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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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#### a)

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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.

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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
 Element U Value (W/m2K) Area(m2) \n\$\\Delta\$T oC (Ti-To)\n \nHeat Loss (W)\nQ= 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
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#### b)

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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:

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

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

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

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

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#### c)

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

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

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

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

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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
 \nElement \n \nU value \n(W/m2k) \n \nArea \n(m2) \n \nΔT (oC) \n(Ti –To) \n \nHeat Loss (W) \nQ= U A ΔT \n \nWindow \n \nAs before \n \n[[6]]\n \nDoor \n \nAs before \n \n [[7]]\n \nWall \n \n[[15]]\n \n[[2]]\n \n[[5]]\n \n [[17]]\n \nRoof \n [[16]] \n[[3]]\n \n[[5]]\n [[18]] \nFloor \n \nAs before \n \n [[10]]\n \nTotal Fabric Heat Loss (Qf) \n \n=  [[19]] W\n
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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
 \nElement \n \nU value \n(W/m2k) \n \nArea \n(m2) \n \nΔT (oC) \n(Ti –To) \n \nHeat Loss (W) \nQ= U A ΔT \n \nWindow \n \n [[20]]\n \n [[0]]\n \n[[5]]\n \n [[21]]\n \nDoor \n \nAs before \n \n [[7]]\n \nWall \n \nAs before \n \n [[8]]\n \nRoof \n \nAs before \n \n [[9]]\n \nFloor \n \nAs before \n \n [[10]]\n \nTotal Fabric Heat Loss (Qf) \n \n=  [[22]] W\n
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Annual saving with new Insulation (€)= [[23]]

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

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#### d)

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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.

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The capital costs of each option are as follows:

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• Fit 50mm insulation to walls and roof €5,000.
• \n
• Replace all windows with double glazing €800.
• \n
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Payback Period for new Insulation (Years) = [[25]]

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

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Which Option should the building manager choose?

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[[27]]

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Why? [[28]]

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