Q:

How can I calculate the accumulation rate for water vapor condensation on a horizontal surface? I know the vapor pressures, temperatures, surface area for condensation and the air vapor density.

- AO

VA Tech, Blacksburg, VA, USA

- AO

VA Tech, Blacksburg, VA, USA

A:

There are quite a few things which affect how fast water vapor will condense, more than the ones you mention.

It takes 540 calories per gram of water to make it turn into vapor. The water releases this same amount when it condenses. This heat energy has to be dissipated somewhere. If the air is still, then the heat flow will follow the heat transfer equation, which is similar to the diffusion equation. It depends on the thermal conductivity of the surface and also of the air, and on the temperatures far from the surface. Heat will flow in two directions here. You have to worry about both the thermal conductivity of the cold surface and also that of the layer of water that has condensed, as the heat must flow through that, too. If the condensing water freezes (makes frost), then the thermal conductivity of the ice must be used. The frost will also in general not be horizontal, and this will change the surface area. If the water layer is thick, convection will play a role and then life gets even more complicated.

The other effect will be the rate at which water vapor can diffuse through the air to reach the surface. This depends on pressure and temperature.

It is probably a safe assumption that the top layer of water is in equilibrium with the water vapor in the air layer immediately above it (this isn't quite the case as water vapor is condensing, but if the condensation is limited by heat transfer and diffusion, this is the way to go). The temperature of this top layer will not be the same as that of the cold material or of the air far away. This means solving the diffusion and heat equations together and making the boundary conditions match using the vapor pressure as a function of temperature.

This is not a simple calculation! Why not try some actual experiments?

Tom

It takes 540 calories per gram of water to make it turn into vapor. The water releases this same amount when it condenses. This heat energy has to be dissipated somewhere. If the air is still, then the heat flow will follow the heat transfer equation, which is similar to the diffusion equation. It depends on the thermal conductivity of the surface and also of the air, and on the temperatures far from the surface. Heat will flow in two directions here. You have to worry about both the thermal conductivity of the cold surface and also that of the layer of water that has condensed, as the heat must flow through that, too. If the condensing water freezes (makes frost), then the thermal conductivity of the ice must be used. The frost will also in general not be horizontal, and this will change the surface area. If the water layer is thick, convection will play a role and then life gets even more complicated.

The other effect will be the rate at which water vapor can diffuse through the air to reach the surface. This depends on pressure and temperature.

It is probably a safe assumption that the top layer of water is in equilibrium with the water vapor in the air layer immediately above it (this isn't quite the case as water vapor is condensing, but if the condensation is limited by heat transfer and diffusion, this is the way to go). The temperature of this top layer will not be the same as that of the cold material or of the air far away. This means solving the diffusion and heat equations together and making the boundary conditions match using the vapor pressure as a function of temperature.

This is not a simple calculation! Why not try some actual experiments?

Tom

*(published on 10/22/2007)*

Q:

formula for rate of condensation???

- robinho (age 24)

hartford,connecticut,US

- robinho (age 24)

hartford,connecticut,US

A:

If such a formula exists, it’s very complicated. Please re-read the answer to question 1448 very carefully

LeeH

LeeH

*(published on 10/22/2007)*

Q:

Condensation rate = Total Heat Transfer/Heat of VaporizationC.R.=Q/h-sub(fg)h-sub(fg)can be found for the pressure or temperature of your problem->Google->(thermophysical properties of saturated water table)

- Juan

- Juan

A:

Yes, one can express the rate of condensation in terms of the rate at which heat is released in the process but that does not tell someone what the rates are. For that detailed facts must be known. For example, if the water is not stirred at all the condensation will warm the top layer and thus speed up evaporation, slowing the net condensation rate. Stirring will keep the top layer from warming as much and thus give a higher net condensation rate. Similar effects occur in the atmosphere.

Mike W.

*(published on 05/07/2016)*