In a chemical plant, a certain chemical is heated by hot water supplied by a
natural gas furnace. The hot water \(\left(c_{p}=\right.\) \(4180 \mathrm{~J} /
\mathrm{kg} \cdot \mathrm{K})\) is then discharged at \(60^{\circ} \mathrm{C}\)
at a rate of \(8 \mathrm{~kg} / \mathrm{min}\). The plant operates \(8
\mathrm{~h}\) a day, 5 days a week, 52 weeks a year. The furnace has an
efficiency of 78 percent, and the cost of the natural gas is \(\$ 1.00\) per
therm ( 1 therm \(=105,500 \mathrm{~kJ})\). The average temperature of the cold
water entering the furnace throughout the year is \(14^{\circ} \mathrm{C}\). In
order to save energy, it is proposed to install a water-to-water heat
exchanger to preheat the incoming cold water by the drained hot water.
Assuming that the heat exchanger will recover 72 percent of the available heat
in the hot water, determine the heat transfer rating of the heat exchanger
that needs to be purchased and suggest a suitable type. Also, determine the
amount of money this heat exchanger will save the company per year from
natural gas savings.