In a dairy plant, milk at $4{^\circ}C$ is pasteurized continuously at $72{^\circ}C$ at a rate of $10.8$ $L/s$ for $24 h$ a day and $365$ days a year. The milk is heated to the pasteurizing temperature by hot water heated in a natural-gas-fired boiler that has an efficiency of $80.7$ percent. The pasteurized milk is then cooled by cold water at $18{^\circ}C$ before it is finally refrigerated back to $4{^\circ}C$. To save energy and money, the plant installs a regenerator that has an effectiveness of $76.8 \%$. If the cost of natural gas is $1.15$ dollar/therm (1 therm = $105,500 kJ$), determine:
  1. how much heat should transfer to the milk
  2. how much heat will be saved in the current regenerator
  3. how much energy and money the company saves per year

(assume $\rho_{milk}=1$ $kg/L$ and $C_{p_{milk}}$ is $3.79 kJ/kg\cdot{^\circ}C$)

$\dot{Q_{milk}}=$ $kJ/s$

Heat saved in the regenerator = $kJ/s$

Energy saved due to saving fuel feeding the boiler per year = $therm/yr$

Money saved due to saving fuel feeding the boiler per year = $$/yr$

# Pay attention to the unit of each parameter