Calculating Heat Transfer in a Cavity Block Wall with Windows

[Darth Frodo]

Homework Statement

A cavity block wall of area 10m² constructed of 100 mm concrete, 50 mm air gap, 50 mm of polystyrene and a second 100 mm wall of concrete. The wall contains three windows with dimensions of 0.5 m x 0.7 m with glass 4 mm thick. The outside temperature is 5 °c and the inside temperature is 20°C.

Calculate
(A) the flow of heat through the glass, and
(B) the total heat flow through the wall.

Average thermal conductivities are
Concrete 0.6 W m·' K-'.
Polystyrene 0.03 W m-' K-'.
Air 0.024 Wm-' K-'.
Glass 0.8 W m-' K-'.

Homework Equations

H = kA$\frac{ΔT}{L}$

H = $\frac{A(ΔT)}{\sum\frac{l}{k}}$

The Attempt at a Solution

(A) H = (0.8)(0.35)($\frac{15}{0.004}$)

H = 1050 J/K

Total Heat through Glass = 3150(B): Total heat = Heat though Cavity wall + Heat though windows + Heat through the concrete surrounding the windows

$\frac{10(15)}{\frac{0.1}{0.6}+ \frac{0.05}{0.024}+ \frac{0.05}{0.03}}$ + 3150 + $\frac{(8.95)(15)(0.6)}{0.1}$

total = 3993.8 J/K

Is this correct?

 

[haruspex]

(B): Total heat = Heat though Cavity wall + Heat though windows + Heat through the concrete surrounding the windows

I don't understand the third term there. That would suggest there's an area of concrete surrounding the windows which is not cavity wall.

$\frac{10(15)}{\frac{0.1}{0.6}+ \frac{0.05}{0.03}+ \frac{0.05}{0.03}}$ + 3150 + $\frac{(8.95)(15)(0.6)}{0.1}$

Some problems there.
You have 0.03 instead of 0.24 for air conductivity. The second concrete wall should be represented by a fourth term below the line in the first expression, not as a third expression added on the end.

 

[Darth Frodo]

Sorry for the confusion. By "Heat though Cavity wall" I meant those sections of the cavity wall that were 10 square metres in area. Then the outer most wall was split into 2 parts, The windows and the surrounding concrete?"The second concrete wall should be represented by a fourth term below the line in the first expression" But the area of the second outermost wall isn't 10 square metres

 

[haruspex]

Sorry for the confusion. By "Heat though Cavity wall" I meant those sections of the cavity wall that were 10 square metres in area. Then the outer most wall was split into 2 parts, The windows and the surrounding concrete?

I think you are misreading the problem:

A cavity block wall constructed of ... and a second wall of concrete. The wall contains three windows​

The 'cavity block wall' consists of four layers: concrete-air-polystyrene-concrete.
The 'wall' that contains three windows is the cavity block wall as a whole, not just the second layer of concrete. (Otherwise you wouldn't be able to see through the windows.)
And I forgot to mention (as follows from this) that the 10(15) in your first expression should have the window area subtracted.

 

[Darth Frodo]

Oh god! I feel like a fool! I really misread that bloody question! I assumed I had x-ray vision. Thanks!