Fundamental Evaluation of Thermal Switch Based on Ionic Wind

: A signiﬁcant amount of thermal energy (mainly under 200 ◦ C) is wasted in the world. To utilize the waste heat, e ﬃ cient heat management and thermal switching is required. The basic characteristics of a thermal switch that controls the ﬂow of heat by switching on / o ﬀ the ionic wind is discussed in this study. The study was conducted through experiments and numerical simulations. A heater made of aluminum block maintained at 100 ◦ C was used as a heat source, and the rate of heat ﬂow to a copper plate placed over it was measured. Ionic wind was induced by corona discharge with a needle placed on the heater. The ratio of heat transfer coe ﬃ cients was obtained in the range of 3–4, with an energy e ﬃ ciency of around 10. The heat ﬂux at this condition was approximately 400 W / m 2 . The numerical simulations indicate that the heat transfer is enhanced by ionic winds, and the results were found to corroborate well with the experimental ones.


Introduction
The global thermal energy waste amounts to a significant fraction of the total energy consumption. For instance, only the industrial sector in Japan is discharging around 3.3 × 10 18 J/y heat as waste [1], despite the enormous efforts that have been put for waste heat recovery since the oil crisis in 1973. In fact, the amount corresponds to approximately 40% of the total energy consumption in Japan [2], indicating that efficient waste heat recovery is crucial to save fossil fuels and reduce CO 2 emission. Therefore, a thermal switch that controls the flow of heat is essential. Literature shows that a thermal switch could stabilize the high temperature at the hot end of a thermoelectric element and improve the electrical output [3]. Further, the low energy conversion efficiency of thermoelectric devices limit their use in a low temperature range (<200 • C, waste heat in this range contributes to 60% of the waste heat from the Japanese industry [1]), and heat energy has to be utilized as heat if possible. However, a thermal switch enables the thermoelectric device to operate in low temperature ranges.
Various thermal switch technologies have been studied in the literature including mechanical control of the contact between two surfaces [3], the phase transition of VO 2 between electrical conductor and insulator [4], the use of liquid-vapor phase transition of working fluid [5], and electrowetting of liquid [6][7][8][9]. Nonetheless, the devices are desired to be simple without any moving parts and should be able to control the flow of heat at any temperature to have precise and long-term thermal management for an effective heat recovery. The reported techniques fail to meet all of these requirements in one. Thus, the present author proposes a simple method that uses ionic wind. In this method, the ionic wind induced by corona discharge between two surfaces controls convective heat transfer. The device has a simple structure and can control heat flow at any temperature without any moving part.
It is worth mentioning that heat transfer enhancement by using ionic wind devices has been studied for decades [10][11][12][13][14][15][16][17][18][19]. For example, [18] showed that ionic wind induced by a wire-type discharge electrode enhanced the heat transfer between two of the surfaces that face each other of a rectangular Figure 1 shows the schematic of the setup for thermal switch tests. The temperature of the 10 mm thick and 50 mm square aluminum block was maintained at 100 • C using an embedded nichrome-wire heater and a temperature controller. This configuration supposed a minimum unit that is taken out of a thermal switch which has multiple discharging electrodes in a regular pattern. The electric current and driving voltage of the heater were obtained using voltages V 1 and V 2 (refer to Figure 1). A 0.5 mm thick copper plate was placed at a vertical distance of 12.5 mm from the block. The heat transfer happened between upper surfaces of the aluminum block and the copper plate. Corona needles with 1 mm diameters and different heights (L = 6-9 mm) were placed at the center on the block. The needles were made from brass and polished with an abrasive compound before use. When high positive DC voltage, V c , was applied to the copper plate with respect to the aluminum block (connected to the ground), negative ions were generated at the vicinity of the needle tip and ionic wind was induced in the gap. The electric current due to the corona discharge was calculated by measuring the voltage across a 10 kΩ resistor (refer to Figure 1). The temperature at the top surface of the copper plate was measured using a thermographic camera. This temperature could not be measured with contacting probes such as thermocouples because of the high voltage applied to the copper plate. The top surface of the copper plate and the electrode holder was painted with a black paint (suspension of graphite particles, F-142  The copper plate and the aluminum block were separated with acrylic spacers. To minimize unintended heat conduction (a) the acrylic spacers were placed on an aluminum plate (t = 1 mm) that was connected only at four corners of the square, and (b) 1 mm gaps were provided between the edges of the block and the spacer unit (shown in detailed illustration presented in Figure 1). The set was thermally insulated by using ceramic wool. Because the ceramic wool is permeable to air, the gap space was not strictly sealed, but probably air slightly entered and exited through the 1 mm gap. The complete setup was enclosed in a plastic mesh to restrict any wind from the surrounding without affecting the natural convection over the copper plate.

