Re: Humidifier - Hot vs Cold Water Experiment

trader4@xxxxxxxxxxxxx wrote:
On Feb 11, 2:31 pm, dpb <n...@xxxxxxx> wrote:
....

Hmmm....along w/ Frank I'm puzzled by the apparent paradox in the
thermodynamics here.

My first question would have to do w/ whether the assumption of constant
input flow rate is valid not knowing the Aprilaire at all. Secondly the
exit temperatures seem puzzling.

The flow rate is determined by the water pressure and by an orifice
with a small hole at the solenoid valve. It's hard to imagine that
hot water would flow at a slower rate through it, which is what would
be needed to skew the results.

I was commenting simply on the design of the experiment is extremely sensitive to the assumption that that is indeed a constant. As noted, I have no knowledge of the device itself, so if there were a float or somesuch, it's a possibility that the lower evaporation rates influence the inlet volumes.

What's puzzling about the exit temps? They are for practical
purposes all the same. Which is what one would expect. If you start
with cold water, then the water temp rises on it's way down the
panel. If it's hot water, it cools on it's way down. Either way,
with a lot of air blowing on the panel, it seems reasonable that it
reaches a final temp somewhere before the end of the panel.

Again, that is dependent on details I'm unaware of...if there's sufficient time/distance for a secondary heat transfer to occur then it really is a case of the red herring in the data--it has no really bearing on the experiment. Again, just commenting...

The only thing that is a little surprising to me is the amount of
difference hot vs cold made. I would have thought that there could be
a 25 to 50% difference. I think it has to do with the fact that
evaporation in this case is a complex process, not entirely described
by latent heat. ...

I had the "aha!" moment shortly after I posted and was coming back to amplify and, I think, answer the "why" question.

Looked up water vapor pressure as a function of temperature. The results you got and the vapor pressure and some derived values that will discuss on down are as follows. You can see the vapor pressure is quite sensitive to temperature as was your evaporation rate.

Normalized to 51F Normalized to 51F
T(F) Evap(oz) VP(mm Hg) Evap VP VP**3
51 6.5 9.5 1.0 1.0 1.0
102 11.5 52 5.5 1.8 5.5
135 15.0 130 13.7 2.3 12.2

Assuming there's more than adequate heat available to evaporate the water, the problem is one of residence time and heat transfer. My conjecture is the vapor pressure is key in atomizing and thereby increasing the effective heat transfer (and probably also increasing the residence time some, to boot).

The normalized columns show the relative effectiveness of the evaporation as compared to the cold water as the temperature was raised (again, assuming there isn't any major bias in the experiment which I'm willing to accept is probably not too bad given the orifice as a rate controller for the key variable of input). It shows the effective evaporation went up by an even faster rate than the vapor pressure.

But interestingly enough, the magnitude of the numbers caught my eye and I just guessed at a power law exponent of 3 and voila! -- the agreement is quite nice...

I think this is the basis for underlying the phenomenon.

I didn't look for engineering correlations for predictions of evaporative rates, but they undoubtedly exist and Perry's Handbook would be a reasonable place to start. It would be interesting to see if such correlations did follow a power law but I'm not inclined to pursue it further to see--I really don't know why I got in before (other than the single measurement sensitivity in the experiment caught my eye being a thing I was heavily involved in in many real situations in an earlier life).

Anyway, maybe that will add some cannons to the fodder... :)

--

.

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