# Development of a Novel Concrete Curing Method Using Induction Heating System
## 2 Optimization of Induction Heating System for Concrete Curing
### Finite Element Method (FEM) Analysis for Concrete Curing  
As a first step in the application of an induction heating system for concrete curing, FEM-based thermal analysis was carried out in this study to select the most appropriate materials for fabricating concrete formwork. In the analysis, metallic forms made using three different materials (steel, stainless steel, and aluminum) were heated by induced magnetic field and the maximum temperatures generated in the forms were evaluated. It is well known that the efficiency of an induction heating system is the highest when the system has closed coils because this type of coil is useful for producing a strong magnetic field. Therefore, concrete structures applicable to closed coils, such as columns and piers, were selected. Concrete cylindrical specimens with a diameter and height of 150 mm and 300 mm, respectively, were used to simulate actual columns or piers. Figure 2 illustrates the metallic forms and coil that were simulated in the FEM analysis. The induction coil was designed as a circular tube with outer and inner diameters of 5 mm and 4 mm, respectively, on a copper conductor. The distance between the coil and form was 35 mm, and one-turn coil was applied. A commercial FEM simulator, Altair FLUX, was used to analyze the formwork heating conditions. In the FEM simulation, the convergence criterion was set to \(10^{-4}\) of accuracy threshold with 100 of maximum iterations for computing the relaxation factor for Newton-Raphson [15]. Figure 3 shows the temperature distribution of the inner surface of the forms made from the three different materials (aluminum, stainless steel, and steel), obtained by FEM analysis. The increase in temperature of the formwork was analyzed to select the most appropriate form material. The position of the coil was set at the midpoint of the height of the formwork so that the temperature distribution was symmetrical. It was observed that  
Figure 1: Induction heating system: (**a**) block diagram; (**b**) induction heating principle. Figure 2: Details of metallic forms with a coil for finite element method (FEM) simulation. the maximum temperature of the steel form increased to 89 \({}^{\circ}\)C, whereas the temperature of the stainless steel and aluminum forms rarely increased. The general equation for power, \(P\), produced by eddy currents in a conducting mass is:  
\[P=H^{2}\cdot\sqrt{\mu f}\sqrt{10\rho_{a}}\cdot l\cdot S\left[mW\right] \tag{1}\]  
where \(H\) is the magnetizing force, \(\mu\) is the permeability of the material, \(f\) is the frequency, \(\rho_{a}\) is the resistivity of the material, \(l\) is the length of the conductor, and \(S\) is the shape factor of the conductor which is a value affected by the structure's shape [16]. From Equation (1), the higher the permeability of the conductor, the higher is the power produced by eddy current. Equation (1) verifies that induction heating by steel is more efficient because the relative permeability of steel, stainless steel, and aluminum is 4000, 500, and 1, respectively, in the simulation. The uniform distribution of the heat generated in the metallic form should be distributed uniformly along the entire height to ensure homogenous curing of the concrete. For this purpose, a suitable arrangement of induction coils should be determined. An excessive number of coil turns causes not only low profit, but also a decrease in system efficiency due to mismatch with the inverter. Therefore, FEM analyses considering the arrangement of induction coils from one to three turns were carried out in this study. This analysis result was compared with the result of the heating performance test of formwork. A steel form that generated a significantly high temperature by induced magnetic field, as shown in Figure 3d, was used as the concrete form.