Experimental Methods
The temperature at the top surface of the copper plate was measured using a thermographic camera. This temperature could not be measured with contacting probes such as thermocouples because of the high voltage applied to the copper plate. The top surface of the copper plate and the electrode holder was painted with a black paint (suspension of graphite particles, F-142 manufactured by Fine Chemicals Japan Co., Ltd., Tokyo, Japan) to avoid the measurement errors caused by emissivity less than one. Although the Infrared camera can observe the temperature distribution, the standard deviations of the temperature over the copper surface were approximately found to be 0.3 • C. The heat transfer coefficient (K) is defined as, where Q is the rate of heat flow (in Watt) from the surface of the aluminum block to the copper plate, A is the area of the surfaces between which heat is transferred (equal to the surface area of the aluminum block and the copper plate in the present case), T h is the temperature of the top surface of the aluminum block, and T s is the average temperature of the top surface of the copper plate. Q was determined by the power supplied to the heater to maintain T h at 100 • C. Further details to determine Q are discussed in the results section.

Numerical Simulation
Airflow and transfer of heat induced by corona discharge were numerically simulated using finite element method in COMSOL Multiphysics 5.3. The calculations were performed on an axisymmetric region having 25 mm radius, as illustrated in Figure 2. The region was vertically divided into two parts-one part had air (12.5 mm), and the other had copper (0.5 mm). A needle was placed in the air gap such that its axis aligned with the axis of the region and its base touched the bottom surface. The needle consisted of a conical tip (with 2 mm height and 0.05 mm radius of curvature of the tip) and a cylindrical base of 0.5 mm radius. The radius of curvature of the tip was determined from the needle typically used in such experiments ( Figure 3). Henceforth, "the tip" indicates the surface that has a radius of curvature of 0.05 mm. The sizes of the elements (for finite element method) at the surface of the needle tip were kept less than 2 µm × 2 µm to calculate ionic flow correctly.     To simulate the corona discharge, electrical potential (V) and negative ion density (Nn) in the airfilled region were estimated using Poisson's Equation (2) and continuity Equation (3). Further, the space charge was assumed to consist of negative ions of molecular oxygen (O2 − ) only. Due to two orders of magnitude higher speed of ions than airstream in corona discharge (in general), the effect of airflow on the transportation of ions was neglected.
Here e is the elementary charge, μn is the mobility of the negative ions, and Dn is the diffusion coefficient of the negative ions. Mobility μn was calculated by multiplying Tg/293. 15 with the value at 293.15 K (1.69 × 10 −4 m 2 /V·s) [20,21], where Tg (=(Th + Ts)/2) is the average temperature in the air-filled region. Further, the Einstein's relation was used to determine Dn using μn at temperature Tg.
