Difference between revisions of "Projects:2019s1-113 High Curie Temperature Magnetic Materials"

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== Introduction ==
 
== Introduction ==
 
===Overview===
 
===Overview===
 +
The current electric power sector is attempting to improve the availability, reliability, and security of energy supply to its consumers [1]. This has increased the need to integrate renewable energy into the electricity sector as a method to solve the issue of energy deficiency, particularly in remote off-grid settlements. However, the variability in the sources of renewable supply, accompanied by changes in the level of energy
 +
consumption has brought to focus the necessity for electrical energy storage systems (ESS)[1].
  
The current electric power sector is trying to increase the availability, reliability and security of energy supply to the consumers. This pursuit has increased the need to integrate renewable energy (RE) into the electricity sector as a strategy to curb the problem of energy deficiency especially in isolated off-grid settlements. However, the variability in the sources of Renewable supply coupled with conditional changes in the level of energy consumption with respect to time has brought to focus the necessity for electrical energy storage systems (ESSs) [1].  
+
Currently, the Australian energy sector is using battery energy storage systems (BESS) which offers a significant saving in off-grid applications, but voltage fluctuations are a major issue with the integration of renewable energy [2]. Furthermore, BESS have reduced the efficiency with prolonged use due to degradation caused by high voltages [3]. As technology continues to improve more ESS emerge such as thermal energy storage
 +
systems (TESS), pumped hydro system (PHS), compressed air energy storage (CAES), fuel cell (FC) and superconducting magnetic energy storage (SMES)[1].
  
Currently, in the energy sector the issue of intermittency is currently solved using battery energy storage systems (BESS). However, BESS faces some key challenges. Once the batteries get full, battery storage will lead to wastage of all other surplus renewable energy. Battery storage also faces reduced efficiency as the batteries get older due to degradation caused by the presence of high voltages [2].
+
1414 Degrees is an Australian based company that specializes in TESS. They have developed a special silicon-based Phase Change Material (PCM), which has a high latent heat of fusion and high energy density. This means it can hold large amounts of energy and delivers high energy efficiency simultaneously. A brief overview of how the TESS works is first the PCM is heated using electricity up to 1414 K at this temperature, the silicon transitions to a molten phase. This allows the storage of a significant amount of energy which can be reclaimed at the desired time. During times of high electrical demand, the PCM is cooled causing transitions from molten to solid resulting in the release of heat energy
 +
[4]. This heat energy is passed through an energy recovery system and a turbine to convert it to electrical energy [4].
  
As the technologies continue to grow, more and more ESSs emerged with increased efficiency such as thermal energy storage systems (TESS), pumped hydro system (PHS), compressed air energy storage (CAES), fuel cell (FC) and  superconducting magnetic energy storage (SMES) [3].  
+
The PCM is heated using an electrical resistance heating system. This specific method of heating leads to heat loss through the various ports and openings that are needed to run various heating elements. A possible solution to this problem is to use an electromagnetic heating system. To perform electromagnetic heating a material needs be identified that retains permanent magnetism at temperatures above 1414K.
  
1414 Degrees is a company that specializes in Thermal Energy Storage Systems(TESS). They have developed a special Phase Change Material(PCM) with a high latent heat of fusion which they use in their TESS. A brief overview of how the TESS works is the PCM is heated using electricity up to 1414°C at this temperature, the silicon transitions to a molten phase. This allowing the storage of a significant amount of energy which can be reclaimed at a desired time i.e. when there is a demand for electricity.  During times of high electrical demand, the silicon transitions from liquid to solid causing a release of heat energy. This heat energy is transformed into electrical energy via turbines that can service electrical demand[**].
 
  
The PCM is heated via electrical resistive heating that generates a lot of thermal energy losses. This project will tackle the problem of TESS using electromagnetic heating system  which requires a high magnetic flux density in the presence a PCM with a high Curie temperature (Tc). Tc is the temperature above which certain materials lose their permanent magnetic properties, to be replaced by induced magnetism [4].
+
=== Project Objectives ===
 
+
The long-term aims of this project would be to provide 1414 Degrees with a device that would further their technological advancement; replacing their current method of resistive heating with electromagnetic heating. The project aims as reproduced from the project brief are to:
 +
# Conduct a literature/ product-search for materials that are solid and permanent magnets at temperatures above 1400K.
 +
# Model an electromagnetically actuated device that is capable of operation at temperatures above 1400K.
 +
# Build and test such a device.
 +
 
