Nothing stops you from reusing most of the heat in the draining hot water.

@CuriousOne - True, but this doesn't address the question. IF it turns out that heating the air WOULD yield energy savings, then one could compare the savings to those from reusing the heat in the draining hot water. And then there would be the question of cost of both solutions.

Nothing stops you from doing the rather trivial calculation that shows that it doesn't and that you are better served by reusing the heat in the water. Just my two cents.

Apparently nothing stops you from snarky responses. I posted here because while the calculations are "rather trivial," to you, it would take me quite a bit of background research to do them. My hope is that the calculations would be so trivial to members of physics.stackexchange.com that I could get an answer without attitude.

What's snarky about giving you the correct answer?

If it is an answer, then it should be posted in Answers, not Comments. And quality Answers on Stack Exchange require more than someone saying "it does" or "it doesn't." So if you are going to answer the question, I request you show your work - or at least provide links to supporting info.

It's such a trivial answer that it doesn't really deserve to be one. It's much better left in comments. If someone wants to spend time on a trivial calculation, that's up to them. I do agree with you, though, that cold showers are refreshing. I do them all the time when I am in the tropics.

Let us continue this discussion in chat.

Hint for those who want to actually calculate this: Air temperature is not the actual problem and air is not what needs to be heated to feel comfortable or even hot in a room. It's the temperature of the walls that sets the radiation losses of the human body, which means that the heat in the hot water would have to be used to heat not just the air but also the surface of the walls. For any reasonable sized bathroom that's a losing proposition. Alternatively you can put mirrors on all walls... but that looks really awkward.

Perhaps I should clarify that we're talking about a confined shower stall. Also that this question entered my mind when using a steam shower at a friend's house. I don't know what temperature the steam got to, but I do know that I was most comfortable using cooler water. But I had no way of measuring the temperature of the air nor the shower water. Would the temperature of the walls still control the radiation losses of the human body in such an environment?

@CuriousOne Do you really think that radiation is the primary heat transfer mechanism from the body to the surroundings? If that were the case, then on a cold day, the presence or absence of wind would have negligible effect on your skin temperature. In my judgment (and experience) conduction and convection to the air are much more important than radiation.

@ChesterMiller: Yes, the temperature of the walls still controls how comfortable you feel. The human body has an area of about 2m^2. A black body at the body temperature of humans would radiate about 1kW of power into empty space, i.e. we can only stay warm with our internal 100W heat source because our environment radiates almost as much radiation back as we lose. If you lower the radiation temperature of the environment to a mere 16 degrees C, the power we get back is 800W, i.e. we have basically no way of staying warm without clothing that reduces radiation losses.

This also explains why steam in the shower feels so good: it condenses on the walls and immediately raises their temperature very considerably. Warm air would not do this nearly as quickly and the radiation losses would make the shower feel cold.

It's funny how some people always post meaningless comments, but never answer the question. Perhaps to look inteligent?

@Pablo: You mean the OP didn't consider radiation? Yes, it's not something totally obvious, especially since high school science used to teach the wrong explanation for why we need clothing (to protect against cold air), at least when I was in high school. I hope that they are teaching the correct explanation now, that clothing protects against air and radiation losses. There are also some awesome black body calculators around like hyperphysics.phy-astr.gsu.edu/hbase/quantum/radfrac.html. Give it a spin!

Sounds like using draining shower water to heat the walls might be a way to improve the feeling of warmth.

"Nothing stops you from reusing most of the heat in the draining hot water."... hey... didn't I write that in my first comment? Say, why didn't you like it the first time around and why are you plagiarizing it now?

Not plagiarizing - imitation - which, as you know, is the sincerest form of flattery. But it still doesn't answer the original question.

Would you agree that my additional comments do and that they explain why I am not particularly interested in running trough the entire numerical argument with an example bathroom or a more general discussion? Like I said, if someone is willing to do the calculations, more power to them, I just don't see your suggestion as popping out as a general solution to saving energy. Even the heat exchanger will, as you obviously noticed, quickly turn into an engineering nightmare because of hair and human skin cells clogging its pipes. :-)

I mean the whole discussion doesn't relate much to the question

@Pablo: You would be correct, except that it actually answers it completely. Did you try that black body calculator, yet? After you do, you can write a complete answer for the OP and I will give you a +1 for your efforts. :-)

@CuriousOne I would if I understood blackbody radiation...

@CuriousOne With all due respect, I still contend that conduction and convection dominate the heat transfer.

@ChesterMiller: You are welcome to run the numbers. I would also suggest that you do an experiment in a cold room with some aluminum foil or an aluminized mylar emergency blanket. Wrap the foil around an uncovered arm or a leg, leaving some distance for air. One can feel the difference due to the reflected heat quite easily. When I go into a cold outdoor environment I always take one of these with me... it could easily become the difference between life and death and they weigh next to nothing.

@Pablo: This is a great example to get an intuitive feeling for it. Seriously, punch a few numbers into that online calculator. You will be amazed how much radiation changes between room temperature and body temperature.

Hi again @CuriousOne. I've done a little research on this, and it looks like to some degree, we're both right. google.com/…. According to the references I've seen, for typical temperature differences, the heat losses from naked bodies from radiation and convection are about on the same order. I checked you 100 W value, and it seems about right. So, I stand corrected.

@ChesterMiller - could you take a look at what I posted below. It's a starting place.

@ChesterMiller: Sounds about right. If this helps: Intuitively I didn't believe it initially myself, but radiation losses are a serious problem for humans, even in relatively mild temperatures.