Water Vapor Transfer Coefficient

[Tubik]

Hello,
in the wufi-wiki is described calculation of water vapor transfer coefficient. It is convective component of the heat transfer coefficient multiplied by constant 7·10-9. I would like to know how you received the constant. Is it based on a physical relation?

Thanks for your reply Tomas

[Thomas]

Hi Tomas,
the relationship between the water vapor transfer coefficient beta and the convective component of the heat transfer coefficient, alpha_c, is described by similarity theory. I'd have to consult with Dr. Künzel to tell precisely how he arrived at the factor 7·10-9 he gives in his thesis, but for a quick and simplified estimate (and please remember that WUFI is a simplified model anyway), we may refer to [1]:

After Lewis, we have for turbulent air flow:

beta_turb = alpha_c / (rho cp R T)

rho: density of the air/vapor mixture
cp: specific heat capacity of the air/vapor mixture at constant pressure
R: gas constant of water vapor = 462 J/(kg K)

For laminar flow, we have

beta_lam = D * alpha_c / (lambda R T)

D: diffusion coefficient of water vapor in air
lambda: thermal conductivity of air.

In both cases, beta can be seen to be proportional to alpha_c. We may therefore assume that this is also the case for practical situations which are some mixture of turbulent and laminar flow. Neglecting the influence of the temperature, the influence of the vapor content on the properties of the air and a few other subtleties, we may use the values

rho = 1.24 kg/m3
cp = 1005 J/(kg K)
lambda(10°C) = 0.024 W/(m K)
D(10°C) = 2.57e-5 m2/s
T = 283 K

and we arrive at the estimates

beta_turb = 6.1e-9 * alpha_c
beta_lam = 8.2e-9 * alpha_c

So if a constant representative value is to be used, 7e-9 appears to be a plausible choice. The neglected dependence on the temperature is small (as can be seen if temperature-dependent values for lambda etc are used), so it is to be expected that the error involved by using a constant average value is mainly caused by neglecting the various different degrees of turbulence occurring in practice.

Kind regards,
Thomas

[1] W. Illig: Die Größe der Wasserdampfübergangszahl bei Diffusionsvorgängen in Wänden von Wohnungen, Stallungen und Kühlräumen, Gesundheits-Ingenieur, Band 73 (1952), Heft 7/8, S. 124-127

[Tubik]

Hi,
thanks a lot for your quick reply. Receive the mentioned article is problematic and it will take a time. But now it is clear and obvious.

Best wishes Tomas

[Thomas]

Receive the mentioned article is problematic and it will take a time.

If you are interested in a more in-depth treatment of the surface transfer coefficients arising under various circumstances, you should probably consult a modern textbook on heat and mass transfer. The mentioned article does not give any theoretical background, it just cites some formulas and discusses their practical application for building physics. I just quoted that old article because I had it at hand (and it may have influenced the choice of the 7e-9 for WUFI), not because it is somehow very fundamental.

Kind regards,
Thomas