## 2 3D Thermal Model  
The thermal distribution of the SRM provides knowledge to the designer. The SRM considered in this paper has an outer water-cooled peripheral casing structure. Water-cooled, the SRM for mining applications utilizes a closed structure. When the motor is working most of the heat delivered within the stator and rotor is passed to the housing through heat conduction, then the water flowing in the waterways dissipates the heat of the housing. The following presumptions are carried out to explain the model:  
1. The insulating material completely covers windings;
2. The stator and the rotor iron losses remain constant with uniform heat generation;
3. Thermal conductivities of motor materials are isotropic.  
Established on these presumptions, the structure of the 72/48 SRM considered in this paper is shown in Figure 1. The properties of isotropic material for each motor part are given in Table 1. The list of the geometrical dimensions is described in Table 2.  
Thermal studies of electric motors hold great significance as all of the materials employed are sensitive to heat. There are three methods by which heat can transfer: conduction, convection and radiation. Heat transfer by conduction is heat transferring through direct contact of materials, whereas heat transfer by convection is heat transferred by a fluid or gas. Heat transfer by radiation is when heat energy travels in actual waves. For isotropic media, the steady-state heat transfer governing equations and its boundary conditions can be presented as [15]:  
\begin{table}
\begin{tabular}{l l l l l l l} \hline \hline \multirow{2}{*}{**Components**} & \multirow{2}{*}{**Materials**} & \multirow{2}{*}{**Density**} & **Specific** & **Thermal** & **Young’s** & **Poisson’s** \\  & & **[kg/m\({}^{3}\)]** & **Heat** & **Conductivity** & **Modulus** & **Ratio** \\  & & **[J/kg/\({}^{\circ}\)C]** & **[W/m-\({}^{\circ}\)C]** & **[GPa]** & **Ratio** \\ \hline Cover and Chassis & Aluminium alloy & 2790 & 833 & 168 & 69 & 0.33 \\ Stator/Rotor core & M19-29 gauge steel & 7800 & 460 & 28 & 200 & 0.29 \\ Winding & Copper ( Pure) & 8933 & 385 & 401 & 116 & 0.35 \\ Insulating layer & Composite material & 1400 & 1000 & 0.21 & 3.5 & 0.3 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Material properties of motor parts used in the simulations.  
Figure 1: The structure view of the 72/48 switched reluctance motor (SRM).  
\begin{table}
\begin{tabular}{l l l l} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline Number of stator poles & 72 & Stack length [mm] & 340 \\ Number of rotor poles & 48 & Air gap length [mm] & 1 \\ Stator out diameter [mm] & 1000 & Rotor out diameter [mm] & 798 \\ Stator pole arc angle [deg] & 2.85 & Rotor pole arc angle [deg] & 3.15 \\ Stator pole width [mm] & 19.89 & Rotor pole width [mm] & 21.93 \\ Stator yoke thickness [mm] & 18 & Rotor yoke thickness [mm] & 20 \\ Stator slot depth [mm] & 82 & Rotor slot depth [mm] & 39 \\ Number of turns per pole [Turns] & 15 & Shaft diameter [mm] & 680 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The geometrical dimensions of the 72/48 SRM.  
\[k_{xx}\frac{\partial^{2}T}{\partial x^{2}}+k_{yy}\frac{\partial^{2}T}{\partial y^{2 }}+k_{zz}\frac{\partial^{2}T}{\partial z^{2}}+h_{cv}(T-T_{amb})=Q, \tag{1}\]  
where \(k\) is thermal conductivity [W/m\({}^{\cdot}\)\({}^{\circ}\)C], \(T_{amb}\) and \(T\) are ambient and unknown temperature [\({}^{\circ}\)C], \(Q\) is the heat source [W/m\({}^{3}\)], and \(h_{cv}\) is heat transfer coefficient [W/m\({}^{2}\). \({}^{\circ}\)C].  
To estimate the temperature distribution, the heat transfer coefficient and the total losses in the SRM are required inputs. The heat sources leading to the temperature rise of the motor come from all losses of the motor. These losses consist of the copper, core, and mechanical loss. Heat transfer convection helps the motor to be cool.