## 1 Introduction  
Within the last five decades, induction heating has become a favorable method for the heating of metallic workpieces throughout various industrial branches (e.g., transportation, aerospace, marine industry, etc.) [1]. It is mostly used to (pre)heat ferromagnetic materials, such as steel [2], since they intensify the magnetic field and thus induce the induction effect already at relatively low frequencies. However, the selection of the particular frequency depends on the geometry of the workpiece and its material properties, since both the electric conductivity and magnetic permeability can be (highly) temperature-dependent. Nevertheless, induction heating is also preferred for other applications,such as the melting of metals [3], the annealing and quenching of metallic components and surfaces [4], the preheating of workpieces intended for subsequent deformation processing [5], surface heating prior to specific surface treatments [6], and more. Under optimized conditions, induction heating can be precisely controlled to enable accurate gradual heating at relatively low costs. On the other hand, unsuitable settings of the heating process result in insufficient and/or inhomogeneous heating of the workpiece, and increase the possibility of the occurrence of microstructure inhomogeneities and defects within the material (e.g., local melting or overheating resulting in undesired abnormal grain growth), as well as the development of an unfavorable stress state, which can result in the occurrence of residual stress during subsequent processing [7; 8; 9]. The design of induction heating processes in the industry should be performed considering the technological, as well as metallurgical, viewpoints, especially for materials prepared via specific technological procedures, such as via powder metallurgy. Such specific materials should be processed with the highest care, since unnecessary increases in the heating time can non-negligibly affect their structures, as well as provoke surface oxidation [10]. The oxidation of workpieces during heating, which can hardly be avoided in industrial conditions, is an important issue in general. Increasing the heating time significantly affects not only the structures, but also the level of surface oxidation of the workpieces. While the level of surface oxidation can more or less be affected via the modification of furnace atmosphere or the usage of protective coatings during heating in conventional furnaces [11], possible structure changes are usually complex and their control is complicated (for example, the grains grow exponentially with increasing heating time [7]). The application of a rapid induction heating is thus very favorable, not only for challenging materials. The optimization of the induction heating process can be advantageously performed with the help of numerical modeling. Others have presented numerous models applicable for induction heating in specific cases. For example, [PERSON] et al. [12] developed numerical and mathematical models of induction heating for several specific inductor geometries, [PERSON] et al. [13] proposed a numerical method to predict the temperature field of induction heating and investigated the distribution of temperature, and [PERSON] et al. [14] compared different numerical models and performed electromagnetic analyses of the bonding of reinforced polymer components with induction heating. Some authors even proposed the induction heating process as a supportive method to fabricate long tubular parts from tungsten heavy alloys (THAs) [15]. Nevertheless, studies focusing on the induction heating of THAs intended to be plastically deformed after heating are scarce, possibly primarily due to the paramagnetic behavior of these materials. Despite the fact that their pre-process heating via induction is a challenge, the usage of paramagnetic materials in the industrial and commercial spheres is on the rise.