Feature Article Figure 5. Geometry and boundary conditions of the thermal threedimensional model. surface is calculated. Therefore an external current density is defined on the coil connection point. The external current density is defined as followed: [1] Je is the external current density, p is the generator power in percentage of the maximum generator power, I10 is the experimental determined average electric current at 10% generator power (637 Ampere), do and di are the pipe outer and inner diameter respectively (do= 3 mm and di= 2 mm). In a second step the electromagnetic field and joule losses in the two laminates are calculated. The calculated surface current density on the coil surface and the generator frequency (400 kHz) are the input parameters. In the third step the temperature of the laminates are calculated. The before calculated joule losses are implemented as an internal heat source inside the laminate. The solution is generated by moving the material stepwise against the process direction while the overall net of the model is fixed. For each material movement the temperature is calculated. Due to the constant boundary conditions the calculation is finished and the simulation converged, when a state of equilibrium is reached and the calculated temperature distribution in the laminates doesn't change with the next material movement. Figure 6. Process diagram specification based on the surface and joining temperature in the middle of the joining area. 44 SAMPE Journal, Volume 53, No. 1, January/February 2017