Home Induction heating process of ferromagnetic filled carbon nanotubes based on 3-D model
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Induction heating process of ferromagnetic filled carbon nanotubes based on 3-D model

  • Sławomir Wiak , Anna Firych-Nowacka EMAIL logo , Krzysztof Smółka , Łukasz Pietrzak , Zbigniew Kołaciński and Łukasz Szymański
Published/Copyright: December 29, 2017

Abstract

Since their discovery by Iijima in 1991 [1], carbon nanotubes have sparked unwavering interest among researchers all over the world. This is due to the unique properties of carbon nanotubes (CNTs). Carbon nanotubes have excellent mechanical and electrical properties with high chemical and thermal stability. In addition, carbon nanotubes have a very large surface area and are hollow inside. This gives a very broad spectrum of nanotube applications, such as in combination with polymers as polymer composites in the automotive, aerospace or textile industries. At present, many methods of nanotube synthesis are known [2, 3, 4, 5, 6]. It is also possible to use carbon nanotubes in biomedical applications [7, 8, 9, 10, 11, 12, 13, 14], including the destruction of cancer cells using iron-filled carbon nanotubes in the hyperthermia process. Computer modelling results of Fe-CNTs induction heating process are presented in the paper. As an object used for computer model creation, Fe-CNTs were synthesized by the authors using CCVD technique.

1 Introduction

Carbon nanotubes were discovered by Ijima in 1991. Since that discovery many researchers all over the world have performed experiments concerning CNTs usage. The reason of unwavering interest among scientists is caused by unique properties of carbon nanotubes - electrical [15], mechanical [16], high temperature stability [17] and chemical resistance. Consequently, there is a very wide spectrum of possible CNT applications - e.g. consumer electronics, textile industry, or even as a filler in polymer composites [18] and a variety of material in industrial and medical applications.

Among others, the biomedical application is one of the most important. Due to the large specific surface of CNTs and hollow interior, carbon nanotubes can be used as precise addressed drug carriers (with proper protein-ligands attached). Addressing due to functional groups attached to surface and ferromagnetic material filling gives unique “nanocontainers” - Fe-CNTs capable of selective tumor cell destruction. This process is realized with the use of an electromagnetic field, causing energy (heat) generation by Fe-CNTs. This process ends with the necrosis of cancer cells. Usage of Fe-CNTs with proper protein-ligands is selective and safe for patient, which is in stark contrast to current antitumor agents used in cancer treatment. In the presented paper, computer 3-D models of Fe-CNTs used in hyperthermal destruction of tumor cell process are described.

2 Fe - CNTs synthesis and material propperties

The use of carbon nanotubes is conditioned by the development of an efficient synthesis process capable of producing a material with specific, desirable properties.

In this work, Fe-CNTs are obtained as a result of synthesis process, in which catalytic-chemical CCVD vapour deposition with continuous catalyst solution delivery was used. In the literature, this process is described as a liquid source chemical vapour deposition [19]. In the case of Fe - CNTs, the choice of possible catalysts is limited to metalorganic compounds of general formula (Me-(C5H5)2), where Me is a transition metal. Cytotoxicity of the obtained material is a matter of a great importance, and this is the reason of ferrocene (Fe(C5H5)2) usage. The choice of the method is dictated by the ability to control the synthesis parameters: catalyst solution feed rate, process temperature and carrier gas flow. The Fe-CNTs growth process temperature was 1070K, and the catalyst solution evaporation temperature was 570K. A carrier gas Ar/H2, 500 to 80 SLPM (standard liter per minute, 1 SLPM = 1.68875 Pa·m3/s) mixture was used. Catalyst (10% by weight solution) was used with feed rate of 8 ccm per hour. Fe-CNTs obtained in synthesis process, grow in the form of a “carpet”, perpendicularly to the base (Figure 1). Carbon nanotubes, visible in Figure 1, had been used to create computer models and numerical calculations presented in the paper. The placement and the amount of ferromagnetic material, encapsulated inside Fe-CNTs, was examined using TEM and TGA techniques (see Figures 1 and 2, respectively).

