Computational Model of the Effective Thermal Conductivity of a Bundle of Round Steel Bars

During the heat treatment of round steel bars, a heated charge in the form of a cylindrically formed bundle is placed in a furnace. This type of charge is a porous granular medium in which a complex heat flow occurs during heating. The following heat transfer mechanisms occur simultaneously in this medium: conduction in bars, conduction within the gas, thermal radiation between the surfaces of the bars, and contact conduction across the joints between the adjacent bars. This complex heat transfer can be quantified in terms of effective thermal conductivity. This article presents the original model of the effective thermal conductivity of a bundle of round steel bars. This model is based on the thermo-electric analogy. Each heat transfer mechanism is assigned an appropriate thermal resistance. As a result of the calculations, the impact of the following parameters on the intensity of heat transfer in the bundle was examined: temperature, the thermal conductivity of the bars, the thermal conductivity of the gas, diameter, and emissivity of the bar, and bundle porosity. Calculations were performed for a temperature range of 25-800 °C, covering a wide spectrum of variables, including bar diameters, bundle porosity, and type of gas. The knowledge obtained thanks to the calculations performed will facilitate the optimization of heat treatment processes for the considered charge. The greatest scientific value of the presented research is the demonstration that, thanks to the developed computational model, it is possible to analyze a very complex heat transfer phenomenon using relatively simple mathematical relationships.