The simulations were performed under the following boundary conditions. The boundary conditions for the potential (V) were determined using the Dirichlet conditions (Equations (4) and (5)) at the top surface and the bottom surface including the needle and the Neumann condition (Equation (6)) at the sidewall. Likewise, Neumann boundary condition (Equation (7)) was used for ion density Nn at the top surface of the air-filled region. The ion flux was set to zero at the sidewall (Equation (8)). Further, the ion density at the bottom surface except for the tip of the needle was set to zero (Equation (9)), while the ion density at the tip was set to Nn0 (Equation (10)). The following To simulate the corona discharge, electrical potential (V) and negative ion density (N n ) in the air-filled region were estimated using Poisson's Equation (2) and continuity Equation (3). Further, the space charge was assumed to consist of negative ions of molecular oxygen (O 2 − ) only. Due to two orders of magnitude higher speed of ions than airstream in corona discharge (in general), the effect of airflow on the transportation of ions was neglected.
Here e is the elementary charge, µ n is the mobility of the negative ions, and D n is the diffusion coefficient of the negative ions. Mobility µ n was calculated by multiplying T g /293.15 with the value at 293.15 K (1.69 × 10 −4 m 2 /V·s) [20,21], where T g (=(T h + T s )/2) is the average temperature in the air-filled region. Further, the Einstein's relation was used to determine D n using µ n at temperature T g .
The simulations were performed under the following boundary conditions. The boundary conditions for the potential (V) were determined using the Dirichlet conditions (Equations (4) and (5)) at the top surface and the bottom surface including the needle and the Neumann condition (Equation (6)) at the sidewall. Likewise, Neumann boundary condition (Equation (7)) was used for ion density N n at the top surface of the air-filled region. The ion flux was set to zero at the sidewall (Equation (8)). Further, the ion density at the bottom surface except for the tip of the needle was set to zero (Equation (9)), while the ion density at the tip was set to N n0 (Equation (10)). The following procedure was followed to determine N n0 : i) first, the corona onset voltage (V o ) was determined for each needle length (L) through experiments, ii) second, the maximum electric field strength (E max ) at the tip of the needle (the field strength when V o is applied to the needle without the corona discharge) was calculated, and iii) third, N n0 was adjusted so that the maximum field strength at the tip became E max when V c was applied to the needle. This procedure is based on Katpzov's hypothesis [22] and validated through numerical simulation, e.g., by Umezu et al. [23].
The velocity field (u) of the laminar flow induced by the corona discharge was determined by the Navier-Stokes Equation (11) at a stationary state. The equation uses volume force (eN n ∇V) exerted by the ion movement and buoyancy force (−ρ a g) to determine u. To solve the equation, the wall was considered to have zero slip (Equation (12)). However, the thin opening between the acrylic spacer and the aluminum block (see the experimental setup section) was represented by setting stress normal to the bottom 1 mm part of the sidewall to zero (Equation (13)).
Here ρ a is the density of air, p is a static pressure, η is the viscosity of air, and g is the acceleration due to gravity. Air density and viscosity are the functions of temperature and were determined as discussed below.
The temperature field (T) in the air-filled region and at the copper plate was calculated to determine the rate of heat flux. Dissipation Equations (14) and (15) govern the temperature field in the air-filled and the copper-filled regions, respectively. Boundary condition (16) was used at the surface of the heater block and the needle. The experimentally measured value of T s was used in boundary condition (17). The temperature gradient in the normal direction at the bottom 1 mm opening of the sidewall was set to zero (Equation (18)).
In the above equations, C p,a is the isobaric specific heat of air, k a and k c are the thermal conductivity of air and copper, respectively. k a approximated by Equation (19) (Reference [24]) at T g (= (T s + T h )/2) was used.

