Application of radial effective thermal conductivity for heat transfer model of steel coils in HPH furnace

The hot/cold rolled steel coil can be considered as a periodically laminated material composed of layers of steel strips and gas gaps in the radial direction. The conduction of steel, of gas, of contact points due to the surface roughness, as well as radiation have been included in a determination of the radial effective thermal conductivity. Based on the analysis of heat transfer mechanisms in radial coils, a new formula for the radial effective thermal conductivity has been derived, which depends not only on the temperature but also on the type of atmosphere gas, the surface characteristic of coils, strip thickness, and compressive stress. Using this effective conductivity, a detailed mathematical model has been developed to predict the temperature distribution of coils in a high performance hydrogen (HPH) furnace. The calculated annealing curves are in good agreement with experimental data.