In WUFI, the moisture transport equation is shown below.
moisture transport equation.jpg (5.97 KiB) Viewed 6210 times
However, this equation does not include the source term introduced by the air change source.
If the air change source needs to be included in the moisture transport equation, the equation will look like this:
moisture transport.png (8.56 KiB) Viewed 6210 times
yes, for use with the transport equation the \(d_\mathrm{cavity}\) should be removed.
In the transport equation, the water content \(w\) is a volume density (kg/m³), so any moisture source term should be a volumetric source density (kg/(m³ s)). \(w\) describes the moisture density at one point in the volume, and \(S_w\) describes the moisture source density at that point.
If we compare two layers containing air change sources, with the air change rates being the same but the second layer twice as thick, then we expect the absolute amount of moisture released by the source in the thicker layer to be twice the amount released in the thinner layer because the thicker layer has twice the volume. But since the double amount is spread over twice the volume, the volumetric source density remains the same. So for a given air change rate the source density is independent of the volume and thus independent of the layer thickness.
The layer thickness \(d_\mathrm{cavity}\)should be included if the total moisture released in a given cross section of the wall is to be described (that is, in each square meter of the wall this or that amount of moisture is released). But this is not what is required for the transport equation.
Always learning something from your reply, appreciate it!
Another quick question: the above equations are for the 1D model, right?
In WUFI 2D, the partial x should be replaced by ∇. Is that correct?
Cheers
