Dolphins and other marine mammals are able to maintain a surprisingly high body temperature even though they are swimming in ocean water at 4°C. Since the dolphin tail has a large surface area, much of the heat loss occurs there.

(a) Develop a model to describe heat transfer from the tail of the dolphin to the ocean water assuming that the tail is represented as a two-tube pass heat exchanger. Blood enters the tail at 40°C with a flow rate of 0.3 kg/s and returns to the body of the dolphin at a lower temperature. The overall heat transfer coefficient in the tail is U_° = 420 W/m² K, and the heat transfer area is A_° = 3.0 m². Determine the temperature of the blood returning to the main part of the body of the dolphin for these conditions.

(b) Develop a model to describe heat transfer from the tail of the dolphin to the water assuming that the tail is represented again as a two-tube pass heat exchanger, but that prior to returning to the main part of the body the blood passes through an internal counter-current heat exchanger where heat transfer occurs between the warm blood going to the tail and the cooler blood returning from the tail. The overall heat transfer coefficient in this internal heat exchanger is U_° = 630 W/m² K and its heat transfer area is A_° = 2.0 m². Determine the temperature of the blood returning to the main part of the body of the dolphin under these conditions.

Also determine the fraction of heat loss that is saved by this arrangement compared to that in part (a). For this problem, assume that the properties of blood are approximated by those of water. It is possible that the ears of elephants and other large mammals work in a similar way with an internal heat exchanger by-passed when cooling is needed and turned on to conserve energy.