A machine shop has a 500 m^2 metal frame roof that is uninsulated. Determine the payback period of adding insulation (R = 2.0°C.m^2/W). The building is electrically heated.The cost of electricity is $0.07/kWh. The machine shop is located in Paris (Le Bourget,France) and operates 24 hours/day,

Question

A machine shop has a 500 [latex]m^{2}[/latex] metal frame roof that is uninsulated. Determine the payback period of adding insulation (R = 2.0°C.[latex]m^{2}[/latex]/W). The building is electrically heated.The cost of electricity is $0.07/kWh. The machine shop is located in Paris (Le Bourget,France) and operates 24 hours/day, 7 days/week throughout the heating season. Assume that the installed cost of the insulation is $15/[latex]m^{2}[/latex].

Accepted Answer

Based on the ASHRAE Handbook, the existing U-value for a metal frame roof is about 1.44 W/[latex]m^{2}[/latex]×°C. To determine the energy savings due to the addition of insulation, we assume that the annual heating degree-days before and after the retrofit remained unchanged and are close to 18°C. Using Eq. (6.21) with the retrofitted roof U-value to be 0.37 W/[latex]m^{2}[/latex]×°C and heating system efficiency set to be unity (electrical system), the energy savings are calculated to be:

[latex]DE_(H,R) =E_(H,E)-E_(H,R)=\frac{24.(BLC_{E}.DD_H (T_{B,E})-BLC_{R}.DD_H (T_{B,R}))}{h_{H}}[/latex] (6.21)

[latex]ΔE=24.500 m^{2}*[(1.44-0.37)W/m^{2}°C]*2758°C.day/yr=35.413kWh/yr[/latex]

Thus, the payback period for adding insulation on the roof can be estimated to be:

[latex]Payback=\frac{500m^{2}*15\$/m^{2}}{35.413kWh/yr*0.07\$/kWh}[/latex]=3.0 years

Therefore, the addition of insulation seems to be cost-effective. Further analysis is warranted to determine the cost-effectiveness of this measure more precisely.

Question 6.3: A machine shop has a 500 m^2 metal frame roof that is uninsu...

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