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Heat transfer in Cavity wall

  1. Dec 16, 2012 #1
    1. The problem statement, all variables and given/known data
    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-'.


    2. Relevant equations

    H = kA[itex]\frac{ΔT}{L}[/itex]

    H = [itex]\frac{A(ΔT)}{\sum\frac{l}{k}}[/itex]


    3. The attempt at a solution

    (A) H = (0.8)(0.35)([itex]\frac{15}{0.004}[/itex])

    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

    [itex]\frac{10(15)}{\frac{0.1}{0.6}+ \frac{0.05}{0.024}+ \frac{0.05}{0.03}}[/itex] + 3150 + [itex]\frac{(8.95)(15)(0.6)}{0.1}[/itex]

    total = 3993.8 J/K

    Is this correct?
     
    Last edited: Dec 16, 2012
  2. jcsd
  3. Dec 16, 2012 #2

    haruspex

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    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.
    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.
     
  4. Dec 16, 2012 #3
    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
     
  5. Dec 16, 2012 #4

    haruspex

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    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.
     
  6. Dec 16, 2012 #5
    Oh god!! I feel like a fool! I really misread that bloody question! I assumed I had x-ray vision. Thanks!!
     
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