Will Condensation Form on My Roof's Steel Structure?

[cyn1117]

Hi ! I need to know whether condensation could appear within this roofing structure.

The top layer (exposed to outside weather, hot and humid) is composed of (1) Glass reinforced fibre cement panels, underneath it is a layer of (2) thermal insulation, (3) an air gap, (4) steel structure, (5) another insulating layer. The inside air is air-conditioned.

I am trying to find out whether condensation would occur within the air gap and condense on the steel structure??

I look up online and found,

t(i) - t(s) = {t(i)-t(o)}/{R(is) + R(os)} x R(is)

to calculate surface temperature, then obtain dew point from psychrometric chart...however, how do I calculate the surface temperature at the steel structure when I don't know the temperature of the air gap (since it is affected by outside hot temperature too)

Also, should I be using another approach which I found, by calculating vapour pressure drop, then calculate surface temperatures etc...but then again, I don't know the temperature of the air gap...?

Pls help! Thanks in advance!:

 

[haruspex]

how do I calculate the surface temperature at the steel structure when I don't know the temperature of the air gap

Assume steady state heat flow. Given the inside and outside temperatures and all the gaps and conduction coefficients, you can calculate the heat flow rate. Then you can find each of the individual temperature drops.