Thermal Therapy - RF/Microwave Interaction with Biological Tissues - page 159

Heating material

I 0

I

Φ

a

(a)

(b)

FIGURE 4.14 Principle of inductive heating.

an eddy current; it flows in the vortex state. Its calculation derives from the
electromagnetic induction law of Faraday, as shown in the following equations.
The derivative type of the EM induction law is

= ∂

B
dt

—¥ E (4.8)

where E is the electric field and B the magnetic flux density. The relationship
between the electric field and the current density J is expressed as

JE = k A m

- 2

(4.9)

where k is the conductivity. From Eqns. (4.8) and (4.9), the following equation
is obtained:

∂
∂

B

—¥ J =- k (4.10)

t

This equation suggests that there is current rotation when a magnetic flux
changes in the conductor, which means the generation of current in the vortex
state.
Now, let us consider the case in which the coil is wound around the heating
material of the cylindrical conductor, as shown in Figure 4.14 b , with high-
frequency current flowing in this coil to generate an alternating magnetic field
in the form of a sine wave. The result is that the heating material is heated
by the eddy current generation.
In the analysis of the power loss (absorbed electric power) in this case, mod-
ified Bessel functions appear (ber and bei functions). The analysis becomes
complicated, which is why only the result is shown here: The power loss over
an axial length l (in centimers) for a cross section A (in square centimeters)
of the cylindrical conductor is given by the expression