6.14 Two heat exchangers in a circulating water loop transfer heat from a fluid condensing at 175°F to a boiling fluid at 68°F, as shown in Figure P6.14. The overall heat transfer coefficients of the evaporator and condenser are UE =

5.3 Btu/h·ft2·°F and UC = 7 Btu/h·ft2·°F, respectively. The first cost of the heat exchangers is $21.50/ft2, and the present worth of the lifetime pumping costs is 11.75[$·h/lbm]m w. This system must accomplish a heat transfer rate of 220,000 Btu/h between the condensing and boiling fluids. Using a numerical optimization algorithm, determine the heat exchanger areas, A1 and A2, that minimize the total present worth of costs.