The Heat Transfer by Natural Convection and Analysis of the Rate of Heat Flow (Q)
In the absence of a needle in the gap, the heat is transferred by natural convection from the heater surface to the copper plate. This section discusses the rate of heat flow (Q) by natural convection. Figure 4 shows the variation of heater powers with respect to elapsed time in two cases: (a) when the copper plate is exposed to the atmosphere, as illustrated in Figure 1, and (b) when the copper plate is insulated from the atmosphere by using ceramic wool. Since a significant amount of heat leaks from the sidewalls and the bottom surface of the heater, the difference in the heater powers in two cases is expected to be equivalent to the rate of heat flow from heater to copper plate by natural convection. The average difference in the heater powers in two cases is 0.36 W (the stabilized heater powers are 6.17 and 5.81 W). The average temperature of the top surface of the copper plate (T s ) is 46.8, while the temperature of the heater (T h ) is 101 • C. With this temperature difference, only the thermal conduction insulated from the atmosphere by using ceramic wool. Since a significant amount of heat leaks from the sidewalls and the bottom surface of the heater, the difference in the heater powers in two cases is expected to be equivalent to the rate of heat flow from heater to copper plate by natural convection. The average difference in the heater powers in two cases is 0.36 W (the stabilized heater powers are 6.17 and 5.81 W). The average temperature of the top surface of the copper plate (Ts) is 46.8, while the temperature of the heater (Th) is 101 °C. With this temperature difference, only the thermal conduction provides approximately 0.33 W heat flow. That implies most of the heat is transferred by thermal conduction alone.     In the purview of the above results, herein, Q in the absence of ionic wind can be approximated as 0.33 W. Accordingly, the heat flow rate in the presence of ionic wind can be given by where Ph0 is the heater power upon stabilization before the corona discharge, and Ph1 is that 30 min after the beginning of the corona discharge.

The Effect of Ionic Wind
3.2.1. The Corona Onset Voltages (Vo) Figure 6 shows the experimental results of corona discharge current (Ic) as a function of applied DC voltage (Vc) for needle length L ranging from 6 mm to 9 mm. In most of the cases, Equation (21) with a constant C [25] very closely approximates Ic (Vo in the equation is the corona onset voltage). However, for L = 9 mm some outliers against the fitting curve at lower voltages (less than 3 kV) can be observed, probably because of oxidation of the needle tip. In the purview of the above results, herein, Q in the absence of ionic wind can be approximated as 0.33 W. Accordingly, the heat flow rate in the presence of ionic wind can be given by where P h0 is the heater power upon stabilization before the corona discharge, and P h1 is that 30 min after the beginning of the corona discharge. However, for L = 9 mm some outliers against the fitting curve at lower voltages (less than 3 kV) can be observed, probably because of oxidation of the needle tip.
where Ph0 is the heater power upon stabilization before the corona discharge, and Ph1 is that 30 min after the beginning of the corona discharge.

The Effect of Ionic Wind
3.2.1. The Corona Onset Voltages (Vo) Figure 6 shows the experimental results of corona discharge current (Ic) as a function of applied DC voltage (Vc) for needle length L ranging from 6 mm to 9 mm. In most of the cases, Equation (21) with a constant C [25] very closely approximates Ic (Vo in the equation is the corona onset voltage). However, for L = 9 mm some outliers against the fitting curve at lower voltages (less than 3 kV) can be observed, probably because of oxidation of the needle tip. ( ) Table 1 summarizes Vo as obtained by fitting Ic vs. Vc data using Equation (21). It is observed that the onset voltage decreases with decrease in the gap between the needle tip and the copper plate.  Table 1 summarizes V o as obtained by fitting I c vs. V c data using Equation (21). It is observed that the onset voltage decreases with decrease in the gap between the needle tip and the copper plate.  Figure 7 shows I c as a function of V c , as obtained from numerical simulations. Like the experimental results, the relationship between V c and I c can be expressed by Equation (21), and I c is larger for larger L. However, the magnitudes of the corona discharge currents are significantly smaller than that in the experiment. Interestingly, the difference between the simulated and the experimental I c values increases with L, e. g., the numerically simulated values are around one-fifth of the experimental values for L = 6 mm, while the same are one-tenth of the experimental values for L = 9 mm. It may be due to high local electric field around the nonspherical tip of the needle causing easier breakdown of air; however, the exact reason is not known at this stage. shows Ic as a function of Vc, as obtained from numerical