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Homework Help: Calculating Insulation Thickness for a Building (Engineering)

  1. Jul 15, 2014 #1
    1. The problem statement, all variables and given/known data

    A single roomed building measureing 12.0m x 12.0m x 2.5m is maintained throughout the day at a temperature of between 18-23°C. Each wall is to be constructed from 2 layers of common brick, an internal particle board and a layer of insulation. The building is heated using standard space heaters that will run on natural gas. The gas currently costs 7p/kWh and is burnt at an efficiency of 70%. During heating calculations it is assumed that the same thickness of insulation is applied to floor, wall and roof and that mineral wool at a current price of £55/m3 is utilised. Calculate the the optimum thickness for insulation over a 12 months period.

    2. Relevant equations

    q = ΔT/∑Rth
    therefore: q with insulation/q without insulation = 0.3 = ∑Rth (with)/∑Rth (without)
    Thermal resistance Rth = Δx/k

    3. The attempt at a solution

    So far I've assumed that due to it being over 12 months, there will be a change in outside temperature during the different seasons. Also assumed that there is no air gap between the wall. The k values I have found so far are: brick = 0.7, particle board = 0.15 and k for wool is 0.04, so I can calculate the Thermal resistance and heat loss.
    R wool = L/kA = x/0.4*1 = x/0.4 °C/W
    R brick = L/kA = 0.1/0.7*1 = 1.429*2 = 0.2858 °C/W
    R P.board = L/kA = 0.01/0.15*1 = 0.067 °C/W

    I just need help in finding the equation for calculating Energy cost.
    Last edited: Jul 15, 2014
  2. jcsd
  3. Jul 16, 2014 #2


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    Science Advisor
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    Gold Member

    In order to maintain a constant temperature the energy supplied by the heating must equal the heat loss through the structure. So calculate the energy loss over a year in Joules. The same amount of energy must be delivered by the gas heating.

    Because the heating is not 100% efficient more energy must be supplied from the gas main than calculated above so do that calculation.

    Once you have a figure for the total energy needed (in Joules) remember that:

    1 Watt = 1 Joule per second
    1 Joule = 1 Watt for 1 second

    You have been provided a cost figure of 7p/kWh so a bit more work is needed to arrive at the total cost in pence.
  4. Jul 19, 2014 #3
    You will also need to know something about the outdoor temperatures where the building is located. An average winter outdoor temperature is a start but not very accurate, average temperature by month would be better, heating degree days are also used, bin data is also used.
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