A swimmer with body mass 50 kg is pulled from the ocean with hypothermia. Her body temperature is 27°C. She is connected to a shell and tube heat exchanger. Blood flow through the device is kept constant at 1,000 ml/min. The perfusionist adjusts the flow rate in the perfusion fluid Qs(t); so blood leaving the heat exchanger always has a constant temperature of 37°C. The inlet fluid temperature to the shell is kept constant at 45°C. At time t = 0, the shell flow rate is 5,000 ml/min. Density and specific heats of blood, tissue, and perfusion fluid are the same: ? = 1 g/ml; Cp = 4 J g-1K-1. (a) What is the outlet shell temperature Tso at t = 0? (b) What minimum product of overall heat transfer coefficient and exchange area must the heat exchanger have to allow the initial amount of heat exchange? (c) Perform an energy balance on the body to determine how long it will take to heat the body to a temperature 35°C.