Which variables determine the exact output of this condensing device?

[anikad]

This version can work. Purple arrows.

Let's say the hot air reached 40°C 70% RH levels (after absorbing lots of moisture from the wheel) . And we bring it in contact with ambient air at 20°C.
Is there a physics equation that can tell whether that hot stream of air when brought to contact with a 20°C ambient air- can reach 100% RH levels ?

Basically what I want to know- the 70% RH air will be increased to higher RH (since cooler surfaces have higher RH) , but what dictates how much it will increase & whether it will increase to 100% RH so we can get the maximum possible condensate?

Any answer to it will be appreciated

 

[hutchphd]

I do not know a simple answer. You really need to know the various rates involved (for a continuous process). I think a far better design (as has been talked about) is to heat the dessicant directly with the solar flux to expel its trapped moisture.

 

[256bits]

Thank you! Now you really appear to be my accomplice.

So the engineering analysis of this system comes down to this : The greater the temperature difference between hot air & cooler ambient air, the quicker the air picks up enough moisture to reach 100% humidity- to be brought to a cooler surface.Am I thinking correctly?

Maybe.
I haven't done any calculations myself so I won't be quick to say yeas on no.
My point is that at some temp/humidity levels the system will never work at all.

Either do calculations, or experiment. ( But I don't not think that you will get rivers of liquid water for a table top size system .)

 

[anikad]

I do not know a simple answer. You really need to know the various rates involved (for a continuous process). I think a far better design (as has been talked about) is to heat the dessicant directly with the solar flux to expel its trapped moisture.

I agree with you on that design!
What my question was essentially: WHAT physics equation relates the following 4 variables.

Initial T ; Initial RH ; Final T ; Final RH

I believe there's ought to be an equation for this simple relation, since we already know that:
Final RH> initial RH & Final T < Initial T

 

[Tom.G]

This screen capture didn't work very well, but here is the approach.
It is about 35% down in the right column at:
https://www.sciencedirect.com/topics/earth-and-planetary-sciences/dew-point

It is an excerpt from the book :

Theoretical Grounds for Humidity​

Dario Camuffo, in Microclimate for Cultural Heritage (Third Edition), 2019

The DP can be easily computed from RH and air temperature, as in the next formulae. Indeed, considering that the DP is reached with an isobaric process, the vapour pressure at the original dry bulb temperature equals the saturation pressure at DP, i.e. e(T) = esat(DP). By substituting this finding in formula (3.38), with the help of the Magnus & Tetens formula, one obtains:
(3.48)u=etesatt=eDPesatt=esat0×10aDP/b+DPesat0×10atb+t=10aDP/b+DP−at/b+t
hence
(3.49)logu=aDPb+DP−atb+t
and
(3.50)DP=b+DPalogu+b+DPaatb+t≈b+talogu+t
where the last approximate finding has been obtained substituting t to DP in the right-hand side of the first identity. Of course, the first term is negative as u < 1 and log u < 0.
Another formula can be derived considering what happens above an evaporating surface. The air temperature lowers, while the increase of MR raises the DP. The air temperature t continues to decrease until the temperature of the evaporating surface, called wet bulb temperature, tw, is reached (see Section 3.9). When the evaporated vapour reaches saturation, t = tw. Starting from the Clapeyron equation and the definition of w and always considering the difference DP − tw, after some steps and approximations, the following formula is obtained:
(3.51)DP≈bblogu+tlogu+atab−blogu−tlogu
where a and b are the Magnus & Tetens coefficients for vapour in equilibrium with the liquid phase. Eq. (3.50) is a better approximation. The formulae can be used once the RH is known, and obviously
(3.52)logu=logRH100=logRH−2
DP ≤ T and DP = T only when RH = 100%. The DP is determined once the air temperature T and the RH are both known, or also when only the MR (or SH) is known. In particular, maxima of MR correspond to minima of DP, and vice versa, so that the DP can be used for diagnostic purposes instead of the MR and may be useful to express the moisture content in °C.

The dew point spread (also called spread), i.e. the difference ΔDP = T − DP basically depends on both the actual air temperature T and the MR. Following the approximation (Eq. 3.50 ), it can be expressed as a function of air temperature and RH
(3.53)ΔDP≈−b+talogu
It physically shows how much the air temperature is close to, or far from, the DP. The zones having smaller ΔDP are more prone to form condensation, to allow microbiological life and more intense weathering. Useful maps of this variable can be easily drawn for diagnostic purposes. However, although the RH is a very different but related variable, in general the areas with RH maximum are the same as those in which the ΔDP is minimum. If one is not interested to know how much the ambient is above the dew point, i.e. how much wall temperature (not air temperature!) should be raised to avoid condensation, maps of RH are sufficient to give a qualitative idea of most critical areas.

Dew has the typical form of droplets and especially forms on leaves during the nocturnal cooling due to the infrared (IR) emission. The formation of dew on leaves is favoured by the local excess of moisture due to stomatal transpiration. The surface tension of water tends to displace the larger droplets to the edges of the leaves and in particular to the points of leaves, especially the lance-shaped ones. The upward IR loss during clear nights is a very effective cooling mechanism. The surfaces on which dew forms are free from any upper shield and in practice are the same that are reached by rainfall. This is the reason why people often believe that dew falls similarly to drizzle. Dew is favoured over vegetated areas, but it occurs on monuments as well, when their surface temperature falls below the DP. When the temperature of a surface falls below the DP, in the viscous layer surrounding the surface RH >100% and condensation occurs.

Hope this helps!

Cheers,
Tom