simulations. Like the experimental results, the relationship between Vc and Ic can be expressed by Equation (21), and Ic is larger for larger L. However, the magnitudes of the corona discharge currents are significantly smaller than that in the experiment. Interestingly, the difference between the simulated and the experimental Ic values increases with L, e. g., the numerically simulated values are around one-fifth of the experimental values for L = 6 mm, while the same are one-tenth of the experimental values for L = 9 mm. It may be due to high local electric field around the nonspherical tip of the needle causing easier breakdown of air; however, the exact reason is not known at this stage. respectively. For every L, the average heat flux, Q/A, increases with increase in V c, while the surface temperature of the copper plate T s approaches the heater temperature T h . The numerical simulations reproduced the experimental trend between the applied voltage and Q/A. The following discussion further justifies the accuracy of the simulated airstream. In the experiment, an increase in Q causes a decrease in the temperature difference between T h and T s , which in turn decreases Q (negative feedback for Q works). Here, T s obtained from the experiment was used as a boundary condition in the simulation. Accordingly, if the simulated convection were (a) less active than that in the experiment, Q would not have increased with V c , and (b) more active than that in the experiment, Q would have increased more rapidly with V c than was observed in the experiment. The best agreement between experimental and simulated results was observed for L = 7 mm, which could be attributed to the status of the tip of the needle (although any deviation was not apparent). In addition, a few calculations were performed for the V c that were not tested in the experiment. In such cases, the boundary value T s was linearly interpolated from the experimental values.   Table 2 summarizes the heat transfer coefficient K. The ratio Kon/Koff defines the ability of the device to control the flow of heat. Kon/Koff can be increased by applying higher voltages. The maximum value for the same in the present study is 5.12 (Vc = 6.0 kV and L = 7 mm). At 4.0-4.1 kV, K increases with L (experimentally as well as in the simulation), except for L = 7 mm. The result is an outcome of the smaller gap between the needle tip and copper plate resulting in higher electric field and larger discharge current. However, the optimum L in the context of energy efficiency is discussed in the next section.   Table 2 summarizes the heat transfer coefficient K. The ratio K on /K off defines the ability of the device to control the flow of heat. K on /K off can be increased by applying higher voltages. The maximum value for the same in the present study is 5.12 (V c = 6.0 kV and L = 7 mm). At 4.0-4.1 kV, K increases with L (experimentally as well as in the simulation), except for L = 7 mm. The result is an outcome of the smaller gap between the needle tip and copper plate resulting in higher electric field and larger Energies 2019, 12, 2963 9 of 14 discharge current. However, the optimum L in the context of energy efficiency is discussed in the next section. Figure 9a-f shows the simulated distributions of temperature and air flow velocity for L = 6 mm. It is evident that an increase in the speed of flow with the applied voltage increases the temperature gradient on the copper plate right above the needle and on the peripheral area of the heater; hence, enhances the rate of heat transfer. Three types of ionic wind patterns appeared depending on the applied voltages. At the lowest voltage (3.5 kV), when the airstream above the needle reached the copper plate it turned outward, descended, cooled down, reached the sidewall, and then returned to the axis. Thus, the wind circulated clockwise. Regardless, a slight clockwise circulation occurred at a peripheral region due to natural convection. At V c = 4.0 kV, the circular flow at the center region induced a counterclockwise circulation at the peripheral region. At the highest V (5.0 kV), the discharge-induced flow at the axis went outward along the copper plate and reached the sidewall, then descended before being cooled. It resulted in the formation of a high-speed flow layer near the center of the upper surface which grows with increase in V c . Further, the flow layer breaks down the temperature boundary layer and results in an enhanced rate of heat transfer. Additionally, for the other values of L, the same orders of flow pattern were observed including a single circulation localized to the central region, twin circulation, and a global single circulation, as it was for L = 6 mm. then descended before being cooled. It resulted in the formation of a high-speed flow layer near the center of the upper surface which grows with increase in Vc. Further, the flow layer breaks down the temperature boundary layer and results in an enhanced rate of heat transfer. Additionally, for the other values of L, the same orders of flow pattern were observed including a single circulation localized to the central region, twin circulation, and a global single circulation, as it was for L = 6 mm.  