 +
===Significance===
 +
The ability of our project to help reduce the power that is lost during the heating of 1414 Degree’s storage material represents a direct benefit to the project sponsor. This project also benefits the broader engineering community. Electromagnetically actuated devices that can reliably operate in high-temperature environments would reduce the need for cooling considerations and thermal insulation
 +
 
 +
== Previous studies ==
 +
=== Curie temperature (Tc) of ferromagnetic materials===
 +
Tc is the temperature above which certain ferromagnetic materials lose their permanent magnetic properties, to be replaced by induced magnetism [5]. Once a ferromagnetic material is sufficiently heated, the tendency to disorder overtakes the tendency of spin magnetic moments to align themselves and cause spontaneous magnetization [6, 7]. Essentially, the magnetic moments are disarranged and can no longer inherently produce a magnetic field. The magnetization and magnetic coercivity approach zero and the relative permeability approach that of free space as the temperature of a ferromagnetic material approaches its Curie temperature.
 +
 
 +
===Types of magnetism===
 +
Magnetism is a phenomenon associated with magnetic fields, which arise from the motion of electric charges. This motion can take many forms. It can be an electric current in a conductor or charged particles moving through space [9]. There are many types of magnetism but in this project, the focus will be on and Ferromagnetic and Paramagnetic. Ferromagnetism is when all magnetic moments are aligned and is experienced when the temperature is lower than the Tc of a material [9]. On the other hand, paramagnetic is when random magnetic moments will align with an applied magnetic field experienced when the temperature is above Tc of a material [9]. Therefore, when a magnetic material is heated up to its Tc it will switch from ferromagnetic state to paramagnetic state.
  
=== Project Objectives ===
+
Bozorth [6] aptly summarized the important attributes of ferromagnetic materials as being:
To create an electromagnetically actuated high temperature device with the following features:
+
# A dependence of permeability on the field strength and on the previous magnetic history (hysteresis)
#  A small heater that can achieve the highest possible temperature, preferably at least 1400 K
+
# The approach of the magnetization to a finite limit as the field strength is indefinitely increased (saturation)
#  A “switch” that can directly thermostatically control a heating load, preferably to at least 1400 K​
+
# The presence of small, magnetized regions(domains) in the absence of an externally applied magnetic field(spontaneous magnetization),
# A wireless thermometer
+
# The disappearance of the characteristics already mentioned when the temperature is raised to a certain temperature, the Curie temperature.
 +
 
 +
===Thin-film ferromagnetic materials===
 +
A lot of research has been done on thin-film alloys concerning high Tc magnetic materials. Since thin-film ferromagnetic materials have a single ferromagnetic domain of macroscopic extension [10]. Which means thin ferromagnetic films are essentially one big domain as opposed to regular materials that are composed of many differently aligned domains making them easier to examine. Analysis of thin films has shown that the Tc is seen to increase when either the thickness of the film or the concentration of magnetic atoms increases [11]. Furthermore, when mixing elements, it is important to consider thermal effects on the magnetic moment. In some cases, the interface region will behave as an alloy of a non-magnetic and a magnetic
 +
compound [11].
 +
 
 +
In addition, soft magnetic thin films with higher saturation flux density have the advantage in the high-frequency operation of avoiding ferromagnetic resonance and are key in realizing high density magnetic recording systems [12]. If materials with a Tc higher than 1414 K cannot be identified the knowledge of thin films can be applied to make a compound that will satisfy this requirement.
 +
 
 +
===Electrical heating===
 +
====Low frequency range (50Hz to 1MHz)====
 +
When the frequency range is low ohmic heating or inductive heating can be implemented. Ohmic heating is when an electric current is passed through the heating sample, resulting in a temperature rise due to the conversion of the electric energy into heat [12]. It provides energy-saving while reducing heating time when compared to conventional heating methods. This is currently the technique used by 1414 Degrees. However, comes with some challenges such as it requires a narrow operating frequency band and complex coupling between temperature and electrical filed distribution [12].
 +
 
 +
This project intends to implementing inductive heating between the frequency range of 5-30 kilohertz. Inductive heating is the process of heating an electrically conducting object by electromagnetic induction, through heat generated in the object using eddy
 +
currents [13]. Inductive heating is based on two main principles electromagnetic induction and ohmic heating. The energy transfer to the object to be heated occurs by means of electromagnetic induction. Any electrically conductive material placed in a variable magnetic field in the site of induced electric currents (eddy currents) will eventually lead to ohmic heating [13].
  
