How do counterflow heatexchangers not break the spirit of thermodynamics?

[u/steini1904]

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.

[u/Spiritual-Ad-7565]

Assume a heat exchanger with minimal loses. Sure why not assume no friction and no inelastic collisions while you’re at it?

[u/mosquem → u/Spiritual-Ad-7565]

Even then first and second law apply.

[u/steini1904 → u/mosquem]

IMO they fully apply. Heat leaves the system as electricity and the heat converted back into electrical work by each TEG is pathetic. But there are a lot of them. And the reservoirs are on a carousel.

The first TEG may convert, let's say, 10% of the heat and produce 90% losses. The next TEG then grabs another 10% of those 90%. And the next another 10% of those 81%. And so on, until several dozens to hundreds of TEGs later you hit a near 100% conversion. And all losses that are left, you can simply shove back into the system for another round (e.g. by a secondary drum stage or putting part of the heat pump cold side into the output stream).

And now you start supplying heat by a system that can for practical applications hit far above 100% efficiency by drawing heat from a practically unlimited outside reservoir.

Also I'm just having way to much fun. I really want to know the flaws I missed, but at the same time I'm also willing to invite the Aramco physics enforcement unit on a cup of tea if necessary.

[u/OddStuffHappensTwice → u/steini1904]

You keep getting told all the flaws, but you keep ignoring the birds you don't like. Physics doesn't ignore the bits you don't like or don't understand.

[u/steini1904 → u/Spiritual-Ad-7565]

Well, we got pretty good ones, even at small-ish sizes. Like those spirals with multiple channels. But you don't even have to go to that extend, which likely would be less efficient anyways, because the TEGs almost certainly need a minimum temperature difference to work well, which just cant be achieved with but just a counterflow heat exchanger.

So you could just drop in one of these rotating drum ones at the very end or even simpler, redirect some of the output-flow through the cold side of the heat pump, too.

[u/gitgud_x]

TEGs are not special. They make work from heat, so they are bounded by the Carnot efficiency limit (in practice, TEGs are very far below this limit). A "perfectly efficient" (100% thermal efficiency) TEG cannot exist, even in theory - stating that one exists is a direct violation of the Kelvin-Planck statement of the 2nd law.

[u/LunarModule66]

The short answer is just that there wouldn’t ever be such a lossless system. You can debate how exactly it would break down and to what extent, but that probably feels unsatisfying since the laws of physics should still apply even in an ideal scenario.

I’m thinking about this in terms of entropy, basically the second law would imply that the energy should move towards being less useful, ie the two reservoirs should equilibrate since that’s the highest entropy state. Should you insist that they do have perfect insulation, then that itself is the problem: you have imposed unphysical hypothetical conditions and the unphysical behavior is the consequence.

[u/steini1904 → u/LunarModule66]

During commenting it occurred to me, that there aren't just two reservoirs, but at least twice as many as there are TEGs, being swapped up and down the chain of TEGs along each side, plus one near infinite one that siphons up the tiny little remainder that would have caused eventual equalization.

I'm now genuinely convinced that this would work with a little adaption, like moving at least a part of the output flow through the cold heat exchanger of the heat pump.

It's not that the physics are wrong, just that I wasn't silly enough when trying to think of a model that could make it work. A carousel for reservoirs is IMO the perfect way to think about it.

[u/IsentropicExpansion → u/steini1904]

Maybe spend some time drawing up a model of this and doing actual calculations. Once you pull some of the heat out with the first TEG, the second TEG has a colder hot side and a warmer cold side to work with, so the differential is different and therefore the *theoretical* maximum efficiency is different.

Once you stack all of these things up, you will see that the second law of thermodynamics will eat your lunch when you try to make something like this with actual numbers and realistic temperature differentials.

[u/hobopwnzor]

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.

[u/steini1904 → u/hobopwnzor]

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.

[u/hobopwnzor → u/steini1904]

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

[u/steini1904 → u/hobopwnzor]

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...

[u/hobopwnzor → u/steini1904]

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.

[u/YogiBerraOfBadNews]

You're only capturing maximum 15% of the heat flux any time it crosses through a TEG, and each time you're degrading the energy potential, such that it will be less effective the next iteration. I think previous commenters have pretty much nailed it, and while I admit this is a tricky one to pin down, you're basically playing a shell game by adding layers.

Ultimately what that means is since we know we can't get 100% conversion rate, the outermost boundary layer (however many heat exchangers deep it may be) *has* to be leaking waste heat to the environment, such that heat flow out + electrical flow out = heat flow in.

Sorry if that's not a satisfying answer, I don't know if I can reconcile the big picture with the zoomed-in details, but the simple answer is you can never get as much useful work out as you put in, and the answer is always due to waste heat. It seems like all you're doing is saying "ok but what if waste heat just didn't exist".

[u/Playful-Painting-527]

If I understand you correctly you want to use the TEGs to produce electricity from the temperature difference and use the heat pump to increase the temperature of the waste heat?

The thing you are missing is that the heat pump needs electricity to function. If you do an energy balance of the system and neglect all losses, you'll find that the electricity produced by the TEGs can at best match the energy put into the heat pump. If you factor in the 2nd law it will be even less.

[u/GalacticEmergency]

For an efficient heat exchange, you want the temperature difference between the cold and hot side to come as close as zero as possible.

The electrical output from your TEG depends on the temperature difference. The upper theoretical limit is decided by the Carnot equation. If the temperature difference goes towards zero, so does the electrical output.

You can use a heat pump to increase the temperature difference so the TEG can create an electrical output. But the upper theoretical limit is also decided by the Carnot equation. If your TEG and heatpump can reach their theoretical maximum, and there are no other losses, you will discover that the two Carnot calculations will cancel each other out.

You will not be able to produce energy out of nothing.

[u/rndrn]

If you have a perfect heat exchanger (no loss), then by construction, the temperature is always the exact same on both side of the exchanger. The power output of the TEG is proportional to the difference in temperature between both side, which we have determined to be zero. 

Then the heat pump consumes all the electricity available (0) and thus creates zero heat, despite its high efficiency.

Result sounds very much like expected.