Two heat exchangers in a circulating water loop transfer heat from a fluid condensing at 175F to a boiling fluid at 68F, 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 $21.50/ft, and the present worth of the lifetime pumping costs is 11.75[$.h/lbm]m. 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, A, and A, that minimize the total present worth of costs. Condensing fluid T = 175F Condenser Uc=7 Btu/h-ft2.F ww www T = 175F FIGURE P6.14 Water 1 2 O Tb = 68F www www Evaporator UE = 5.3 Btu/h-ft.F Boiling fluid Tb = 68F