Induction and Direct Resistance Heating

This chapter is the introduction of the book. Induction and direct resistance heating are presented in an unified theory that, starting from the solution of Maxwell’s equations, gives the basic quantities that characterizes thermal processes based on internal heating sources. The penetration depth of electromagnetic waves is a parameter that characterizes all the relevant phenomena in these heating applications. A qualitative description is provided about the several effects that affect distribution of current density and, as a consequence, of heating sources: proximity effect (that occurs between two conductors that carry electrical current), ring effect (that occur in bended conductors), slot effect (that occurs in conductor placed in the slot of a magnetic yoke), end and edge effects (that occur due to the finite length of inductor and load and their relative position). Active and reactive power in the workpiece are computed by applying Poynting’s theorem for both induction and direct resistance heating.

This chapter deals with the induction or direct resistance heating of flat bodies. Analytical solutions are derived for some typical configurations in order to calculate the main process parameters, like active and reactive power in the workpiece and power sources distributions [1]. The chapter is subdivided into four paragraphs and in each paragraph the solution is provided both for induction and direct resistance heating. In the first paragraph, solutions are presented for heating bodies of infinite dimensions having linear material properties. In the second chapter the same geometrical configuration is studied for ferromagnetic bodies. In the third paragraph, the solution of the electromagnetic problem is firstly obtained for the induction heating of a two-layers slab, than a workpiece of rectangular cross-section with finite dimensions is taken into account in a longitudinal flux system. The direct resistance heating of a finite dimension cross-section is then discussed. The last paragraph details the induction and resistance heating of finite cross-section loads, evaluating the current distribution near to different shaped edges.

The third chapter deals with the induction and direct resistance heating of cylindrical workpieces. For the induction heating cases, solenoidal inductors are considered, leading to an axisymmetric configuration. The chapter is subdivided into 4 sections. In Sect. 3.1, the induction and direct resistance heating are considered for solid cylindrical workpieces made of nonferrous metals. Analytical solutions of the electromagnetic problem give the distributions of the heating sources and main integral parameters, like equivalent resistance and reactance. The analytical solutions lead to quite complex formulas that can be easily evaluated thanks to dimensionless diagrams. In Sect. 3.2, analytical solutions are provided for nonlinear material, like ferromagnetic steel. The Sects. 3.3 and 3.4 deal with the heating of tubes, made of nonferrous and ferrous materials respectively. For induction heating cases, the use of internal or external inductors is considered. The main integral quantities can be easily evaluated with diagrams that are function of the dimensionless thickness and radii, internal and external, of the tube.

This chapter deals with some specific applications of induction and direct resistance heating, that have been investigated also by the authors of this book. When available, analytical solutions for these ‘special’ applications are provided. Section 4.1 is about the resistance heating of ferromagnetic workpieces of rectangular cross-section, Sect. 4.2 describes the direct resistance heating of bended conductors. The transverse flux heating is a technology that is applied for treating thin slabs and stripes with high electrical efficiency and is the topic of the Sect. 4.3. Planar coils, often named pancake inductors, are described in the Sect. 4.4, while the effects due to the finite length of inductor are discussed in Sect. 4.5. Induction hardening of workpieces of complex geometry is one of the most important applications of induction heating, single and dual frequency processes for contour hardening are presented in Sect. 4.6. The innovative process of through heating by rotating a nonferrous billet inside a DC field produced by superconductive coils is detailed in Sect. 4.7, while in Sect. 4.8 the induction heating is produced by rotation of permanent magnets. Section 4.9 deals with the induction heating of hollow workpieces heated by internal inductors and Sect. 4.10 describes the forces acting in induction heating applications.

This chapter is about the analytical and numerical methods that have been successfully applied for modeling induction and direct resistance heating processes. In Sect. 5.1, calculation of induction heating system is presented by applying the equivalent magnetic circuit method. Analytical methods are extensively described in the previous chapters and briefly summarized in the Sect. 5.2 of this chapter. The Sect. 5.3 presents a simple procedure to solve coupled EM and Thermal induction heating problem by means of the finite difference method in 1D axis-symmetric domain. The procedure is fully detailed and can be easily implemented in a code. Typical results produced by a commercial code based on 1D finite difference method are shown in Sect. 5.4. Volume integral methods have been also successfully used in coupled electromagnetic and thermal calculations: these numerical techniques are detailed in the Sect. 5.5. Calculation of parameters of direct resistance heating systems and the importance of the feeding circuit parameters are dealt with in Sect. 5.6 by applying analytical solutions while in Sect. 5.7 the calculation is carried out by resorting again to the 1D finite difference method. Finite element method is the numerical technique most applied in commercial software dedicated to electromagnetic design. Finite element models are nowadays extensively used in electro thermal applications and a short description focused on practical use of finite element is presented in the closing section of the book.