Figure 10 shows the Nusselt number (Nu) as a function of the Reynolds number (Re) based on the numerical simulation results. The gap height d = 12.5 mm is adopted as the representative length d. The representative velocity is the average airstream speed in the radial direction at 1 mm below the upper surface of the gap (|u|ave defined by Equation (23)). There is a significant correlation between Nu and Re. It should be noted that this correlation does not depend on L and this correlation means that the effect of the change in the convection regime (twin or single circulation) can be reduced to Re. It can be understood that the flow in the radial direction induces the circulating flows in the gap, which transfer heat.  Figure 10 shows the Nusselt number (Nu) as a function of the Reynolds number (Re) based on the numerical simulation results. The gap height d = 12.5 mm is adopted as the representative length d. The representative velocity is the average airstream speed in the radial direction at 1 mm below the upper surface of the gap (|u| ave defined by Equation (23)). There is a significant correlation between Nu and Re. It should be noted that this correlation does not depend on L and this correlation means that the effect of the change in the convection regime (twin or single circulation) can be reduced to Re. It can be understood that the flow in the radial direction induces the circulating flows in the gap, which transfer heat.

Energy Efficiencies
In the present study, energy efficiency (η) can be defined as the ratio of the increased rate of heat flow (ΔQ) to the input discharge power Pc (= Ic × Vc) (see Equation (25)). The experimental and simulated values of the same are shown in Figures 11 and 12, respectively.

Energy Efficiencies
In the present study, energy efficiency (η) can be defined as the ratio of the increased rate of heat flow (∆Q) to the input discharge power P c (= I c × V c ) (see Equation (25)). The experimental and simulated values of the same are shown in Figures 11 and 12, respectively.
where ∆Q = Q on − Q off (Q on is Q in the presence of corona discharge, and Q off is Q in the absence of corona discharge). As evident from Figure 11, the efficiency is extremely high if Q/A is less than 200 W/m 2 , then it decreases rapidly with increase in the voltage. As can be found in Figure 10, in the almost absence of convection, only a small radial flow has a large enhancement effect for heat transfer, which is the reason for high η at low Q/A region. The decrease in η with higher Q/A is attributed to decrease in conversion efficiency from electrical energy to the kinetic energy of airstream. In the range of Q/A larger than 250 W/m 2 , the needle with L = 7 mm resulted in the highest η, followed by 6, 8, and 9 mm (the order is hard to determine in the range less than 250 W/m 2 ). The reason of the low efficiencies for larger values of L is the less amount of air in the space above the needles, which reduces the effect of the discharge on the rate of heat transfer. Further, L = 6 mm did not give the highest efficiency because of the weaker outward flow compared with that of L = 7 mm that resulted due to the lower velocity at the axis. However, the reason of larger variation in η in the experiment than in the numerical simulation is not fully understood in this study. Among the reasons would be that the incomplete spherical shape of the needle tips might have increased current that did not contribute to creation of the air flow, especially in cases of L = 8 and 9 mm (see Section 3.2.1). The energy efficiency is more than one for all the conditions in the range of this study. For example, it is~10 when L is 7 mm and Q/A is~400 W/m 2 (K on /K off = 3-4). In a viewpoint of energy consumption, these results mean that transferring thermal energy from where waste heat is exhausted has an advantage compared with newly creating heat at the site. The simulations' results ( Figure 12) show the same trend as the experiment, with the highest η for L = 7 mm. However, the much larger efficiencies obtained from simulations are due to smaller discharge current compared with that of the experiment. Analysis indicates that for V c = 4.1 kV and L = 7 mm, Q/A and η are 370 W/m 2 and 12.0, respectively, in the experiment, while the corresponding simulated values are 353 W/m 2 and 58.0. Very large values of efficiency obtained from simulation show a great potential of the ionic wind-based thermal switches. Although this device is promising from the energy efficiency point of view, the heat flux needs to be 2-3 orders of magnitude higher for practical purposes. Accordingly, while keeping in mind the advantage of ionic wind that it can be generated in a small region (like the heat transfer gap in this study), the future studies should identify the optimum arrangement of multiple needles that could generate mutually driving winds, causing a very strong circulating flow. based thermal switches.