 +
===Toroidal induction===
 +
The presence of a large air gap in the toroidal core will prevent the core from attaining its peak saturation due to the fringing effect. The fringing effect is especially evident for large air gaps, as the B does not cross the air gap in straight lines but instead enters far into the
 +
neighboring areas crosses the coil, and induces voltage within it, which in turn causes eddy currents to occur [14]. The fringing flux is a function of the size of the air gap, the cross-sectional area of the core, and the geometry of the windings, as well as the operating frequency [14].
  
== Relevant work ==
+
There are a number of methods for reducing of the effects of the fringing field such as spacing the windings away from the gap or replacing a portion of the core with a material of low permeability are possible solutions [14]. Therefore, the air gap in the magnetic core should be made as small as possible, the ends of the core should be narrower (tapered) and the windings should be spaced away from the air gap to reduce fringing flux.
== Background ==
 
=== Curie temperature ===
 
The Curie temperature is the temperature above which the spontanteous magnetization (ferromagnetism) vanishes; it separated the disordered paramagnetic phase T > T_c from the ordered ferromagnetic phase at T < T_c[1].
 
  
 
==Proposal ==
 
==Proposal ==
 +
===Test bench design===
 +
The core will be made of silicon steel laminations with electrical windings to generate flux in the core. The laminations will be cut using a water jet into rectangles and quarter circles for the corners. In order to, maximize the area available for windings while minimizing the magnetic path length, the dimensions of the core will be the length is twice the width.  Thus, the test bench will be made of a soft magnetic C-shaped core with toroidal windings connected to power electronics as a source of flux [13,14].
 +
 +
****picture***
 +
 +
===Power electronics===
 +
Current in the windings is one of the factors that will determine how much B is generated in the core. The power electronics connected to the toroidal coil will need to provide adequate current to produce a strong magnetic field thus, generate adequate flux. Therefore, it will contain the following features:
 +
# 240 volt (AC) 3-phase power supply – To provide power to the windings
 +
# A 3-phase bridge rectifier - converts a three-phase AC voltage at the input to a DC voltage at the output.
 +
# A bandpass filter centered at 0Hz - To limit the bandwidth of the output signal to the band allocated for the transmission (smoothen the output from the 3-phase bridge rectifier).
 +
# H-bridge circuit (switching electronics) - switches the polarity of a voltage applied to a
 +
load.
 +
 +
****picture of connection*****
 +
 +
  
 
== Method ==
 
== Method ==
Line 58: Line 103:
  
 
== References ==
 
== References ==
[1] [1] Yekini Suberu, M., Wazir Mustafa, M. and Bashir, N. (2014). Energy storage systems for renewable energy power sector integration and mitigation of intermittency. [online] ELSEVIER.  
+
[1] M. Yekini Suberu, M. Wazir Mustafa and N. Bashir, “Energy storage systems for renewable energy power sector integration and mitigation of intermittency” Renewable and sustainable energy, 2014. [Online]. Available at: Renewable and Sustainable Energy
 +
Reviews.
 +
 
 +
[2] Ertugrul, N. (2018).4062 Distributed Generation Technologies 7075 Distributed Generation Tech (PG) - Battery energy storage. 1st ed. Adelaide: University of Adelaide.
 +
 +
[3] K.C. Divya and J. Ostergaard,” Battery energy storage technology for power systems —an overview” Electric Power Systems Research 2009; 79:511–20. Available: Electric Power Systems Research.
 +
 
 +
[4] 1414 degrees, “What is 1414 Degrees?” 2019. Available at: WHAT IS 1414 DEGREES? [Accessed 2 Jun. 2019].
 +
 
 +
[5] C. Kittel, Introduction to solid-state physics. New York: J. Wiley & Sons, 1971.
 +
 
 +
[6] R. Bozorth, Ferromagnetism, 1st ed. Piscataway, NJ: IEEE Press, 1993, pp. 5-6.
 +
 
 +
[8] R. Skomski, Simple models of magnetism, 1st ed. Oxford: Oxford University Press, 2008, p. 149.
 +
 
