In steel processing industry, structural steel products are fabricated by heating, rolling and then cooling process....
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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 900°C 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 900°C to 650°C; while the internal heat generation rate vanishes for the steel temperature below 650°C. Although the steel properties vary as the temperature is lowered, constant values may be assumed reasonably with density p = 7832 kg/m³, 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 = 200°C, if the room air temperature is maintained at To = 30°C. 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 650°C. How much decrease in cooling time can be achieved by doing this? %3D 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 900°C 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 900°C to 650°C; while the internal heat generation rate vanishes for the steel temperature below 650°C. Although the steel properties vary as the temperature is lowered, constant values may be assumed reasonably with density p = 7832 kg/m³, 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 = 200°C, if the room air temperature is maintained at To = 30°C. 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 650°C. How much decrease in cooling time can be achieved by doing this? %3D
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Related Book For
Vector Mechanics for Engineers Statics and Dynamics
ISBN: 978-0073212227
8th Edition
Authors: Ferdinand Beer, E. Russell Johnston, Jr., Elliot Eisenberg, William Clausen, David Mazurek, Phillip Cornwell
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