A cross-flow heat exchanger used in a cardio-pulmonary bypass procedure cools blood flowing at 5 liter/min from a body temperature of 37°C to 25°C in order to induce body hypothermia, which reduces metabolic and oxygen requirements. The coolant is ice water at 0°C, and its flow rate is adjusted to provide an outlet temperature of 15°C. The heat exchanger operates with both fluids unmixed, and the overall heat transfer coefficient is 750 W/m² ∙ K. The density and specific heat of the blood are 1050 kg/m³ and 3740 J/kg ∙ K, respectively.

(a) Determine the heat transfer rate for the exchanger.

(b) Calculate the water flow rate.

(c) What is the surface area of the heat exchanger?

(d) Calculate and plot the blood and water outlet temperatures as a function of the water flow rate for the range 2 to 4 liter/min, assuming all other parameters remain unchanged. Comment on how the changes in the outlet temperatures are affected by changes in the water flow rate. Explain this behavior and why it is an advantage for this application.