Chapter 11, Problem 11.38P

For health reasons, public spaces require the continuous exchange of a specified mass of stale indoor airwith fresh outdoor air. To conserve energy during theheating season, it is expedient to recover the thermalenergy in the exhausted, warm indoor air and transferit to the incoming, cold fresh air. A coupled single pass, cross-flow heat exchanger with both fluidsunmixed is installed in the intake and return ducts of aheating system as shown in the schematic. Water containing an anti-freeze agent is used as the workingfluid in the coupled heat exchange device, which iscomposed of individual heat exchangers A and B.Hence, heat is transferred from the warm stale air tothe cold fresh air by way of the pumped water.

Consider a specified air mass flow rate (ineach duct) of $\stackrel{\dot{}}{m}=1.50\text{kg/s}$ an overall heat transfer coefficient-area product of $UA=2500\text{W/K}$ (foreach heat exchanger), an outdoor temperature of
$T_{c,i,A}=-4°C$ and an indoor temperature of $T_{h,i,B}=23°C$ . Since the warm air has been humidified, excessive heat transfer can result in unwanted condensationin the ductwork. What water how rate is necessary to maximize heat transfer while ensuring the outlettemperature associated with heat exchanger B does notfall below the dew point temperature, $T_{h,o,B}=T_{dp}=13°C$ ? Hint: Assume the maximum heat capacity rateis associated with the air.