## 2 Heat Generation Model for Reinforcing Steel  
### Definition and Mechanism of High-Frequency Induction Heating  
Induction heating is a method of heating conductive resistors, such as metals, using electrical energy converted from high-frequency current transport conductors known as induction coils [50]. When an alternating current flow through the coil, a magnetic field is generated according to the principle of electromagnetic induction. The magnetic field changes with the current in an alternating current. Therefore, as shown in Figure 1, an induced eddy current (overcurrent) is generated in the metallic body in the coil without conducting wires, thereby generating heat due to resistance loss. Further, when an alternating current flow through the coil, a magnetic flux is generated inside the metal body surrounded by the coil. If the metal body is a magnetic body such as iron, the magnetic flux draws a hysteresis loop for the alternating current. Every time the loop is drawn once, the energy corresponding to the area enclosed by the loop is supplied from the external magnetic field to the magnetic body, whose magnetic energy is then converted into heat energy. In general, however, induction heating does not produce a closed magnetic path like a transformer, and the magnetic flux density is extremely large at 1 T (tesla = 1 Wb/m\({}^{2}\))), so the effective permeability and the hysteresis coefficient are also small. Moreover, as the frequency used increases above 10 KHz, the hysteresis loss becomes negligible because the eddy current loss increases proportionally with the square of the frequency. As illustrated in Figure 1, placing an electrically conducting material (typically metal) near it causes an eddy current to flow through the metal under the influence of the changing magnetic line of force. Metals typically exhibit electrical resistance; thus, when current flows through the metal, Joule heat corresponding to \"power = square of current \(\times\) resistance\" is generated, thereby heating the metal. This phenomenon is known as induction heating [51]. Induction heating can be used only for heating metals; consequently, the risk of temperature rise outside the heating part is low and heat loss is low. An eddy current is the electric current induced by a change in the magnetic field. In general, when magnetic flux penetrates the fuselage or the magnetic flux in the fuselage moves relatively to cause a change in time, current may flow through any closed circuit that is formed locally in the direction that interferes with this change, and this current is called eddy current [1; 2; 3]. The magnitude and streamline of this current can be determined by the shape, step, conductivity, and magnetic flux of the conductor. When eddy currents are generated in the fuselage, they affect the normal current distribution and generate Joule heat, causing a power loss known eddy current loss [52]. Most of the eddy current is concentrated at a penetration depth of 90% from the surface; therefore, the average power Pm can be considered to be the same as the eddy current loss Pe. The eddy current loss is proportional to the square of the alternating flux and maximum magnetic flux density [53; 54; 55] and is inversely proportional to the resistivity; therefore, the conductivity of the conductor can be defined as the eddy current loss per unit volume (W), and is given by Equation (1). \[\mathrm{P}_{e}\propto\sigma^{2}\mathrm{B}_{m}{}^{2} \tag{1}\]  
where \(\mathrm{B}_{m}\left(\frac{\mathrm{wb}}{\mathrm{m}^{2}}\right)\) is the maximum magnetic flux density. In Equation (1), the power generated when heating with a large frequency change to an arbitrary load increases in proportion to the square of the frequency when the frequency is low, but increases in proportion to the square of the frequency when the frequency exceeds a certain frequency. This is because the magnetic lines of force intersect with and offset each other in the load when they are too low in comparison with the penetration depth.