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Calculate the heat losses from a model building based on the U values, dimensions and other parameters specified. In addition calculate the annual running costs and payback period for improvements to the building Fabric.

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length of building

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width of building

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U value of wall

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u value of windows

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u value of the roof

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 U value of the roof

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internal temperature

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External Design Temperature

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U value of the door

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area of windows

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area of doors

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area of walls

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area of roof

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delat T

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heat loss through windows

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heat loss through door

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heat loss through walls

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heat loss through roof

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heat loss through floor

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hours a day heat is on

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boiler efficiency

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cost per kwh of gas

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new cost of heating office after fitting insulation

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cost of heating the building

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heat loss from building with new windows

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cost of heating office with new windows

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fuel required by boiler

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heat load for office

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a)

\n

An office is $\\var{l}$m long by $\\var{w}$m wide by 3m high. In the external walls there are 5 windows and 2 doors. Each window measures 2m by 1m and each door measures 1m by 2m. Calculate the heat loss from the office when, the internal temperature is $\\var{ti}$oC and the external temperature is $\\var{to}$oC.

\n

Fill in the answers in the table below.

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
ElementU Value (W/m2K)Area(m2)\n

$\\Delta$T oC (Ti-To)

\n		\n

Heat Loss (W)

\n

Q= UA$\\Delta$T

\n
Windows$\\var{uwi}$[[0]][[5]][[6]]
Doors$\\var{udo}$[[1]][[5]][[7]]
External Walls$\\var{uwa}$[[2]][[5]][[8]]
Roof$\\var{uro}$[[3]][[5]][[9]]
Floor$\\var{ufl}$[[4]][[5]][[10]]
Total[[11]] W
\n

\n

b)

\n

\n

The office above is heated by a condensing gas boiler, which is connected to a low surface temperature radiator system. The heating system operates during the winter period for {hours} hours per day, 5 days per week, 4 weeks per month and 7 months per year. The average external temperature during the Winter is 7oC. If the boiler has an operating efficiency of {eff}% and the cost of gas is {cost}c/kWh, calculate the following:

\n

\n

The ratio of Operating  ΔT to Design ΔT   [[29]]

\n

The annual heat output required from the heating system in kWh (Assume 4 weeks in a month) [[12]]

\n

The annual fuel input required by the heating system in kWh. [[13]]

\n

Annual cost of running the heating system in €. [[14]]

\n

\n

c)

\n

To reduce the running costs of the heating system the office manager has proposed the following two options: 

\n

i)  Fit 50mm insulation with a thermal conductivity of 0.05W/m.K to the walls and roof

\n

ii) Replace all windows with double glazing having a U-value of 2W/m2K

\n
    \n

    Using both tables below calculate the annual saving for both options.

    \n

    \n

    Option i) - fit 50mm insulation with a thermal conductivity of 0.05W/m.K to the walls and roof 

    \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
    \n

    Element 

    \n    		\n

    U value 

    \n

    (W/m2k) 

    \n    		\n

    Area 

    \n

    (m2) 

    \n    		\n

    ΔT (oC) 

    \n

    (Ti –To) 

    \n    		\n

    Heat Loss (W) 

    \n

    Q= U A ΔT 

    \n
    \n

    Window 

    \n    		\n

    As before 

    \n    		\n

    [[6]]

    \n
    \n

    Door 

    \n    		\n

    As before 

    \n    		\n

    [[7]]

    \n
    \n

    Wall 

    \n    		\n

    [[15]]

    \n    		\n

    [[2]]

    \n    		\n

    [[5]]

    \n    		\n

    [[17]]

    \n
    \n

    Roof 

    \n    		[[16]]\n

    [[3]]

    \n    		\n

    [[5]]

    \n    		[[18]]
    \n

    Floor 

    \n    		\n

    As before 

    \n    		\n

    [[10]]

    \n
    \n

    Total Fabric Heat Loss (Qf) 

    \n    		\n

    =  [[19]] W

    \n
    \n

    \n

    Option ii) - Replace all windows with double glazing having a U-value of 2W/m2K 

    \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
    \n

    Element 

    \n    		\n

    U value 

    \n

    (W/m2k) 

    \n    		\n

    Area 

    \n

    (m2) 

    \n    		\n

    ΔT (oC) 

    \n

    (Ti –To) 

    \n    		\n

    Heat Loss (W) 

    \n

    Q= U A ΔT 

    \n
    \n

    Window 

    \n    		\n

    [[20]]

    \n    		\n

    [[0]]

    \n    		\n

    [[5]]

    \n    		\n

    [[21]]

    \n
    \n

    Door 

    \n    		\n

    As before 

    \n    		\n

    [[7]]

    \n
    \n

    Wall 

    \n    		\n

    As before 

    \n    		\n

    [[8]]

    \n
    \n

    Roof 

    \n    		\n

    As before 

    \n    		\n

    [[9]]

    \n
    \n

    Floor 

    \n    		\n

    As before 

    \n    		\n

    [[10]]

    \n
    \n

    Total Fabric Heat Loss (Qf) 

    \n    		\n

    =  [[22]] W

    \n
    \n

    \n

    Annual saving with new Insulation (€)= [[23]]

    \n

    Annual saving with new Windows (€)= [[24]]

    \n

    \n

    d)

    \n

    The office manager has asked you to calculate the simple payback period for both proposed options and advise which is the best option to choose and why.  

    \n

    The capital costs of each option are as follows: 

    \n\n

    Payback Period for new Insulation (Years) = [[25]]

    \n

    Payback period for new Windows (Years) = [[26]]

    \n

    Which Option should the building manager choose?

    \n

    [[27]]

    \n

    Why? [[28]]

    \n

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