Consider a water-to-water counter-flow heat exchanger with these
specifications. Hot water enters at \(95^{\circ} \mathrm{C}\) while cold water
enters at \(20^{\circ} \mathrm{C}\). The exit temperature of hot water is
\(15^{\circ} \mathrm{C}\) greater than that of cold water, and the mass flow
rate of hot water is 50 percent greater than that of cold water. The product
of heat transfer surface area and the overall heat transfer coefficient is
\(1400 \mathrm{~W} / \mathrm{K}\). Taking the specific heat of both cold and hot
water to be \(c_{p}=4180 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\), determine
(a) the outlet temperature of the cold water, \((b)\) the effectiveness of the
heat exchanger, \((c)\) the mass flow rate of the cold water, and \((d)\) the heat
transfer rate.