 +
[9] E. Kashy, F. Robinson, B. Bleaney, E. Suckling and S. McGrayne, “Magnetism | Definition, Examples, Physics, & Facts” Encyclopedia Britannica, 2019. Available at: Magnetism [Accessed 2 Jun. 2019].
 +
 
 +
[10] A. Corciovei, G. Costache, and D. Vamanu, "Ferromagnetic Thin Films" Solid State Physics, pp. 237-350, 1972. Available at: Ferromagnetic thin films.
 +
 
 +
[11] P. Jensen, H. Dreyssé and K. Bennemann, “Thickness dependence of the magnetization and the Curie temperature of ferromagnetic thin films” Surface Science, 1992. [Online] Available at: Thickness dependence of the magnetization and the Curie temperature of ferromagnetic thin films
  
[2] Divya KC, Ostergaard J. Battery energy storage technology for power systems —an overview. Electr Power Syst Res 2009;79:511–20.
+
[12] M. Hayakawa “Characteristics of soft magnetic thin films for magnetic head core application” Journal of Magnetism and Magnetic Materials, 1994. Available at: Characteristics of soft magnetic thin films for magnetic head core application. [Accessed
 +
2 Jun. 2019].
  
[3]  
+
[13] E. Ter Maten and J. Melissen, “SIMULATION OF INDUCTIVE HEATING”, ieee transactions on magnetics, 1992. Available at: SIMULATION OF INDUCTIVE
 +
HEATING.
  
[4] C. Kittel, Introduction to solid state physics. New York: J. Wiley & Sons, 1971
+
[14] R. Kasikowski, "Impact of the fringing effect on temperature distribution in windings and physical properties of toroidal ferrite inductors with a dual air gap", Yadda.icm.edu.pl, 2017. [Online]. Available: Impact of the fringing effect . [Accessed: 05- Jun- 2019]

Latest revision as of 13:38, 1 October 2019

Abstract here

Project members

Project students

  • Gitonga Njeru
  • Nikko Mugweru Kahindi

Supervisors

  • Dr Andrew Allison

1414 Degrees contacts

  • Jordan Parham
  • Grant Mathieson

Mechanical engineering contacts

  • Dr Reza Ghomashchi
  • Will Robertson
  • James Anderson


Introduction

Overview

The current electric power sector is attempting to improve the availability, reliability, and security of energy supply to its consumers [1]. This has increased the need to integrate renewable energy into the electricity sector as a method to solve the issue of energy deficiency, particularly in remote off-grid settlements. However, the variability in the sources of renewable supply, accompanied by changes in the level of energy consumption has brought to focus the necessity for electrical energy storage systems (ESS)[1].

Currently, the Australian energy sector is using battery energy storage systems (BESS) which offers a significant saving in off-grid applications, but voltage fluctuations are a major issue with the integration of renewable energy [2]. Furthermore, BESS have reduced the efficiency with prolonged use due to degradation caused by high voltages [3]. As technology continues to improve more ESS emerge such as thermal energy storage systems (TESS), pumped hydro system (PHS), compressed air energy storage (CAES), fuel cell (FC) and superconducting magnetic energy storage (SMES)[1].

1414 Degrees is an Australian based company that specializes in TESS. They have developed a special silicon-based Phase Change Material (PCM), which has a high latent heat of fusion and high energy density. This means it can hold large amounts of energy and delivers high energy efficiency simultaneously. A brief overview of how the TESS works is first the PCM is heated using electricity up to 1414 K at this temperature, the silicon transitions to a molten phase. This allows the storage of a significant amount of energy which can be reclaimed at the desired time. During times of high electrical demand, the PCM is cooled causing transitions from molten to solid resulting in the release of heat energy [4]. This heat energy is passed through an energy recovery system and a turbine to convert it to electrical energy [4].

The PCM is heated using an electrical resistance heating system. This specific method of heating leads to heat loss through the various ports and openings that are needed to run various heating elements. A possible solution to this problem is to use an electromagnetic heating system. To perform electromagnetic heating a material needs be identified that retains permanent magnetism at temperatures above 1414K.


Project Objectives

The long-term aims of this project would be to provide 1414 Degrees with a device that would further their technological advancement; replacing their current method of resistive heating with electromagnetic heating. The project aims as reproduced from the project brief are to:

  1. Conduct a literature/ product-search for materials that are solid and permanent magnets at temperatures above 1400K.
  2. Model an electromagnetically actuated device that is capable of operation at temperatures above 1400K.
  3. Build and test such a device.

