(Solved): A cross-flow heat exchanger used in a cardiopulmonary bypass procedure cools blood flowing at \( 0. ...

A cross-flow heat exchanger used in a cardiopulmonary bypass procedure cools blood flowing at \( 0.005 \) \( \mathrm{m}^{3} / \mathrm{min} \) from a body temperature of \( 37^{\circ} \mathrm{C} \) to \( 25^{\circ} \mathrm{C} \) in order to induce body hypothermia, which reduces metabolic and oxygen requirements. The coolant is ice water at \( 0^{\circ} \mathrm{C} \), and its flow rate is adjusted to provide and outlet temperature of \( 15^{\circ} \mathrm{C} \). The heat exchanger operates with both fluids unmixed, and overall heat transfer coefficient is \( 750 \mathrm{~W} / \mathrm{m}^{2}-\mathrm{K} \). The density and specific heat of the blood are \( 1050 \mathrm{~kg} / \mathrm{m}^{3} \) and \( 3740 \mathrm{~J} / \mathrm{kg}-\mathrm{K} \), respectively. (a) Determine the heat exchange rate. (b) Calculate the water flow rate. (c) What is the surface area of the heat exchanger?