In order to provide the technical guidance for heat treatment process of backup roll which is a rolling part of press a hot iron, unsteady solutions of temperature distributions, in which thermodynamic properties of specific heat, Cp and thermal conductivity, K are a function of temperature, are solved by a finite difference numerical method.
First, unsteady solutions to a heat conduction equation with the known surface temperature in infinite solid bar are investigated to obtain proper thermodynamic properties and the surface heating rate of the roll.
These results are also compared with the calculated and experimental data reported by Kobe iron company.
Second, the unsteady 2-dimensional solutions with thermal radiative and convective boundary condition in real roll of irregular shapes are obtained, where the numerical method of the Implicit-Alternating-Direction is used.
From these calculations, the following results are obtained.
1) The heating area near the surface of the roll, which is an important place for the heat treatment does not much depend on variation of thermodynamic properties of the roll.
2) A high or low limitation of the surface heating rate is considered.
3) The thermal radiation analysis with the weighted sum of gray gases model is effective to predict the gas temperature in the furnace.
4) The even insulations on both side of real roll is required to obtain a uniform heating temperature contour near the surface.
