# Numerical Analysis of the Cooling Performance in a 7.2 kW Integrated Bidirectional OBC/LDC Module
## 2 Development of the Numerical Model
### Numerical Model  
A numerical model was constructed to verify the heat flow characteristics of the 7.2 kW integrated bidirectional OBC/LDC module. Note that this model contained a simplified representation of the module that included only the major heating elements. This approach was adopted as the remaining elements had only a small impact on the heat flow characteristics. In addition, the bolts or nuts used to mount the outer structure in the EV were ignored. The configuration and shape of the integrated module from several perspectives are illustrated in Figure 5. This was used when mounting the module in a vehicle, which was the objective of the analysis in this study. The module body is composed of a top cover, main body, and bottom cover. Figure 4: Operating modes in the 7.2 kW integrated bidirectional OBC/LDC module. There is an OBC circuit inside the top cover, which is sealed to protect the internal devices. Inside the main body, there is internal support for the OBC/LDC circuits and a cooling channel for recovering heat from the device. These components are also sealed to protect the internal devices. The parts inside the module that generate the most heat are six inductors, one transformer, 16 MOSFETs, and 11 N-MOSFETs. The heating value of each device was estimated in the previously described circuit simulation and varies depending on the mode. Cooling water is injected into the inlet and flows along the parallel channels to recover heat from the heating elements. In the numerical model, the heat is assumed to be transferred from the components to the cooling water via natural convection through the air layer inside the charger. When evaluated, this approach provided a result close to that of the actual model. To verify the flow characteristics of the integrated module, a flow and heat transfer analysis was performed. To accomplish this, a three-dimensional model of the simplified charger was constructed and an unsteady-state analysis was performed to observe the initial temperature changes inside the charger. The physical properties of the body of the charger and the internal fluid were assumed to be constant, and it was also assumed that heat was generated uniformly in each heating element area. Based on these assumptions, the governing equations for the flow and heat transfer analysis were as follows:  
* Mass conservation equation \[\frac{\partial\rho}{\partial t}+\
abla\cdot\left(\rho\overrightarrow{u} \right)=0.\] (7)
* Momentum conservation equation \[\frac{\partial\!\left(\rho\overrightarrow{u}\right)}{\partial t}+\
abla\cdot \left(\rho\overrightarrow{u}\overrightarrow{u}\right)=-\
abla p+\
abla\cdot \left(\mu\
abla\overrightarrow{u}\right).\] (8)  
Figure 5: Geometry of the 7.2 kW integrated bidirectional OBC/LDC module. * Transport equation for \(\kappa\) (standard k-\(\varepsilon\) model) \[\frac{\partial(\rho k)}{\partial t}+\
abla\cdot\left(\rho k\overset{\rightarrow} {u}\right)=\
abla\cdot\left[\left(\mu+\frac{\mu_{t}}{\sigma_{k}}\right)\
abla k \right]+G_{k}+G_{b}-\rho\varepsilon.\] (9)
* Transport equation for \(\varepsilon\) (standard k-\(\varepsilon\) model). \[\frac{\partial(\rho\varepsilon)}{\partial t}+\
abla\cdot\left(\rho\varepsilon \overset{\rightarrow}{u}\right)=\
abla\cdot\left[\left(\mu+\frac{\mu_{t}}{ \sigma_{\varepsilon}}\right)\
abla\varepsilon\right]+C_{1\varepsilon}\frac{ \varepsilon}{k}(G_{k}+G_{3\varepsilon}G_{b})+C_{2\varepsilon}\rho\frac{ \varepsilon^{2}}{k}.\] (10)
* Energy conservation equation \[\frac{\partial\left(\rho C_{p}T\right)}{\partial t}+\
abla\cdot\left(\rho C_{ p}T\right)=\
abla\cdot\left(k_{eff}\
abla T\right)+S_{\varepsilon}.\] (11)  
First, the fluid flow was analyzed by solving the continuity and momentum equations. Then, the equation describing the k-\(\varepsilon\) standard model was solved to account for the turbulence caused by the high Reynolds number of the fluid (Re = 7453). Next, the energy conservation equation was solved to determine the heat transfer to the internal heating elements and the surroundings.