Significance

The ability of our project to help reduce the power that is lost during the heating of 1414 Degree’s storage material represents a direct benefit to the project sponsor. This project also benefits the broader engineering community. Electromagnetically actuated devices that can reliably operate in high-temperature environments would reduce the need for cooling considerations and thermal insulation

Previous studies

Curie temperature (Tc) of ferromagnetic materials

Tc is the temperature above which certain ferromagnetic materials lose their permanent magnetic properties, to be replaced by induced magnetism [5]. Once a ferromagnetic material is sufficiently heated, the tendency to disorder overtakes the tendency of spin magnetic moments to align themselves and cause spontaneous magnetization [6, 7]. Essentially, the magnetic moments are disarranged and can no longer inherently produce a magnetic field. The magnetization and magnetic coercivity approach zero and the relative permeability approach that of free space as the temperature of a ferromagnetic material approaches its Curie temperature.

Types of magnetism

Magnetism is a phenomenon associated with magnetic fields, which arise from the motion of electric charges. This motion can take many forms. It can be an electric current in a conductor or charged particles moving through space [9]. There are many types of magnetism but in this project, the focus will be on and Ferromagnetic and Paramagnetic. Ferromagnetism is when all magnetic moments are aligned and is experienced when the temperature is lower than the Tc of a material [9]. On the other hand, paramagnetic is when random magnetic moments will align with an applied magnetic field experienced when the temperature is above Tc of a material [9]. Therefore, when a magnetic material is heated up to its Tc it will switch from ferromagnetic state to paramagnetic state.

Bozorth [6] aptly summarized the important attributes of ferromagnetic materials as being:

  1. A dependence of permeability on the field strength and on the previous magnetic history (hysteresis)
  2. The approach of the magnetization to a finite limit as the field strength is indefinitely increased (saturation)
  3. The presence of small, magnetized regions(domains) in the absence of an externally applied magnetic field(spontaneous magnetization),
  4. The disappearance of the characteristics already mentioned when the temperature is raised to a certain temperature, the Curie temperature.

Thin-film ferromagnetic materials

A lot of research has been done on thin-film alloys concerning high Tc magnetic materials. Since thin-film ferromagnetic materials have a single ferromagnetic domain of macroscopic extension [10]. Which means thin ferromagnetic films are essentially one big domain as opposed to regular materials that are composed of many differently aligned domains making them easier to examine. Analysis of thin films has shown that the Tc is seen to increase when either the thickness of the film or the concentration of magnetic atoms increases [11]. Furthermore, when mixing elements, it is important to consider thermal effects on the magnetic moment. In some cases, the interface region will behave as an alloy of a non-magnetic and a magnetic compound [11].

In addition, soft magnetic thin films with higher saturation flux density have the advantage in the high-frequency operation of avoiding ferromagnetic resonance and are key in realizing high density magnetic recording systems [12]. If materials with a Tc higher than 1414 K cannot be identified the knowledge of thin films can be applied to make a compound that will satisfy this requirement.

Electrical heating

Low frequency range (50Hz to 1MHz)

When the frequency range is low ohmic heating or inductive heating can be implemented. Ohmic heating is when an electric current is passed through the heating sample, resulting in a temperature rise due to the conversion of the electric energy into heat [12]. It provides energy-saving while reducing heating time when compared to conventional heating methods. This is currently the technique used by 1414 Degrees. However, comes with some challenges such as it requires a narrow operating frequency band and complex coupling between temperature and electrical filed distribution [12].

This project intends to implementing inductive heating between the frequency range of 5-30 kilohertz. Inductive heating is the process of heating an electrically conducting object by electromagnetic induction, through heat generated in the object using eddy currents [13]. Inductive heating is based on two main principles electromagnetic induction and ohmic heating. The energy transfer to the object to be heated occurs by means of electromagnetic induction. Any electrically conductive material placed in a variable magnetic field in the site of induced electric currents (eddy currents) will eventually lead to ohmic heating [13].

Toroidal induction

The presence of a large air gap in the toroidal core will prevent the core from attaining its peak saturation due to the fringing effect. The fringing effect is especially evident for large air gaps, as the B does not cross the air gap in straight lines but instead enters far into the neighboring areas crosses the coil, and induces voltage within it, which in turn causes eddy currents to occur [14]. The fringing flux is a function of the size of the air gap, the cross-sectional area of the core, and the geometry of the windings, as well as the operating frequency [14].

