How Do I Calculate Heat Transfer Through a Multi-Layered Ceiling?

[Ziga Casar]

Hello guys,

I have a problem and I don't know how to solve it properly ...

So I have this situation:

And I must calculate the heat transfer (Q) through it ...

I know that the Indoor Temperature is 21C and the outdoor Temperature is 0C, I also know the following data for all layers:
Concrete: d (thickes) = 0.4m, k (Thermal conductivity) = 1.10 W/mK
Air: d = 2.25m, k = 0.0244 W/mK
Armstrong plate: d = 0.015m, k = 0.06 W/mK

And the surface is S = 731.9 m^2

I know I should calculate through this expression: Q = U S (T1-T2) and 1/U = SUM(d/k) = SUM(1/alpha)

the sum of d/k is no problem but for sum of 1/alpha, I do not know hot to calculate the alphas (Convection coefficient), because there is one alpha from air to Armstrong and one alpha from concrete to air (Or are there 2 alphas for each because the temperature under Armstrong plate is higher that the temperature above the Armstrong plate ...?)

So here is the problem, because there is a natural motion of air and a big horizontal plate I do not know hot to calculate the alphas... Can somebody please help me?

 

[Simon Bridge]

You need to concentrate on what the variables represent - and think: resistors in series.

 

[Ziga Casar]

I do not exactly understand what you mean. Can you explain it a little bit better?

 

[Simon Bridge]

How would you find the current through resistors in series?
Now: heat flow = current, temperature difference voltage.

 

[MarkJW]

Take a look at this: http://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node118.html

 

[Ziga Casar]

I completely understand the resistance circuits. But when I calculate the heat flux through the concrete only I get 42 253W, but when I calculate the heat flux through concrete, air and plate I get 165.5W. But this is only conduction, in real there is there also convection, and for convection I need alphas ... or is it not important to consider convection by calculating the heat flow?

I mean the heat flux difference is huge. I can not imagine that if you lower a ceiling with this plates you safe so much of energy? Air is a good isolator, but so good?