E. J. Davies

Basic induction heating

We started this book with the conduction heating of metals because this is nearer to our everyday experience. We moved from the simple passage of DC in the metal to the complications that arise from the use of alternating current and, during the derivations, saw that it is normally preferable to use DC, whenever possible. Another reason for starting with conduction was that it is a very effective way to heat metals if the shape is right. It allowed us to develop the theory from first principles in a way that closely matches the way we were taught, starting with Ohms law and with the current passing from end to end of the material between the electrodes. The understanding that has been de veloped in those chapters can now be extended into the realm of induction heating.

Induction heating of tubes

This chapter tackles about the basic theory of induction heating of tubes, but with different boundary conditions at the inner diameter. The solution is akin to that of conduction heating of tubes, but there is an added complication due to the flux inside the tube. We derive it to bring out the principles.

Direct resistance heating

This chapter is necessarily vaguer than Chapters 22-25 because there are fewer established uses of direct resistance heating (DRH). This is sad because, as shown in Chapters 1-6, there are great advantages, especially if DC is used. Before looking at DC, let us discuss some reasons for the neglect. Direct resistance heating is ideally suited to heating steel pieces having a uniform cross-section which are long compared to their other dimensions. Very rapid heating is possible, avoiding scale formation and surface decarburisation, and giving high production rates. Efficiencies higher than 90% have been obtained. Heating times of less than a minute can be expected.

Other applications of induction heating

This chapter discusses applications of induction heating, including: soldering and brazing; tube welding; heating of resin kettles and other vessels; paint drying; induction heating in plastic working; annealing and stress relieving; longitudinal flux induction heating; transverse-flux heating; semiconductor processing; and travelling-wave heaters.

Alternating currents in conductors: circular cross-section

The circular cross-section problem is the problem that is normally solved in the literature, both because of its inherent importance and because it is an excellent example of the use of Bessel functions. Most of these solutions are aimed at the circuit viewpoint, i.e. resistance, reactance and impedance, rather than power loss, which is the purpose of direct resistance heating (DRH). A.G. Warren (“Mathematics Applied to Electrical Engineering”, Chapman and Hall, London, 1949) has an excellent section (pp. 243ff.) on current in a circular conductor but the book has long been out-of-print; also, it uses unrationalised CGS concepts, so we shall start again from first principles. For the reader not conversant with Bessel functions, we do not make a lot of fuss about them here: suffice it to say that they are the equivalent in a cylindrical world of the sinusoids and exponentials of the previous chapters and, like them, are described by infinite series. We find that there is a close similarity between the solutions for the slab and those for the cylinder. Just as, in the thin slab, we found that the two sides interacted to give hyperbolic functions, Bessel functions are needed because every point in the section of a circular conductor is affected by the currents flowing in the rest of the conductor.

Through-heating by induction

Induction heating is a convenient method for bulk-heating metals to a set temperature. It replaces furnaces, which tend to be large and which have the disadvantage of long start-up and shut-down times, so that their effectiveness is low. By contrast, the induction heater is relatively small in size and is immediate ly available for use. It is clean and relatively efficient. The power goes directly into the workpiece. The heating times are usually short a few minutes (except when a large thermal mass is being heated) and the process fits well into automated production methods. Although electricity costs are higher per unit of energy, this is offset by higher efficiencies. In Chapter 7, it was shown that induction heating takes place within about one skin depth (say 9 mm for iron, 10 mm for copper at 50 Hz, cold). The heat has to reach the rest of the billet or slab by conduction. Since non-ferrous metals have high heat conductivities this presents few problems, but for steel and other low-conductivity metals we have to avoid surface overheating, or perhaps even melting. Heat flow is an important part of the study of through-heating.

Effect of current depth and radiation

In this chapter, we modify the previous assumptions to allow for the two practical conditions: (1) the actual heat distribution in the metal; (2) the heat lost by radiation from the surface. The loss equations can be combined with the heat-flow equations to give an accurate solution. To deal with this, we expand the heat-flow equation to include the volumetric production of heat.

Basic heat transfer

In this chapter, we examine further the simple storage of heat, and then present introductory ideas on heat flow. The idealised solutions with all the heat entering at the surface, which we have seen to be a reasonable first assumption, are derived for slabs and cylinders.

Heat transfer during surface hardening

In surface hardening, the work surface is brought rapidly to temperature by a high power-density applied at the surface. The aim is to heat a shallow layer without affecting the rest of the workpiece. These two features the high intensity and the thin layer mean that different criteria from billet heating apply. The skin depth is small, there is no need to use cylindrical coordinates or thin slab ideas; this problem can be treated as a semi-infinite slab. In practice, during hardening, the surface will be heated under one of two conditions: (1) a variable temperature θ(t) applied to the surface (2) a variable power-density P(j) applied to the surface. These are not really separate, since one implies the other; it is a question of which quantity is known. Before discussing these cases, it is helpful to consider the problem of a semi-infinite slab suddenly placed in a new temperature environment. This is not an artificial problem, as it is what happens when a piece to be hardened is heated in an oven, but it is not the induction surface-hardening problem; it is used here to introduce the concepts.

Wire and strip heating

In many industrial metallurgical processes, the material needs to be heated as part of a moving system. Examples are rolling, intermediate annealing, tempering, etc., where the material starts off on one reel and, after going through various processes, including DRH, ends up on another reel. This chapter is not concerned with the process in general, only the part of the run where the work is heated. For present purposes, since the material is usually flexible - wire, small rod or thin narrow strip - we can ignore the problems of current distribution across the section and assume uniform current density and heating.