Solution:
Given Information,
Heat input is ( [tex]Q_{in}[/tex] ) = 5.5 × [tex]10^{6}[/tex] Btu/h
Combustion efficiency of the boiler ([tex]n_{furnance}[/tex]) = 0.7
Combustion efficiency after turn up ([tex]n_{furnance,now}[/tex]) = 0.8
Operation Hour (t) = 5200h
Unit cost (c) = [tex]\frac{23 dollar}{10^{6}Btu }[/tex]
Calculate heat output from the boiler [tex]Q_{out}[/tex] = [tex]Q_{in}[/tex] x [tex]n_{furnance}[/tex]
= 5.5 x [tex]10^{6}[/tex] x 0.7
= 3.85 x [tex]10^{6}[/tex] Btu/h
Calculate the heat input to the boiler after the tune-up
[tex](Q_{in} ){new}[/tex] = [tex]Q_{out}[/tex] / [tex](n_{furnance} ){new}[/tex]
= 3.85 x [tex]10^{6}[/tex] / 0.8
= 4.8125 x [tex]10^{6}[/tex] Btu/h
Calculate the saved energy after the tune-up
[tex](Q_{in} ){saved}[/tex] = [tex]Q_{in}[/tex] - [tex](Q_{in} ){new}[/tex]
= 5.5 x [tex]10^{6}[/tex] - 4.8125 x [tex]10^{6}[/tex] Btu/h
= 0.6875 x [tex]10^{6}[/tex] Btu/h
Calculate the annual energy saving ( [tex]E_{Saving}[/tex] )
[tex]E_{Saving}[/tex] = [tex](Q_{in} ){saved}[/tex] x t
= ( 0.6875 x [tex]10^{6}[/tex] Btu/h ) ( 5200 hr/yr)
= 3575 x [tex]10^{6}[/tex] Btu/h
Calculate the annual cost saving
Annual cost saving = [tex]E_{Annual saving}[/tex] x Unit cost
= 3575 x [tex]10^{6}[/tex] Btu/h x [tex]\frac{23 dollar}{10^{6}Btu }[/tex]
= 82225
