Building Services Engineering 5th Edition Handbook

50 Energy economics
EXAMPLE 2.12
Expanded polystyrene board is to be added to the internal face of a wall having an initial
thermal transmittance of 3.30 W/m 2 K in thicknesses of 25, 50, 75, 100, 125 and 150
mm. Insulated wall thermal transmittances will be 0.96, 0.56, 0.40, 0.31, 0.25 and 0.21
W/m 2 K. The insulation costs £48 per cubic metre fitted and the capital recovery period is to
be 3 years. Fuel costs £8.93 per useful gigajoule. Internal and external design temperatures
are 21 ◦ C and −1 ◦ C respectively, the load factor is 0.608 and the building is to be heated for
3000 h per year. Use the information provided to find the economic thickness of insulation.
fuel cost = U[21 − (−1)]×0.608 × 3000 × 3.6 × 8.93 × 10 −6 £/m 2 year
= 1.29U per m 2 year
insulation cost = £48
m 3 × thickness l m
3 years
= 16 l per m 2 year
The results are shown in Table 2.8. Figure 2.3 shows that the total cost curve can be drawn by
adding the fuel and insulation cost curves for each insulation thickness. The economic thickness
is 50 mm.
The economic thermal transmittance of a structure with a flat surface can be evaluated from
the following equation (Diamant, 1977):
[
]
λαI 1/2
U e =
8.64C(Y + St)
where U e is the economic U value (W/m 2 K), λ is the thermal conductivity (W/mK), α is the depreciation
and interest charges (%), I is the total cost of thermal insulation fitted into the building
(£/m 3 ), C is the cost of useful heat (£/MJ), Y is the annual degree days for a base temperature of
18 ◦ C, S is the length of the heating season (days) and t is the difference between the average
internal air temperature and 18 ◦ C. Once U e has been found, the thermal insulation thickness
can be found from
( 1
l = λ − 1 )
m
U e U
where U is the uninsulated thermal transmittance (W/m 2 K).
Table 2.8 Cost data for Example 2.12.
Thickness l (m) 0.025 0.050 0.075 0.100 0.125 0.150
U (W/m 2 K) 0.96 0.56 0.40 0.31 0.25 0.21
Insulation cost (£) 0.40 0.80 1.20 1.60 2.00 2.40
Fuel cost (£) 1.24 0.72 0.52 0.40 0.32 0.27
Total cost (£) 1.64 1.52 1.72 2.00 2.32 2.67