Calculating Insulation Thickness for a Building (Engineering)

[btec_noob]

Homework Statement

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.

Homework Equations

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

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.

 

[CWatters]

so I can calculate the Thermal resistance and heat loss... I just need help in finding the equation for calculating Energy cost.

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
or
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.

 

[RTW69]

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.