A counter-current, concentric tube heat exchanger uses cooling water to reduce the temperature of a hot oil. The heat exchanger is designed such that the oil is flowing through the inner cylinder while the water is flowing through the outer annulus. The inner radius of the oil-containing pipe is 2 cm and the thickness of the wall that is separating the two fluids is 1cm. The wall is made of cast-iron, which has a thermal conductivity of 50 W/(m*K). The heat transfer coefficient for the inner oil is ho = 500 W/(mK), while the heat transfer coefficient for the outer water is hw = 1200 W/(mK). Oil is fed to the heat exchanger at a rate of 0.2 kg/s and it is required to cool the oil from 100C to 40C. Water is fed to the system at a temperature of 20C. The oil has a Cp of 2131 J/(kgC) and the water has a Cp of 4184 J/(kgC). a. If you want to avoid boiling of the water, what is the minimum flow rate you can have for the water feed (kg/s)? b. You decide to operate the system with a water flow rate of 0.1 kg/s. What is the necessary length of the heat exchanger? c. After running the exchanger for a month, you find that the oil is only reaching a temperature of 50C. After inspecting the system, you find significant amounts of rust and mineral deposit on the outside of the heat exchanger wall (water flow side). Determine the fouling factor. d. Due to supply-chain shortages, it's going to be awhile before you can get the necessary replacement parts. So you're stuck with this fouled heat exchanger for a while. Therefore, you must alter the flow rates to compensate for fouling. Since you have a seemingly unlimited supply of water, you decide to change that flow rate. What flow rate (kg/s) of water is necessary to reduce the oil temperature to 40C in this fouled system?