In steel processing industry, structural steel products are fabricated by heating, rolling and then cooling process. A steel rod of cylindrical shape is at the uniform temperature of 900C at the end of the rolling process, is then placed in a cooling bed to lower its temperature. Assume the rod diameter is D = 40 mm and the length is L = 100 m. During the cooling process, due to the phase transformation inside the steel (such as austenite to perlite), heat is generated internally at the uniform rate of 4 = 5 x 105 W/m3 when the steel temperature is in the range of 900C to 650C; while the internal heat generation rate vanishes for the steel temperature below 650C. Although the steel properties vary as the temperature is lowered, constant values may be assumed reasonably with density p = 7832 kg/m, specific heat at constant pressure Cp = 600 J/kg.K and the thermal conductivity k = 50 W/m.K. The cooling is provided by natural convection of the room air and radiation to the surrounding with a combined heat transfer coefficient of h = 100 W/m2.K. a) Determine the time required for the steel rod to reach the final temperature Tf = 200C, if the room air temperature is maintained at To = 30C. b) In order to shorten the cooling time, it is proposed to switch to forced convection cooling (with a heat transfer coefficient of h = 5000 W/m2.K) after the steel temperature reaches to 650C. How much decrease in cooling time can be achieved by doing this? %3D