Figure 1 “Carpet” of Fe–CNTs
Figure 1

“Carpet” of Fe–CNTs

Figure 2 TEM image – visible black shape inside carbon nanotube is encapsulated Fe nanoparticle
Figure 2

TEM image – visible black shape inside carbon nanotube is encapsulated Fe nanoparticle

Thermograph visible in Figure 3, gives some information about both the CNTs type and chemical composition. One can see a maximum differential curve (the blue one at a temperature close to 620°C). That is the decomposition temperature typical for multiwalled carbon nanotubes. For experiments described in this paper, the residue value is very important. This provides information about ferromagnetic filler content.

Figure 3 TGA analysis thermograph – determined residue corresponding to Fe weight content (∼11%)
Figure 3

TGA analysis thermograph – determined residue corresponding to Fe weight content (∼11%)

3 Induction heating process

Radio frequencies could be defined as electromagnetic field characterized by a frequency fitting with the range of 3 kHz to 300 GHz [20]. One of the greatest advantages of this kind of radiation is, that it is a widely examined interaction with human tissues. Multiple scientific papers report lack of any negative side-effect of this type of treatment [21, 22]. Moreover, deep tissue penetration becomes reachable in contrary to the NIR radiation [23]. An assembly on the above mentioned features results in a vast variety of biomedical applications. In order to achieve the assumed treatment effectiveness the temperature of diseased tissue should be elevated to the level of 43-48°C [24]. The research in the field of RF induced heating is conducted at frequencies of 266 and 231 kHz. Different field intensities were applied with the aim of recognising dependency between particle size, relaxation time, specific absorption rate and amplitude of magnetic field. During our experiments Fe-CNTs the heating tests on variable frequency of electromagnetic field were performed (110 kHz, 165.8 kHz, 329 kHz, 465.6 kHz, 620.9 kHz).

4 Computer models

The computer model of ferromagnetic filled carbon nanotubes was created using COMSOL package. It was made for the tablet that is filled with ferromagnetic carbon ferroalloy. The material is called polyvinylpyrrolidone (K 30). Additionally, a 17 turn coil, which was wound around the tablet to excite the magnetic field. Because of the need to cool the system, the flow of liquid was modelled. This refers to principle of operation of the induction heating process.

In the computer model, Ampere’s Law was used:

jωσω2ε0εrA+×μ01BMσv×B=Je(1)

where:

B=×A(2)

The current excitation is expressed by the equation:

Icoil=Jecoil(3)

and:

Je=σVcoil2πrecoil(4)

In the coupling of the electromagnetic model with the thermal model, the following calculations and equations were used:

ρCpTt+ρCpuT=kT+Qe(5)

where Qe is described as:

Qe=Qrh+Qml(6)
Qrh=12Re(JEs)(7)
Qml=12Re(jωBHs)(8)

In the computer model the following values were used:

  1. Icoil = 2.5 A (current of the coil);

  2. f = 110 kHz, 165.8 kHz, 329 kHz, 465.6 kHz, 620.9 kHz (different frequency settings).

Material properties for thermal and electromagnetic analysis are presented in Table 1.

Table 1

Material properties (T = 293 K).

Element/materialElectrical conductivity [S/m]Thermal conductivity [W/(m·K)]Specific heat [J/(kg·K)]Density [kg/m3]
iron1.12 e73.85641.55800
polymide-0.1511001300
water5.5 e-60.64189.9998
copper5.998 e74003858700

The axial-symmetrical condition (on the longitudinal axis r from Figure 4a) and on the edges of the model (around) for electromagnetic analysis was set:

Figure 4 Mashed model: a) 2-D (axis symmetrical model), b) 3-D (full three-dimensional model)
Figure 4

Mashed model: a) 2-D (axis symmetrical model), b) 3-D (full three-dimensional model)

n×A=0(9)

The heat equation accepts two basic types of boundary conditions: specified temperature:

T=T0(10)

and specified inward heat flux:

nq=q0(11)

The finite element mesh was concentrated around the tablet (circle) to obtain better results of temperature distributions.

5 Results

Figure 5 represents the magnetic field distribution in three dimensional model of induction heating system. The next figures (Figure 6a and b) show the temperature distribution around the tablet before heating (t = 0s) and after two minutes (t = 120s).

