Study on improving heating efficiency of induction cooker system by using an adiabatic layer

Abstract

To improve the heating efficiency of the induction cooker system, this paper adopts the method of introducing an adiabatic layer between the pot bottom and the coil. By using COMSOL software, the electromagnetic - thermal coupling model of the induction cooker is established to analyze the effect of the adiabatic layer on the food temperature and coil temperature, and finally the heating efficiency is explored. The obtained simulation results show good agreements with the experimental results, and then the effectiveness of the proposed method is verified.

Keywords

Induction cooker adiabatic layer heating efficiency electromagnetic - thermal coupling model

1. Introduction

In a induction cooker system, a high-frequency current is produced in the coil to generate alternating magnetic field through the power electronics technology together with the corresponding control circuits. Then in the alternating magnetic field, the induced eddy current is produced in the ferromagnetic conductor pot, which is placed on the top surface of induction cooker. Finally, the pot is heated by the joule heating caused by the induced eddy current and transfers the heat power to the food [1–3]. Compared with the traditional fire kitchenware, induction cooker is known as the “green kitchenware” with several advantages, including the fast heating, the high thermal efficiency, no open flame, no smoke, no harmful gases and good security.

How to increase the heating efficiency of induction cooker is an important issue for energy conservation. In general, the heating efficiency of induction cooker can be divided into the electromagnetic heating efficiency and the heat transfer efficiency. The electromagnetic heating efficiency mainly depends on the working frequency and magnetic flux density. Generally, the iron cores are uniform placed under the coil to increase the magnetic flux density in the pot [4]. Furthermore, the heating efficiency can also be increased effectively through changing the geometry construction of coil, such as a convex coil [5,6]. In order to get a more uniform distribution of heat power, a combination of multiple coils is used in the induction cooker by L.C. Meng et al. [7]. Up to now, most of the existing studies have focused on the electromagnetic heating efficiency, but few researches have been carried out the heat transfer efficiency of the induction cooker.

In the traditional fire cooking system, the thermal energy is obtained by burning fuel, and then the pot bottom absorbs the energy and transfers it to the food. In this case, the heat conduction direction is unidirectional, which is from the fire to the pot to the food. In the induction cooker system, the heat source is the pot and the heat conduction direction is bilateral, one is from the pot bottom to the food and the other is from the pot bottom to the coil. A considerable part of the thermal energy is wasted and the heating efficiency of the induction cooker system declines. Jonghan Kwon et al. have shown that the heating efficiency of the induction cooker is reduced due to the bi-directional conduction of the heat, but the corresponding theoretical analysis and simulation data are not given [8].

Based on the principle of the induction cooker heating system, the electromagnetic-thermal coupling finite element model of induction cooker is established in this paper. And then the temperature distribution of the food and the coil are analyzed when an adiabatic layer is introduced between the pot and the coil. Combined with the experimental data, the effectiveness of this method is verified because it can effectively improve the heating efficiency of induction cooker.

2. Basic principle

The Joule heating caused by the induced eddy current in the pot is the heat source of the induction cooker system, and its magnitude depends mainly on the change rate of magnetic flux density B at the pot bottom and the conductivity of the pot σ: $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle {\nabla}\times E=-\displaystyle \frac{\partial B}{\partial t}\end{eqnarray}$ (1) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle J={\sigma}E\end{eqnarray}$ (2) Where E is the induced electric field intensity and $J$ is the induced current density. The magnetic flux density $B$ is generated by the coil current, which depends on the magnetomotive force of the coil and the magnetoresistance of the system. The change rate of B is related to the operating frequency of the induction cooker.

Based on the Eqs (1) and (2), it is obvious that the induced electric field strength and the induced current density increase with the increase of the operating frequency. However, the effect of the increasing operating frequency on the skin effect is significant: $\begin{eqnarray}\displaystyle d_{s}=\sqrt{1/{\pi}f{\mu}{\sigma}} & & \displaystyle\end{eqnarray}$ (3) Where d _s is the skin depth, $\mu$ and σ are the magnetic permeability and conductivity of the pot, $f$ is the operating frequency of the induction cooker system. The greater the operating frequency, the smaller the skin depth, resulting in the total eddy current in the pot does not increase obviously with the increasing of the frequency. Thus, the frequency of the induction cooker system is usually equal to 25 kHz–30 kHz.

