Engine valves (k = 48 W/m · °C, cp = 440 J/kg · °C, and ρ = 7840 kg/m3) are heated to 800°C in the heat treatment section of a valve manufacturing facility. The valves are then quenched in a large oil bath at an average temperature of 50°C. The heat transfer coefficient in the oil bath is 800 W/m2 · °C. The valves have a cylindrical stem with a diameter of 8 mm and a 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 he 80 percent of the volume of steam. Determine how long it will take for the valve temperature to drop to (a) 400°C, (b) 200°C, and (c) 51°C. and (d) the maximum heat transfer from a single valve.
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