A long metal bar (cp = 450 J/kg.K = 7900 kg/m3) is being conveyed
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A long metal bar (cp = 450 J/kg.K = 7900 kg/m3) is being conveyed through a water bath to be quenched. The metal bar has a cross section of 30 mm 15 mm and it enters the water bath at 700C. During the quenching process 500 kW of heat is released from the bar in the water bath. In order to prevent thermal burn on people handling the metal bar it must exit the water bath at a temperature below 45C. A radiometer is placed normal to and at a distance of 1 m from the bar to monitor the exit temperature. The radiometer receives radiation from a target area of 1 cm2 of the bar surface. Irradiation signal detected by the radiometer is used to control the speed of the bar being conveyed through the water bath so that the exit temperature is safe for handling. If the radiometer detects an irradiation of 0.015 W/m2 determine the speed of the bar being conveyed through the water bath. Assume that the metal bar can be approximated as a blackbody.