Heat exchange during evaporation

[aquatec]

Hi guys this is my first posting.

We are having a debate over on a window cleaning forum about water evaporation. Someone suggests that using hot water on a hot pane of glass creates less evaporation due to the fact that the heat exchange is much lower. And with cold water because of the heat exchange being more rapid more of it would evaporate. This came from a reputable company, and after doing some extensive searching on the Internet I could find no confirmation of this.

Any information or help on this would be appreciated.

Thanks,

Peter

 

[25362]

Rates of evaporation are conditioned by many factors, among them: vapor pressure (as function of temperature), vapor diffusivity in air, air speed, air humidity, air temperature, exposed surface geometry and temperature, etc.

This link may prove to be useful:

http://van.physics.uiuc.edu/qa/listing.php?id=1440

 

[wfn217]

There will be faster evaporation with the hot water. The driving force is the vapor pressure, which is higher at the high temperature.

 

[moltenmetal]

Dunno- sounds suspicious to me. If you put equal masses of hot and cold water onto identical sheets of hot glass under identical conditions, I'd expect the hot water would be gone faster than the cold. The cold has to heat to the dewpoint first before it will evaporate, whereas the hot is already at or above dewpoint. Then again, maybe it's the wetting properties of hot and cold water on glass at play- this is related to washing windows after all, and evaporation is a simultaneous heat and mass transfer problem.

 

[aquatec]

Thanks for the reply,

I had a look at the web link you gave me but I am afraid it is above me.

Given that these 4 points are the same...

1) The temperature of the water at the air-water surface

2) The humidity of the air

3) The area of the air-water surface

4) The temperature of the air

I read that the actual evaporation process can change some of the 4 points above, and accept that. But could say 1 Litre of cold water possible evaporate quicker than 1 Litre of hot water. BTW these panes of glass is only heated by the sun.

Thanks again,

Peter

 

[aquatec]

Thanks guys, I was writing my reply as the other 2 posts came through.

One thing I would like to add the water is purified. Would that make any difference? I shouldn't think so.

Peter

 

[25362]

The reputable company would be right for the following conditions apart from those listed by you:

1. the only heat source for evaporation comes from the warm glass pane kept at a temperature T, and heat is transferred by conduction

2. the starting water film thickness x is equal for the warmer and colder water at T_w, and the final thickness is zero

This is substantiated by the general transient heat transfer equation for time, t

t = [H.[ρ]/(k [Δ]T)](x²/2)​

When dividing the estimated times for cold and for hot water we obtain:

t_c/t_h = [(H.[ρ]/k)]_c/[(H.[ρ]/k)]_h[×][(T-T_w)]_h/[(T-T_w)]_c​

Where H=latent heat of evaporation; [ρ]= water density; k=water's thermal conductivity; c=cold; h=hot.

It is seen that although colder water has a greater H.[ρ]/k, its larger T-T_w may overcompensate and make t smaller.

 

[insult2injury]

I disagree with 25362. Since both the hot and cold water is at atmospheric pressure, the vapor pressure and evaporation temperature are fixed. Those equations would only hold true for the situation where both the hot and cold water were at the vapor corresponding to each water temperature. The cold fluid will take longer to evaporate because it will take longer to heat it to the evaporation temperature than the hot water. The time to evaporate once at the evaporation temperature will be exactly the same.


I2I

 

[25362]

It is assumed that natural air convection currents and undersaturation would remove the vapors as they form. It is also assumed that the latent heat of evaporation is supplied by the window pane (heated by the sun). If we assume also heat gain by solar radiation then the effects may be even enhanced.

 

[chicopee]

This reminds me of a thermodynamic problem which I had in the 60's. The problem was what freezes faster hot or cold water in ice cube trays when placed in the refrigerator freezer compartment.
The answer would amaze anyone who studied heat transfer and thermo. and the reason had nothing to do with water properties.

 

[MortenA]

and i though we were geeks - a window cleaning forum

Best regards

Morten

 

[aquatec]

We done the hot cold water freezing thing years ago as well, and the cold water as expected froze first.

Peter

 

[25362]

I've read thread1088-156114 on the Mpmemba effect and couldn't find a satisfying explanation for its actually taking place.

From unsteady state heat transfer principles applied to freezing machines, the time t is estimated

t = [λ][ρ]x² [÷] (k[Δ]T)​

where [λ]=latent heat of freezing; [ρ]=density of ice; k=thermal conductivity of ice, [Δ]T=temperature difference between unfrozen water and the chilling surface.

Since [Δ]T is greater for the warmer water (thus taking longer to freeze), the only other sufficiently important factor to affect time and offset the effect of [Δ]T is the size of the crystals, measured by x.

It appears that the better distribution of warmer water in the icecream mixture leads to smaller and more homogeneous ice crystals. This results in reduced chilling times.

I wonder whether I'm on the right track. Any comments ?

 

[25362]

A correcting comment: I remember the logic of the postings that stated the impossibility of the Mpmemba effect due to the fact that warm water must reach first the temperature of cold water, thus warm water would take longer to freeze.

It appears, however, that the time for heat transfer through ice predominates over that through the water phase.

The correct equation for the freezing time would be:

t = (??/k) (x²/2 ÷ ?T_ice)​

and although a larger ?T through warmer water prolongs the time for heat transfer, the influence of x²/[Δ]T_ice through ice is much stronger.

Still looking forward to receiving comments.

 

[25362]

t = ([ρ][λ]/k)[([Δ](x²)/2][÷][Δ]T_ice​