# Numerical Simulation on Thermoelectric Cooling of Core Power Devices in Air Conditioning
## 2 Simulations
**Multi-physical field setting:** We invoked four physical field modules in COMSOL Multiphysics 5.6 for coupling solid and fluid heat transfer, laminar flow, current, and thermoelectric effects. Then, we needed to define the initial conditions and boundary conditions to determine the heat generation and heat transfer of the simulation models. Initial conditions: the initial test temperature of all components in the model was 298.15 K (25 \({}^{\circ}\)C), the ambient temperature was 319.15 K (46 \({}^{\circ}\)C), and the wind speed at the inlet of the duct was 1.5 m s\({}^{-1}\). Boundary conditions: The heat source of the power device was set by the domain heat source model in COMSOL, and the generalized source heat densities were 29,040,935.672, 15,393,226.98, and 15,393,226.98 W m\({}^{-3}\). The heat transfer coefficients of the contact surfaces between the heat-sink fins and the air medium in the air duct in the air-cooled region were calculated by the laminar flow model. Natural convection heat dissipation between air, the power device, and the TEC can be described by [PERSON]'s law convective heat transfer process using Equation (1):  
\[Q=h(T_{ambient}-T) \tag{1}\]  
where \(h\) is the convective heat transfer coefficient and \(T_{ambient}\) is the ambient temperature. Referring to the convective heat transfer coefficient calculation model provided in COMSOL, the convective heat transfer coefficients at different locations for different materials in the TEC structure can be divided into three categories: top surface, bottom surface, and side surface, which we will discuss separately below. The convective heat transfer coefficient between the TEC substrate and the electrode top surface (\(h_{top}\)) can be calculated according to Equation (2):  
\[h_{top}=\left\{ \begin{array}{ll}\frac{\kappa}{L}\cdot 0.54 Ra_{L}^{\frac{1}{ 2}}&\quad\text{if }T>T_{ambient}\text{ and }10^{4}\leq Ra_{L}\leq 10^{7}\\ \frac{\kappa}{L}\cdot 0.15 Ra_{L}^{\frac{1}{2}}&\quad\text{if }T<T_{ambient}\text{ and }10^{7}\leq Ra_{L}\leq 10^{11}\\ \frac{\kappa}{L}\cdot 0.27 Ra_{L}^{\frac{1}{2}}&\quad\text{if }T\leq T_{ambient} \text{ and }10^{5}\leq Ra_{L}\leq 10^{10}\end{array} \right. \tag{2}\]  
In the above equation, \(\kappa\) is the thermal conductivity of the heat transfer medium (air), \(L\) is the characteristic length (defined as the area/perimeter of the contact surface), and \(Ra_{L}\) is the Rayleigh number. The heat transfer coefficient of the TEC bottom surface (\(h_{bot}\)) can be calculated the same as the TEC top surface (\(h_{top}\)). The heat transfer coefficient (\(h_{side}\)) of the side of the TEC can be calculated according to Equation (3):  
\[h_{side}=\left\{ \begin{array}{ll}\frac{\kappa}{H}\left(0.68+\frac{0.67 Ra_{L }^{1/4}}{\left(1+\left(\frac{0.492}{\kappa_{P}}\right)^{4/9}\right)}\right)& \quad\text{if }Ra_{L}\leq 10^{9}\\ \frac{\kappa}{H}\left(0.825+\frac{0.387 Ra_{L}^{1/6}}{\left(1+\left(\frac{0.49 2}{\kappa_{P}}\right)^{8/2}\right)}\right)&\quad\text{if }Ra_{L}>10^{9}\end{array} \right. \tag{3}\]  
where \(\mu\) and \(C_{p}\) are the dynamic viscosity and heat capacity of air at qualitative temperature \(T_{q}\), respectively. \(T_{q}\) is defined as \((T_{side}+T_{ambient})/2\). The above sets of equations allowed us to accurately describe the convective heat transfer coefficients at different locations of the TEC in the simulation model, making the simulation results closer to the actual situation. To simplify the model and reduce the amount of calculation, the following reasonable assumptions are proposed:  
1. Only heat convection and heat exchange are considered, and the influence of heat radiation is not considered. 2. The surface of the cooling fin is regarded as an ideal plane, regardless of the influence of surface roughness on the air viscous heat transfer coefficient. 3. The contact interface between the cooling fin and the TEC is simplified, and a thermally conductive silicone grease layer is used as a substitute.