Temperature uniformity of steel coils in High Performance Hydrogen bell-type annealing furnace has a significant effect on their quality and production. The hot rolled coil can be considered as a periodically laminated material composed of steel layers and interface layers in radial direction. A new formula for the radial effective thermal conductivity has been proposed, which is based on surface characteristic, strip thickness and compressive stress of the rolled coil. Furthermore, it has been used to develop a heat transfer mathematical model for steel coils in the HPH furnace. The calculated annealing curves using this mathematical model are in good agreement with the experimental data. Temperature uniformity of steel coils in High Performance Hydrogen bell-type annealing furnace has a significant effect on their quality and production. A new formula for the radial effective thermal conductivity has been proposed, which is based on surface characteristic, strip thickness and compressive stress of the rolled coil. annealing curves using this mathematical model are in good agreement with the experimental data.