Sheet steel emerging from the hot roll section of a steel mill has a temperature of 1200 K, a thickness of ? = 3 mm, and the following distribution for the spectral, hemispherical emissivity. The density and specific heat of the steel are 7900 kg/m3 and 640 J/kg ? K, respectively. What is the total hemispherical emissivity? Accounting for emission from both sides of the sheet and neglecting conduction, convection, and radiation from the surroundings, determines the initial time rate of change of the sheet temperature (dT/dt)i. As the steel cools, it oxidizes and its total, hemispherical emissivity increases. If this increase may be correlated by an expression of the form ? = ?1200 [1200 K/T (K)], how long will it take for the steel to cool from 1200 to 600 K?

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