2. Engine valves (k-48 W/m C, Cp-440 J/kg C, q= 7840 kg/m) are heated to 800 C in the heat treatment section of manufacturing facility. The valves are quenched in oil bath at an average temperature of 45 C. The heat transfer coefficient of the oil bath is 650 W/m C. The valves have a cylindrical system with a diameter of 8 mm and length of 10 cm. The valve head and the stem may be assumed to be of equal surface area, and the volume of the valve head can be taken to be 80 percent of the volume of stem. Determine how long will it take for the valve temperature to drop to a) 400 C, b) 200 C, c) 46 C and the maximum heat transfer from a single valve? (50 points)