Qualitative Analysis of the Heat Transfer in a Package of Square Steel Sections

During the heat treatment of square or rectangular steel sections, a heated charge, arranged in regular packages, is placed inside a furnace. This type of charge forms a porous medium through which a complex heat flow occurs during heating. Several heat transfer mechanisms act simultaneously within this medium: conduction through the section walls, conduction and natural convection within the gas, thermal radiation between the section walls, and complex heat transfer (mainly contact conduction) at the joints between the adjacent sections. This article presents a qualitative analysis of heat transfer, aiming to determine the contribution of individual heat transfer mechanisms to the overall process. For this purpose, an analytical model of complex heat transfer within the package was employed, based on the thermo-electric analogy. The results from experimental studies were used to calculate the natural convection and heat transfer at the joints. It was assumed that the material of the sections was low-carbon steel, and the gas was air. Calculations were performed for the temperature range of 25 °C to 700 °C, considering three different geometrical configurations of the sections. It was shown that the effective thermal conductivity (ETC) of the package for the considered geometrical cases varies between 2.2 and 10.6 W/(m·K), which is an order of magnitude lower than the thermal conductivity of the individual sections. This parameter increased dynamically with the temperature. Moreover, the heat transfer intensity within the package of sections was nearly an order of magnitude lower than the heat conduction observed in a solid steel charge. Additionally, it was shown that the primary heat transfer mechanisms governing the heating process were thermal conduction (in the lower temperature range-up to approximately 350 °C) and thermal radiation (in the higher temperature range-above 350 °C). The gas convection inside the sections had a minimal impact on the heating process of the package. The primary parameters influencing the quality of the results were the joint resistance between the adjacent sections and the emissivity of the sections. The presented model can be used for the optimization of heat treatment processes for the considered charge.