## 2 Materials and Methods
### Evaluation of Temperature Control Performance Using CFD Analysis  
CFD analysis is used in the design of plasma devices to understand fluid dynamics and heat transfer [21]. In this study, CFD analysis using Autodesk CFD (Autodesk Inc., San Rafael, CA, USA) was performed to design the flow channels of the plasma jet. To analyze the heat transfer and gas flow, the continuity, Navier-Stokes, and energy equations are discretized and calculated by the finite element method. The respective equations for incompressible fluids are shown below. The continuity equation is  
\[\rho(\
abla\cdot\mathbf{U})=0 \tag{1}\]  
where \(\rho\) is the density and \(\mathbf{U}\) is the velocity vector. The Navier-Stokes equation is  
\[\rho\frac{\partial\mathbf{U}}{\partial t}+\rho(\
abla\cdot\mathbf{U})\mathbf{U}=\rho\mathbf{g }-\
abla P+\mu\
abla^{2}\mathbf{U} \tag{2}\]  
where \(\mathbf{g}\) are the gravitational acceleration vector, \(P\) is pressure, and \(\mu\) is viscosity. The energy equation is  
\[\frac{\partial\rho C_{p}T}{\partial t}+\
abla\cdot\left(\rho C_{p}T\mathbf{U} \right)=\
abla^{2}kT \tag{3}\]  
where \(C_{p}\) is the constant pressure specific heat, \(T\) is the temperature, and \(k\) is the thermal conductivity. For turbulence analysis, these equations were time-averaged. The Reynolds stress terms generated by this averaging were approximated using the turbulence model k-\(\epsilon\). A modified Petrov-Galerkin method was used for calculation of the convection term in the Navier-Stokes equations. In the simplified model shown in Figure 2, the joints and screws of the parts that did not have a significant effect on the CFD were omitted. The mesh size of the model was set to \"Automatic\", and the parameters are resolution factor: 1.000, edge growth rate: 1.100, minimum points on edge: 2, points on longest edge: 10, surface limiting aspect: 20. The total number of nodes is 236,971 (fluid nodes: 169,458, solid nodes: 67,513), and the total number of elements is 1,008,496 (fluid elements: 532,224, solid elements: 476,272). In the analysis of the low-temperature side (\(-\)30-0 \({}^{\circ}\)C), 80 wt% ethanol was used as the TCF and supplied to the TCF channel at a rate of 0.5 L/min. For the analysis of the high-temperature side (0-90 \({}^{\circ}\)C), water was used as the TCF and supplied to the TCF flow channel at a rate of 0.5 L/min. The TCF was supplied to the plasma jet body using an insulated silicon rubber tube. The pressure at the outlet surface of the TCF flow channel was set to 0 Pa, and there was no pressure loss in the temperature  
Figure 1: Concept of multi-gas temperature-controllable plasma jet: (**a**) concept of flow channel; (**b**) cross-sectional view.  
controlled fluid flow. Dry nitrogen gas at 3 L/min and 24 \({}^{\circ}\)C was used as the gas for plasma generation. The plasma jet body was made of aluminum and surrounded by a 5 mm-thick porous ethylene propylene diene rubber insulation material. The thermal conductivity of the insulation material was set to 0.032 W/m\(\cdot\)k. However, no insulation was placed on the surface where the plasma outlet was placed and on the upper surface because these surfaces are impediments to plasma processing in practical use. To analyze the heat transfer to the external gas, the plasma jet was placed in a nitrogen external fluid. Nitrogen at a temperature of 24 \({}^{\circ}\)C and humidity of 60% was used as the external fluid to match the operating environment. The surface of the external fluid was analyzed assuming no pressure loss. To clarify the effect of the temperature of the TCF on the gas before plasma generation, the temperature of the plasma jet body and gas temperature were calculated by varying the TCF from \(-\)30 to 90 \({}^{\circ}\)C. The temperature at the 2 mm point of the plasma outlet was calculated. A component analysis was performed on the plasma jet body, and the average temperature was calculated. It should be noted that the plasma was not considered in the CFD in this study.