There are a number of methods for reducing of the effects of the fringing field such as spacing the windings away from the gap or replacing a portion of the core with a material of low permeability are possible solutions [14]. Therefore, the air gap in the magnetic core should be made as small as possible, the ends of the core should be narrower (tapered) and the windings should be spaced away from the air gap to reduce fringing flux.

Proposal

Test bench design

The core will be made of silicon steel laminations with electrical windings to generate flux in the core. The laminations will be cut using a water jet into rectangles and quarter circles for the corners. In order to, maximize the area available for windings while minimizing the magnetic path length, the dimensions of the core will be the length is twice the width. Thus, the test bench will be made of a soft magnetic C-shaped core with toroidal windings connected to power electronics as a source of flux [13,14].

        • picture***

Power electronics

Current in the windings is one of the factors that will determine how much B is generated in the core. The power electronics connected to the toroidal coil will need to provide adequate current to produce a strong magnetic field thus, generate adequate flux. Therefore, it will contain the following features:

  1. 240 volt (AC) 3-phase power supply – To provide power to the windings
  2. A 3-phase bridge rectifier - converts a three-phase AC voltage at the input to a DC voltage at the output.
  3. A bandpass filter centered at 0Hz - To limit the bandwidth of the output signal to the band allocated for the transmission (smoothen the output from the 3-phase bridge rectifier).
  4. H-bridge circuit (switching electronics) - switches the polarity of a voltage applied to a

load.

        • picture of connection*****


Method

Results

Conclusion

References

[1] M. Yekini Suberu, M. Wazir Mustafa and N. Bashir, “Energy storage systems for renewable energy power sector integration and mitigation of intermittency” Renewable and sustainable energy, 2014. [Online]. Available at: Renewable and Sustainable Energy Reviews.

[2] Ertugrul, N. (2018).4062 Distributed Generation Technologies 7075 Distributed Generation Tech (PG) - Battery energy storage. 1st ed. Adelaide: University of Adelaide.

[3] K.C. Divya and J. Ostergaard,” Battery energy storage technology for power systems —an overview” Electric Power Systems Research 2009; 79:511–20. Available: Electric Power Systems Research.

[4] 1414 degrees, “What is 1414 Degrees?” 2019. Available at: WHAT IS 1414 DEGREES? [Accessed 2 Jun. 2019].

[5] C. Kittel, Introduction to solid-state physics. New York: J. Wiley & Sons, 1971.

[6] R. Bozorth, Ferromagnetism, 1st ed. Piscataway, NJ: IEEE Press, 1993, pp. 5-6.

[8] R. Skomski, Simple models of magnetism, 1st ed. Oxford: Oxford University Press, 2008, p. 149.

[9] E. Kashy, F. Robinson, B. Bleaney, E. Suckling and S. McGrayne, “Magnetism | Definition, Examples, Physics, & Facts” Encyclopedia Britannica, 2019. Available at: Magnetism [Accessed 2 Jun. 2019].

[10] A. Corciovei, G. Costache, and D. Vamanu, "Ferromagnetic Thin Films" Solid State Physics, pp. 237-350, 1972. Available at: Ferromagnetic thin films.

[11] P. Jensen, H. Dreyssé and K. Bennemann, “Thickness dependence of the magnetization and the Curie temperature of ferromagnetic thin films” Surface Science, 1992. [Online] Available at: Thickness dependence of the magnetization and the Curie temperature of ferromagnetic thin films

[12] M. Hayakawa “Characteristics of soft magnetic thin films for magnetic head core application” Journal of Magnetism and Magnetic Materials, 1994. Available at: Characteristics of soft magnetic thin films for magnetic head core application. [Accessed 2 Jun. 2019].

[13] E. Ter Maten and J. Melissen, “SIMULATION OF INDUCTIVE HEATING”, ieee transactions on magnetics, 1992. Available at: SIMULATION OF INDUCTIVE HEATING.

[14] R. Kasikowski, "Impact of the fringing effect on temperature distribution in windings and physical properties of toroidal ferrite inductors with a dual air gap", Yadda.icm.edu.pl, 2017. [Online]. Available: Impact of the fringing effect . [Accessed: 05- Jun- 2019]