In the induction cooker system, the pot is heated by the Joule heating caused by the induced eddy current: $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle p={\sigma}E^{2}=J^{2}/{\sigma}\end{eqnarray}$ (4) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle {\rho}C_{P}\displaystyle \frac{\partial T}{\partial t}-k{\nabla}^{2}T+{\rho}C_{P}u\cdot {\nabla}T=p\end{eqnarray}$ (5) Where p is the Joule heat power per unit volume of the pot, 𝜌, C _p, $k$ are the density, heat capacity and heat transfer coefficient of the material respectively, $u$ is the fluid velocity in the convective term, and $\nabla$ is the Laplacian operator: $\begin{eqnarray}\displaystyle {\nabla}=a_{x}\displaystyle \frac{\partial }{\partial x}+a_{y}\displaystyle \frac{\partial }{\partial y}+a_{z}\displaystyle \frac{\partial }{\partial z} & & \displaystyle \nonumber\\ \displaystyle {\nabla}^{2}={\nabla}\bullet {\nabla}=\displaystyle \frac{\partial ^{2}}{\partial x^{2}}+\displaystyle \frac{\partial ^{2}}{\partial y^{2}}+\displaystyle \frac{\partial ^{2}}{\partial z^{2}} & & \displaystyle\end{eqnarray}$ (6) Equation (5) shows that the object temperature is related to the heat source, heat transfer coefficient and temperature gradient if the thermal radiation is ignored. When the induction cooker works, the heat source is the pot bottom, and part of the thermal energy is transferred from the pot bottom to the coil, which will lead to the reduction of the food thermal energy during the heat conduction process.

The above analysis shows that the permeability and conductivity of the pot have a significant effect on the heating efficiency of the induction cooker. The pot is generally made by ferromagnetic material, and its magnetic permeability has saturation phenomenon, as shown in Fig. 1.

Fig. 1.

B-H curve of the pot.

Its conductivity is related to the temperature: $\begin{eqnarray}\displaystyle {\sigma}=\displaystyle \frac{{\sigma}_{0}}{1+{\alpha}(T-T_{0})} & & \displaystyle\end{eqnarray}$ (7) Where T ₀ is the initial temperature, σ₀ = 5.43 ×10⁶ S/m is the conductivity of the pot corresponding to T ₀, 𝛼 = 0.004 1∕K is the temperature coefficient. In the induction cooker system, the temperature of the pot does not exceed the Curie temperature, then the effect of temperature on the permeability is ignored.

In the process of heat conduction, the hot boundary of the convective heat transfer is followed by Newton’s cooling law: $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle q=h(T_{P}-T)\end{eqnarray}$ (8) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle q=h(T-T_{ext})\end{eqnarray}$ (9) Where q is the heat flux density, h is the convective heat transfer coefficient, T, T _p and T _ext are the temperature of food, the temperature of pot and the ambient temperature respectively.

3. Electromagnetic-thermal finite element coupled model

In the typical induction cooker system, the spiral coil is used with single turn in the axial direction, and the coil height $H_c$ is generally 3.8–4.2 mm, the inner radius $R_{ci}$ is generally 18–22 mm, the outer diameter is determined by the heating area. The iron cores, made by ferromagnetic material, are placed along the circumference under the coil, and the distance $d$ between the coil and iron cores is generally 0.25 mm. In this paper, the induction cooker system in the literature [8] is used, in which the coil system consists of two serial spiral coils in the same plane. The geometric parameters and material parameters of the model are shown in Table 1.

Table 1
System parameters of induction cooker

Symbol Description Value

Geometric parameters

R_ii Inner radius of Ring-shaped iron cores 18 mm

R_io Outer radius of Ring-shaped iron cores 103 mm

R_ci1 Inner radius of coil 1 20 mm

R_co1 Outer radius of coil 1 55 mm

R_ci2 Inner radius of coil 2 75 mm

R_co2 outer radius of coil 2 100 mm

H_c Height of coil 4 mm

R_p Radius of pot 101 mm

H_p Thickness of pot 1 mm

H_po Height of pot 140 mm

R_s Radius of adiabatic layer 125 mm

H_s Thickness of adiabatic layer 2 mm

R_g Radius of ceramic glass 125 mm

H_g Thickness of ceramic glass 1.5 mm

D_sc Distance between coil and adiabatic layer 5 mm

D_ci Distance between coil and iron cores 0.25 mm

D_cd Distance between coil and air outlet 2 mm

Material parameters

𝜌_s Density of adiabatic layer 0.17 g/cm³

k_s Thermal conductivity of adiabatic layer 0.0155 W/(m ⋅ K)

μ_ri Relative permeability of iron cores 300

V_o Volume of soybean oil 3.6 L

C_o Specific heat of soybean oil 2.4 kJ/(kg ⋅ °C)

