The by-pass factor f can be determined using the fact that the supply temperature provided to the laboratory is the result of mixing two air streams as depicted in the diagram below:

• Outdoor air (representing a fraction f of the total air supply and kept at the temperature T_{oa} = –10°F)

• Heated air [coming from the heat recovery system at the temperature T_{ha} (to be determined), and representing a fraction (1 – f) of the total supply air]

First, the heated air temperature is calculated using the definition of the heat recovery system effectiveness provided by Eq. (14.3):

ε=\frac {(T_{2}-T_{1})}{(T_{4}-T_{1})}        (14.3)

T_{ha} =T_{oa}+ε.( T_{ea}- T_{oa})= −10 °F+ 0.70 * (120°F+10°F ) = 81°F

Then the fraction f can be determined by setting T_{sa} = T_{in}:

T_{in} = T_{oa} . f +T_{ha} .(1− f )

Thus the fraction f is:

f=\frac {(T_{in}-T_{ha})}{(T_{oa}-T_{ha})}=\frac {70-81}{-10-81}=0.12

Using the average winter conditions, the energy rate saved by the heat recovery system can be estimated as following:

ΔE =\dot{m}_{a} .c_{p} .(T_{sa} −\overline{\bar{T}}_{oa} )

where T_{sa} T_{in}= 70°F (assuming that the waste energy is recovered only to temper the make-up air; more thermal energy can actually be recovered if it can be used for other purposes such as space heating) and \overline{\bar{T}}_{oa}= 42.4°F. Thus:

ΔE = (5,000cfm)*(0.91Btu/hr .°F.cfm  )*(70°F − 42.4°F) =124,200 Btu/hr

The savings in fuel use ΔFU can then be calculated using a gas boiler efficiency of 80 percent and a number of operating hours of N_{h} = 6,504 hrs/yr (=24 hrs/day * 271 days/yr):

ΔFU =\frac {ΔE.N_{h}}{η_{b}}=\frac{(124,200 Btu/hr)*( 6,504 hrs/yr)]}{0.80}=1.007*10^{6}Btu/yr=21,021CCF/yr

Thus, the simple payback period for installing the waste heat recovery system is:

SP=\frac{Initial— Cost}{Annual— Savings}=\frac{\$1cfm*5,000 cfm }{\$0.1CCF*21,021CCF/yr}=2.1 years

Therefore, the installation of the heat recovery system in the laboratory is cost-effective.