a conveyer belt of charged batteries. Here we go:

@Catnee

@Catnee

@Catnee

@Catnee

@Catnee I also have a kind-of intuitive explanation: imagine that your flow is super fast, so fast that liquid passing through Hot ot Cold area doesn't have time to change it's temperature, it would mean that the whole volume of liquid will have the same temperature, so you can forget about its speed, from heat transfering view it would behave like some sort of magical thermopaste, or cooling pipe with infinite thermal conductivity, so it is impossible for this substance to have any temperature gradient inside of it. But it doesn't mean that it would transfer infinite energy! Because the heat rate would be determined by thermal conductivity of walls in Hot and Cool areas.

@IsaacKing So, that is why i asked a lot of questions, trying to clarify what do you mean by "heat rate will change". Technically my solution shows that it would "technically" continue to increase, but from practical view it would quickly reach some "measurable limit" and would not exceed it if you will try to pump as much liquid as you can (though at some point either my model would stop working or pumps and pipes would start to collapse)

@Catnee Why would you buy NO? Doesn't your model show the answer is YES?

@BoltonBailey I've already told why i think the answer is NO, and it seems that @IsaacKing agrees with this. There is no practical gain, because of exponentially diminishing returns

@Catnee Hmm, there are definitely exponentially diminishing returns in the limit, but I would argue that in "normal" ranges of fluid flow rate you are in a regime where there is a measurable difference. The prototypical example would be something like an industrial application. Presumably there is a measurable increase in heat transfer with increased flow rate in a situation like this because if there were not, there would be no economic reason to pump the fluid through the system at all.

I'll admit I'm not an expert on this. Do most cooling applications work purely on the basis of convection?

@BoltonBailey * I guess I shouldn't say "no reason to pump fluid through the system at all" rather it should be "no reason not to supply marginally less power to the pumping system". It's an economic argument rather than a physical one but the "normal situation" criterion is so broad I think it's called for. @IsaacKing, what do you think?

@BoltonBailey I think in most cases "power supplied to the pumping system" is negligible, compared to the actual heat transfer of the system. There is a possibility that some industrial systems might be intentionally built such that there are some room to increase or decrease heat transfer rate, for controlling reasons, but i think there are better ways to do it, like increase the cooling area in general, because you are cooling in some big cooling pond of water

I'm also taking the position that this is all correct, but "most normal situations" do not involve pumping at enough speed that the working fluid is perfectly homogenous.

@citrinitas It doesn't need to be perfect, just homogeneous enough that there is no practical reason to pump more.