Figure 5 Surface: magnetic field norm [A/m]; arrow surface: magnetic flux density; time t = 0s
Figure 5

Surface: magnetic field norm [A/m]; arrow surface: magnetic flux density; time t = 0s

Figure 6 Temperature distribution in a) t = 0s and b) t = 120s [K]
Figure 6

Temperature distribution in a) t = 0s and b) t = 120s [K]

Figure 7 presents the temperature vs. time plot depending on the distance of the measuring point related to the tablet.

Figure 7 Transient temperature depending on the distance of the measuring point related to the tablet: a) complete curves, b) logarithmic scale [K]
Figure 7

Transient temperature depending on the distance of the measuring point related to the tablet: a) complete curves, b) logarithmic scale [K]

6 Conclusions

It is clear that interdisciplinary approaches must be taken first of all in these models. Lack of such an approach results in limitation of many real physical phenomena. Presented models allow to solve many practical problems in thermal and electromagnetic analysis of ferromagnetic nanotubes.

The results show that there is a possibility of effectively heating nanotubes with a ferromagnetic filler. In the next stage numerical results versus experimental measurements will be compared.

Acknowledgement

This work has been financed from the budget of science as a research project No. PBS2/A5/31/2013.

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Received: 2017-11-2
Accepted: 2017-11-12
Published Online: 2017-12-29

© 2017 S. Wiak et al.

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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  216. Modelling of magnetostriction of transformer magnetic core for vibration analysis
  217. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  218. Comparison of the fractional power motor with cores made of various magnetic materials
  219. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  220. Dynamics of the line-start reluctance motor with rotor made of SMC material
  221. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  222. Inhomogeneous dielectrics: conformal mapping and finite-element models
  223. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  224. Topology optimization of induction heating model using sequential linear programming based on move limit with adaptive relaxation
  225. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  226. Detection of inter-turn short-circuit at start-up of induction machine based on torque analysis
  227. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  228. Current superimposition variable flux reluctance motor with 8 salient poles
  229. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  230. Modelling axial vibration in windings of power transformers
  231. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  232. Field analysis & eddy current losses calculation in five-phase tubular actuator
  233. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  234. Hybrid excited claw pole generator with skewed and non-skewed permanent magnets
  235. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  236. Electromagnetic phenomena analysis in brushless DC motor with speed control using PWM method
  237. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  238. Field-circuit analysis and measurements of a single-phase self-excited induction generator
  239. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  240. A comparative analysis between classical and modified approach of description of the electrical machine windings by means of T0 method
  241. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  242. Field-based optimal-design of an electric motor: a new sensitivity formulation
  243. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  244. Application of the parametric proper generalized decomposition to the frequency-dependent calculation of the impedance of an AC line with rectangular conductors
  245. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  246. Virtual reality as a new trend in mechanical and electrical engineering education
  247. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  248. Holonomicity analysis of electromechanical systems
  249. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  250. An accurate reactive power control study in virtual flux droop control
  251. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  252. Localized probability of improvement for kriging based multi-objective optimization
  253. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  254. Research of influence of open-winding faults on properties of brushless permanent magnets motor
  255. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  256. Optimal design of the rotor geometry of line-start permanent magnet synchronous motor using the bat algorithm
  257. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  258. Model of depositing layer on cylindrical surface produced by induction-assisted laser cladding process
  259. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  260. Detection of inter-turn faults in transformer winding using the capacitor discharge method
  261. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  262. A novel hybrid genetic algorithm for optimal design of IPM machines for electric vehicle
  263. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  264. Lamination effects on a 3D model of the magnetic core of power transformers
  265. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  266. Detection of vertical disparity in three-dimensional visualizations
  267. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  268. Calculations of magnetic field in dynamo sheets taking into account their texture
  269. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  270. 3-dimensional computer model of electrospinning multicapillary unit used for electrostatic field analysis
  271. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  272. Optimization of wearable microwave antenna with simplified electromagnetic model of the human body
  273. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  274. Induction heating process of ferromagnetic filled carbon nanotubes based on 3-D model
  275. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  276. Speed control of an induction motor by 6-switched 3-level inverter
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