## 2 Model
### Computation Analysis Model  
To examine the hot plate's abnormal thermal behavior, ANSYS Fluent V15.0, which is commercial CFD code, was used to perform computational analysis. The analysis area was the entire hot plate as shown in Figure 1, and 2 million grid cells were used. The RNG \(k-\varepsilon\) model [35] is a method of modeling the turbulence phenomenon based on a mathematical statistical technique called RNG (Renormalization Group) method. The transportation equation for \(k\), \(\varepsilon\) of RNG model is as follows:  
\[\rho\left(U_{i}\frac{\partial k}{\partial x_{i}}\right)=\frac{\partial}{ \partial x_{i}}\left(\sigma_{k}\mu_{eff}\frac{\partial k}{\partial x_{i}} \right)+\mu\left(\frac{\partial U_{i}}{\partial x_{j}}+\frac{\partial U_{j}}{ \partial x_{i}}\right)\frac{\partial U_{i}}{\partial x_{j}}-\rho\varepsilon \tag{1}\]  
\[\rho\left(U_{i}\frac{\partial\varepsilon}{\partial x_{i}}\right)=\frac{ \partial}{\partial x_{i}}\left(\sigma_{\varepsilon}\mu_{eff}\frac{\partial \varepsilon}{\partial x_{i}}\right)+C_{\varepsilon 1}\frac{\varepsilon}{k}\left[\mu_{ \sharp}\left(\frac{\partial U_{i}}{\partial x_{j}}+\frac{\partial U_{j}}{ \partial x_{i}}\right)\frac{\partial U_{i}}{\partial x_{j}}\right]-\left(C_{ \varepsilon 2}+\frac{C_{\mu}\eta\left(1-\frac{\eta}{\eta_{0}}\right)}{1+\beta \eta^{3}}\right)\rho\frac{\varepsilon^{2}}{k} \tag{2}\]  
where, \(\eta=Sk/\varepsilon\), \(S=\left(2S_{ij}S_{ij}\right)^{1/2}\). The coefficient values applied in the above equation are as follows:  
\(\sigma_{k}=0.7194\), \(\sigma_{\varepsilon}=0.7194\), \(C_{\varepsilon 1}=1.42\), \(C_{\varepsilon 2}=1.68\), \(C_{\mu}=0.0845\), \(\eta_{0}=4.38\), \(\beta=0.012\). The heating mode, which raises the hot plate's temperature from room temperature to 200 \({}^{\circ}\)C, and the cooling mode which lowers the temperature from 200 \({}^{\circ}\)C to room temperature, were calculated separately. The computation conditions were set to be similar to a previous study [37]. For Model I, it was assumed that the cooling holes were empty during heating mode. For cooling mode, it was assumed that the refrigerant was flowing into the cooling holes at a temperature of 17.2, and the computations were done at velocity boundary conditions. To increase temperature uniformity, the neighboring cooling holes' refrigerant flows were set to be in opposite directions. For coolant, nitrogen gas and water were used. The coolant's turbulent flow was calculated using the RNG k-\(\varepsilon\) model and an enhanced wall function. The key to Model II is in modeling the heat pipe. The heat pipe's axial effective thermal conductivity is considered to be around 80 times that of copper [20], and the heat pipe was simply modeled as a solid which has 80 times the thermal conductivity of copper. In cooling mode, the cooling of the 30 mm at the end of the heat pipe was performed at boundary conditions with a convective heat transfer coefficient h_heatpipe of 1768.4 W/m\({}^{2}\)K and an external temperature of 17.2. Based on the initial cooling conditions, the cooling capacity corresponds to 150 W, and this study used a maximum electric heat capacity [39] that satisfies the capillary limit of the heat pipe with a 6 mm diameter that was found in a previous study [19]. The hot plate's bottom surface was treated as insulated, and natural convection cooling conditions were applied to the top surface and side surfaces. The laminar natural convection heat transfer correlation equation for the square structure's side and top surfaces is as follows [38].