Symbol	Description	Value
Geometric parameters
R_ii	Inner radius of Ring-shaped iron cores	18 mm
R_io	Outer radius of Ring-shaped iron cores	103 mm
R_ci1	Inner radius of coil 1	20 mm
R_co1	Outer radius of coil 1	55 mm
R_ci2	Inner radius of coil 2	75 mm
R_co2	outer radius of coil 2	100 mm
H_c	Height of coil	4 mm
R_p	Radius of pot	101 mm
H_p	Thickness of pot	1 mm
H_po	Height of pot	140 mm
R_s	Radius of adiabatic layer	125 mm
H_s	Thickness of adiabatic layer	2 mm
R_g	Radius of ceramic glass	125 mm
H_g	Thickness of ceramic glass	1.5 mm
D_sc	Distance between coil and adiabatic layer	5 mm
D_ci	Distance between coil and iron cores	0.25 mm
D_cd	Distance between coil and air outlet	2 mm
Material parameters
𝜌_s	Density of adiabatic layer	0.17 g/cm³
k_s	Thermal conductivity of adiabatic layer	0.0155 W/(m ⋅ K)
μ_ri	Relative permeability of iron cores	300
V_o	Volume of soybean oil	3.6 L
C_o	Specific heat of soybean oil	2.4 kJ/(kg ⋅ °C)

In this paper, an electromagnetic – thermal finite element coupled model is established by COMSOL software, including magnetic field, heat transfer and laminar flow modules. The magnetic field module is used to generate the induced eddy current in the pot. The heat transfer module is used to simulate the temperature change of the induction cooker system. The laminar flow module is used to simulate the natural convection of the food and the forced convection of the cooling fan. In the simulation, the amplitude and frequency of the current density are 2.5 ×10⁶ A/m² and 25 kHz, respectively. This current is used as the load of the spiral coil. In order to simulate the cooling fan, an air field is set as the forced convection area, in which the wind entrance is set at its side boundary and the air outlet is set at the bottom boundary. Due to the cooling fan blows from the side of the coil, the adiabatic layer placed above the coil has minimal influence on the heat dissipation of the coil, thus the effect of the adiabatic layer on the heat dissipation capability of the coil is neglected in this paper.

Because of the existence of the iron cores, the induction cooker system can not be directly simplified as a two-dimensional axisymmetric model. In this paper, the circular uniform distributed iron cores are equivalent to a continuously distributed ring-shaped iron core, and the permeability is converted according to duty ratio to ensure the system reluctance unchanged in the equivalent model. And then the induction cooker system can be simplified as a two-dimensional axisymmetric model. Figure 2 shows the geometrical model of the induction cooker system.

Fig. 2.

Geometrical model of the induction cooker system. (a) Induction cooker, (b) Three-dimensional model, (c) Two-dimensional axisymmetric model.

In order to prove the validity of the two - dimensional axisymmetric model, the average temperature of the pot bottom is calculated by using the three - dimensional model and the two - dimensional model respectively, as shown in Fig. 3. It can be seen that the temperature curve of the two models are almost coincident and the calculation error is less than 1%, which can meet the engineering requirements. Therefore, the two-dimensional axisymmetric model is used in this paper.

Fig. 3.

The average temperature of the pot.

Fig. 4.

The flow chart of the simulation.

4. System heating efficiency analysis

In order to elucidate the heating efficiency of the induction cooker system, the temperature rise of the coil and the food (soybean oil) are firstly analyzed in this paper under different conditions. And then the effect of the adiabatic layer on the heating efficiency of the induction cooker is studied. Figure 4 is the flow chart of the simulation in this paper, three physical models have been established by using a frequency-transient fully coupled solver: (1) “Magnetic Fields” model for electromagnetic analysis to calculate the Eqs (1)–(3), (2) “Heat Transfer” model for temperature field analysis to calculate the Eqs (4)–(5), (3) “Laminar flow” model for the heat transfer fluid analysis to calculate the Eqs (8)–(9). And then the experimental data are derived from the heated experiments of the soybean oil in the literature [8].

4.1. Temperature rise of coil

By the simulation calculation, Fig. 5 shows the temperature rise of coil under different conditions. It can be seen that the temperature of the coil rises with the increasing of the heating time, but its growth rate decreases. When the heating time increases to 15 minutes, the experimental temperature of the coil reaches 131 °C without the adiabatic layer, while it reaches 90 °C with the adiabatic layer, and the temperature rise is decreased by 41°C. The simulation temperature of the coil is 128.5 °C without the adiabatic layer, while it is 84.8 °C with the adiabatic layer, and the temperature rise is decreased by 43.7 °C. The reason for this is a portion of the thermal energy transferred from the pot to the coil is suppressed due to the use of the adiabatic layer between the coil and the pot, resulting in the reduction of temperature rise of the coil. This is of great significance to the lifetime performance of the coil.

Fig. 5.

The temperature of the coil. (1) Data without adiabatic layer, (2) Data with adiabatic layer.

