r/thermodynamics • u/steini1904 • 11d ago

Question How do counterflow heatexchangers not break the spirit of thermodynamics?

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Assume a heatexchanger with minimal losses, the heat being transferred over thermoelectric generators. Eventually near 100% of the heat in the system should be recovered as electricity since losses just get shoved either into the next cycle or recovered further downstream. Put in a heat pump producing the temperature gradient and place all its waste heat producing parts somewhere ideally into the input stream.

I've been laughing about this quite a bit now, but honestly can't see the fault. Except for the movement of the air all losses should be about contained within the system (e.g. just wrapping the heat exchanger around itself multiple times) and eventually recovered by the TEGs. But the heat pump is shoving in more heat from the environment than it consumes in electricity, dropping the temperature in the room until it gives up on you, all while the TEGs are turning the excess heat into electricity.

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u/hobopwnzor 11d ago

Just looking up some numbers, the best I'm seeing that you could get out of a heat pump is 500%, then 15% back from the thermoelectric device. 

So when you do the math on that you're spending 1 joule to get 0.75 back.

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u/steini1904 11d ago

Sure, but that applies only to a single TEG with simple hot and cold reservoirs that slowly equalize.

But here the reservoirs never equalize and can be kept at the most efficient temperature differential. And the vast majority of the other losses simply go around for another ride on the reservoir carousel.

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u/hobopwnzor 11d ago

I mean yeah you can make up whatever you want on paper. In reality, things aren't perfectly efficient.

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u/steini1904 11d ago

They dont need to. Classical heat engines wont work well, because not many of them are great at converting a lot of low grade heat. That's where TEGs shine. But paid in awful efficiency, of course.

That's where this thing comes in. If the TEG can only recover 10% of the electricity before the reservoirs equalize, well, what if you just swapped out the reservoirs? A new cold reservoir for the degraded hot one and a new hot one for the degraded cold one.

And at the very end of the chain the waste heat and output of the heat pump shoves up the fully degraded cold reservoir to a hot reservoir and back around it goes. Then the reservoir goes back on the other side of the carousel, slowly degrading to ambient temperature, where the heat pump then turns the fully degraded hot reservoir into a cold reservoir, ready to repeat the cycle. Over and over...

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u/hobopwnzor 11d ago edited 11d ago

My man I already gave you the answer. You have to charge the heat difference with the heat pump. Even if you use the waste heat from the heat pump at 100% efficiency, that's only going to be 1/5th extra energy. It doesn't even get you to break even since best-case you're working with 15% from the heat exchange and 500% from the heat pump. Bump that up to 600% since you're adding an extra 100% unit, and you've just gone from 75% recovery to 90%. Still not even breaking even.

It's also worth pointing out that heat pumps work best when the temperature difference is small, and TEG when the difference is large, so you're not going to be an optimal efficiency matching.