Although this device is promising from the energy efficiency point of view, the heat flux needs to be 2-3 orders of magnitude higher for practical purposes. Accordingly, while keeping in mind the advantage of ionic wind that it can be generated in a small region (like the heat transfer gap in this study), the future studies should identify the optimum arrangement of multiple needles that could generate mutually driving winds, causing a very strong circulating flow.

The Influence of the Heat Generation by Corona Discharge in the Gap
The numerical simulation results discussed until now did not include the heating effect of the corona discharge. All of the energy from the corona discharge was dissipated in the gap. Since it is difficult to identify the distribution of such a heat source, heat transferred was calculated by assuming a volume heat source distributed uniformly throughout the gap. Heating power per unit volume was determined using Equation (21) at various applied voltages for the case of L = 6 mm. It should be noted that experimental values of the discharge power were used in the calculation. The simulated values of the rate of heat transfer after considering the volume heat sources are shown in Figure 13. Due to a little temperature rise in the gap, the rate of heat flow from the heater surface decreased, while the heat received by the upper surface of the gap increased. The difference (between black triangles and circles in the graph) in the rates of heat flow correspond to the discharge power. The introduction of a volume heat source has less effect on the rate of heat flow at the heater surface as compared with the upper surface (copper plate). This result suggests that the experimental values of Q are hardly affected by the discharge power dissipated in the gap because Q is determined as the heater power in the experiment.

The Influence of the Heat Generation by Corona Discharge in the Gap
The numerical simulation results discussed until now did not include the heating effect of the corona discharge. All of the energy from the corona discharge was dissipated in the gap. Since it is difficult to identify the distribution of such a heat source, heat transferred was calculated by assuming a volume heat source distributed uniformly throughout the gap. Heating power per unit volume was determined using Equation (21) at various applied voltages for the case of L = 6 mm. It should be noted that experimental values of the discharge power were used in the calculation. The simulated values of the rate of heat transfer after considering the volume heat sources are shown in Figure 13. Due to a little temperature rise in the gap, the rate of heat flow from the heater surface decreased, while the heat received by the upper surface of the gap increased. The difference (between black triangles and circles in the graph) in the rates of heat flow correspond to the discharge power. The introduction of a volume heat source has less effect on the rate of heat flow at the heater surface as compared with the upper surface (copper plate). This result suggests that the experimental values of Q are hardly affected by the discharge power dissipated in the gap because Q is determined as the heater power in the experiment. while the heat received by the upper surface of the gap increased. The difference (between black triangles and circles in the graph) in the rates of heat flow correspond to the discharge power. The introduction of a volume heat source has less effect on the rate of heat flow at the heater surface as compared with the upper surface (copper plate). This result suggests that the experimental values of Q are hardly affected by the discharge power dissipated in the gap because Q is determined as the heater power in the experiment.

Conclusions
To summarize, the basic characteristics of the thermal switch using ionic wind were investigated in this study. The ionic wind-based thermal switches could control the rate of heat flow, with energy efficiencies (the ratio of controlled heat flow rate to input discharge power) more than 10. Further, the ratio of heat transfer coefficients between two surfaces in the presence and absence of corona discharge ranged from 3 to 4, and the heat flux was around 400 W/m 2 . The future study should focus to enhance the heat flux in a controlled manner.
Funding: This research received no external funding.