4.2. Temperature rise of soybean oil

Figure 6 shows the temperature rise of the soybean oil with the heating time increasing. In this paper, soybean oil is used as the heating object. The experiment is carried out by using a thermometer to measure the temperature of the soybean oil. However, in the simulation results, due to the fluidity of soybean oil, the temperature of a certain point fluctuates significantly. Thus, the average temperature of the soybean oil is obtained in the simulation, and it is slightly different from the experimental results. However, their tendency is basically the same. In the experiment, the heating time is 10.2 min when the temperature of the soybean oil reaches 150 °C with the adiabatic layer, while it is 11.2 min without the adiabatic layer, and the heating time is reduced by 9.8%. The corresponding simulation data are 11.3 min and 12.5 min respectively, and the heating time is reduced by 10.6%. The reason for this is the adiabatic layer under the ceramic glass inhibits the heat energy transferred from the pot bottom to the coil, and then the heat transferred from the pot to the soybean oil increases. Therefore, the heat power of the soybean oil is increased with the use of the adiabatic layer, then the temperature of the soybean oil rises faster.

Fig. 6.

The temperature of the soybean oil. (1) Data without adiabatic layer, (2) Data with adiabatic layer.

Fig. 7.

The energy transfer of the induction cooker system. (1) Data without adiabatic layer, (2) Data with adiabatic layer.

4.3. Heating efficiency

In order to study the effect of the adiabatic layer on the heating efficiency of the induction cooker, the total consumed energy, the Joule heating energy of the heat source (pot) and the thermal energy obtained by the soybean oil are calculated respectively, as shown in Fig. 7. At 15 minutes, the total consumed energy in the induction cooker system is 1753.422 kJ, the Joule heating energy of the heat source is 1673.325 kJ, so that the efficiency of power conversion from electrical power to heat power is 95.43%. The thermal energy obtained by the soybean oil is 1287.397 kJ without the adiabatic layer, and the heating efficiency is 73.42%, while the thermal energy obtained by the soybean oil is 1486.581 kJ with the adiabatic layer, and the heating efficiency is 84.78%. Obviously, the use of the adiabatic layer can reduce the unnecessary power loss and improve the heating efficiency of the induction cooker system.

5. Conclusion

In order to improve the heating efficiency of the induction cooker system, an adiabatic layer is introduced to change the direction of heat conduction in this paper. The effectiveness of the adiabatic layer has been validated though simulations and experiments. In the induction cooker system, due to the heat source is the pot and the heat conduction direction is bilateral, when an adiabatic layer is introduced, a considerable part of the thermal energy is suppressed and increases the thermal energy for food. The obtained simulation results show that the temperature of the coil falls by 43.75 °C, the heating time is reduced by 10.6% if the temperature of the soybean oil reaches a value of 150 °C, and the heating efficiency of the induction cooker is increased by 10.72%. Thus, the introduction of an adiabatic layer can effectively improve the heating efficiency of the induction cooker, and reduce the temperature of the coil, so as to extend the service life of the coil.

Footnotes

Acknowledgements

This work is supported by the National Natural Science Foundation of China (51507092, 51877122). The authors thank Bairong Song from School of Foreign Languages, China Three Gorges University for her language translating work and Alan Treworgy from Lewiston, Maine, USA, for his language revision advice.

References

Acero

Burdio

J.M.

Barragán

L.A.

, The domestic induction heating appliance: An overview of recent research 2008:651–657.

Qiu

Xiao

Wang

, Design and computation of coil inductance for induction cookers, Russian Electrical Engineering 86(2) (2015), 106–110.

Qiu

Wen

, Study on effect of material property on thermal power in induction cooker system with finite element method, International Journal of Applied Electromagnetics & Mechanics 46(1) (2014), 35–42.

Chen

Huang

, The analysis of near-field magnetic leakage on the domestic induction cooker, Power Electronics and Application Conference and Exposition, IEEE 2015:605–608.

Meng

Cheng

K.W.E.

and Chan

K.W.

, Systematic approach to high-power and energy-efficient industrial induction cooker system: Circuit design, control strategy, and prototype evaluation, IEEE Transactions on Power Electronics 26.12 (2011), 3754–3765.

Meng

L.C.

Cheng

K.W.E.

Chan

K.W.

and Lu

, Variable turn pitch coils design for heating performance enhancement of commercial induction cooker, Iet Power Electronics 5.1 (2012), 134–141.

Meng

L.C.

Cheng

K.W.E.

and Ho

S.L.

, Multicoils design for induction cookers with applying switched exciting method, IEEE Transactions on Magnetics 48.11 (2012), 4503–4506.

Kwon

Nam

Y.J.

Shin

K.H.

, Efficient cooling method for a Cu coil in an induction cooker by using an insulation sheet, Journal of Magnetics 16.1 (2011), 31–35.