## Nanoparticle Heating with Induction

Induction heating is a process, where an electrically conductive material is heated, due to the induction of eddy currents. In most cases, eddy currents are an undesirable effect, since they lead to losses in the materials (i.e. line transformers). In order to reduce the losses in these transformers, their cores are made of electromagnetic steel sheets with thickness of, usually, 0,35mm. By reducing the cross-section of the sheet, less magnetic curves pass through it, leading to smaller losses. In induction heating, however, these are the currents that lead to the heating of metals.

### Nanoparticles

Objects having a diameter of 300 nm (nanometers) or less can be considered as nanoparticles. What is special about these objects is that they are magnetic in nature. As we discussed above, the smaller the cross-section of any object, the less current is induced. In this sense, the nanoparticles are “invisible” to the magnetic field regarding the eddy currents. Their cross-section is so small, that practically no current is induced in them. That’s why nanoparticle heating through induction is way different than any conventional application of the process and that same particle must be magnetic.

In order to heat an object with such small dimensions, we need to use another method. The fact that nearly to no current is induced in the object doesn’t mean that the particles don’t react to the changing field.

Such reaction is the hysteresis effect. The hysteresis curve of the material represents the reorientation of its magnetic dipoles. Each reorientation of any dipole leads to “losses”, or the heating of the material. Therefore, a high frequency alternating magnetic field results in higher “losses” in the particle. A high frequency alternating magnetic field is achieved by using a high frequency system (100 kHz and above). The choice of frequency, however, is limited by the desired temperature, the required heating time and the consideration of other effects that occur during such process. Typical frequencies are [100 – 600] kHz.

Another effect is the Néel effect [ 1 ], which occurs in small enough ferromagnetic nanoparticles. Néels’ theory states that in small enough particles a random flip of the direction of magnetization can occur under the influence of temperature. This is also called supermagnetism.

The third effect leading to nanoparticles heating is the Brownian motion (movement) [4]. Under the effect of an external magnetic field, the particles start rotating and try to align with the field.

The most important parameters considered in such systems are the SAR (specific absorption ratio),

the frequency at which the field is alternating (F), and the magnetic field strength (H).

SAR gives a measure of the power absorbed by the material, or the energy dissipated in heat per unit of mass. The higher the value of this parameter, the faster the particle is heated. SAR can be described as:

where c is the specific heat capacity of the particle, dT/dt is the change of temperature per unit of time

(seconds in most cases) and m_{Fe} is the concentration of iron per ml. This equation also shows the importance of choosing a certain material over another, since the SAR parameter is proportional to the specific heat capacity. The parameter “c” itself shows the amount of energy needed to deliver to one unit of mass in order to cause an increase of one unit in its temperature [3].

Since we’ve already discussed the importance of frequency, lets speak of the magnetic field strength.

Such applications require magnetic field strengths of, typically, 795 [A/m] to 103,4 [kA/m], which is an incredibly strong field. The flux density of such fields can reach up to 50 [mT] (50 . 10^{-3}). To put in comparison, the flux density of any common application of induction heating is in the range of [μT], or

10^{-6}, which is a flux density a thousand times smaller. It’s also good to mention that the magnetic field strength is not spread equally through the length of the coil. The field is strongest in the middle of the coil (or solenoid) and it “disperses” as we move further from the center.

UtraFlex offers equipment for nanoparticle heating of various frequencies.

References:

[ 1 ] Nicholas Kurtis, Selected works of Louis Neel;

[ 2 ] Warren M. Rohsenow, James P. Hartnett, Young I. Cho, Handbook of heat transfer – Third Edition;

[ 3 ] Terry M. Tritt, PHYSICS OF SOLIDS AND LIQUIDS – Thermal Conductivity – Theory, Properties, and Applications;

[ 4 ] Feynman, R. (1964). “The Brownian Movement”. The Feynman Lectures of Physics, Volume I. pp. 41–1.