Abstract
Bundles of steel bars, besides metal foams, are an example of cellular solids. Such bundles constitute a charge during the heat treatment of bars. The paper presents a mathematical model of transient heat transfer in a bundle of rectangular steel bars based on the energy balance method. The key element of this model is the procedure of determining the effective thermal conductivity using the electrical analogy. Different mechanisms of heat transfer occurring within the analysed medium (conduction in steel and contact conduction) are assigned corresponding thermal resistances. The discussed procedure involves expressing these resistances with the use of arithmetic relationships describing their changes in the temperature function. Thermal contact resistance has been described with the use of the relationships determined experimentally. As a result of the performed calculations, the influence of contact conduction between the adjacent bars and bundle arrangement on its heating time was established. The results of the calculations show that the heating time of bundles can be lowered by 5–40% as a result of a decrease in the thermal contact resistance. This effect depends on the bar size and bundle arrangement. From the practical point of view, the analysed problem is connected with the optimization of the heat treatment processes of steel bars.
Highlights
Accepted: 24 September 2021Steel bars are basic products of the steel industry
Since the length of bar bundles is repeatedly bigger than their diameter, their heating is determined by the processes of heat transfer, which occur in the radial direction
The coefficient kef is predominantly growing in the temperature function and, for the analysed bundles, it is in the range from 1.5 to 12.7 W/(m·K), while thermal conductivity of bars kst within the analysed temperature range is decreasing from 51 to 28 W/(m·K)
Summary
In order to provide the required mechanical properties, bars undergo the process of heat treatment, during which they are usually heated in the form of cylindrical bundles. Bundles of bars are an example of a steel porous charge that can be encountered in industrial practice [1,2,3]. Such bundles, besides metal foams, are an example of cellular solids [4]. Since the length of bar bundles is repeatedly bigger than their diameter, their heating is determined by the processes of heat transfer, which occur in the radial direction. The above mentioned characteristics have a decisive influence on the process of bundle heating
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