Assistance on Transient Heat Transfer Problem in Windows

I don't know where this guy lectures, but while some of the principles he uses are OK, his conclusions are way out IMO.

To start with his statement that the single-glazed window loses 6.4kW. That would be true if the 20°C ΔT were across the glass, but it isn't. Most of the resistance to heat flow is due to convection from inside air to glass on room side, and from glass on outside to outside air.

I would calculate convection heat flow first, initially assuming zero ΔT across the glass, so convection ΔT = 10°C both sides. Multiply the heat flow by the glass R-value to get glass ΔT. Can then plug that back in to get a new convection ΔT, and iterate if you want more accuracy. It comes to 64.02W first time round, with glass ΔT 0.2°C, and after only 2 iterations gives 63.23W and 0.2°C. 6.4kW is what a double-glazing salesman might say!

For the double-glazing case, it comes to 50.91W at glass ΔT 3.35°C after 7 iterations, compared with 181W in the video.

That's using 1.8W/m²/K^1.25 for the natural convection coefficient. Obviously it's not an exact science and it would be different if there's a wind blowing outside.

I think that's the practical way to go about it, not sure whether it helps the OP with his finite elements and differential equations!

Try Finite Difference Method it is much simplier.