## 2 Basic Theory  
### Numerical Calculation Theory of Fluid Heat Transfer  
The influence of the underwater vehicle hull on the flow field, the strong disturbance of the flow field by the underwater vehicle propeller, the buoyancy effect of the cooling water jet into the seawater, and the configuration of the free surface of the sea are processes that need to be taken into account in the analysis of the formation mechanism of the underwater vehicle's wake. For the numerical solution of the multiphase flow and heat transfer in this paper, the right turbulence equations and radiative transfer equations must be established in addition to meeting the mass, momentum, and energy conservation equations.  
The mass conservation formula  
Mass conservation between the calculation domain's intake and outflow must be met while the flow condition is steady. The mass in and out of each unit control body when considering flow calculations fulfills the mass conservation equation, as indicated in Equation (1).  
\[\frac{\partial\rho}{\partial t}+\
abla\cdot(\overset{\rightarrow}{\rho V})=S _{m} \tag{1}\]  
where \(t\) is time, \(\rho\) is the density of the fluid, \(\overset{\rightarrow}{V}\) is the velocity vector, and \(S_{m}\) is the mass source term and represents the mass in the control body generated by the custom process.  
Equation for momentum conservation [16]All flow processes are also subject to the conservation of momentum, which is expressed in the equation for conservation of momentum, which is provided in Equation (2) as the conservation of kinetic energy in the form of  
\[\frac{\partial\bigg{(}\rho\
abla\overrightarrow{V}\bigg{)}}{ \partial t}+\
abla\cdot(\rho\overrightarrow{VV})=-\
abla P+\
abla\cdot \overline{\overline{\tau}}+\rho\overline{g}+\overrightarrow{F} \tag{2}\] \[\overline{\overline{\tau}}=\mu\bigg{[}\bigg{(}\
abla \overrightarrow{V}+\
abla\overrightarrow{V}\bigg{)}-\frac{2}{3}\
abla \cdot\overrightarrow{VI}\bigg{]} \tag{3}\]  
where \(\overline{\overline{\tau}}\) represents the stress tensor, \(p\) represents the hydrostatic pressure of the fluid, as shown in Equation (3), \(I\) represents the unit tensor, \(\mu\) represents the dynamic viscosity coefficient of the fluid molecules, \(\overline{g}\) is the acceleration of gravity, taken as \(-9.81\) m/s\({}^{2}\), \(\rho\overline{g}\) represents the volume force due to gravity, and \(\overrightarrow{F}\) represents other external volume forces, also including source terms that are subordinate to other models.  
(3) Equation for energy conservation [16]  
When a heat transfer process occurs simultaneously with a flow process, the process must also adhere to the law of conservation of energy and the law of conservation of energy's equation in the form of Equation (4).  
\[\frac{\partial(\rho E)}{\partial t}+\
abla\cdot\bigg{[}\overrightarrow{V}( \rho E+p)\bigg{]}=\
abla\cdot\bigg{[}k_{off}\
abla T-\sum_{j}h_{j} \overrightarrow{J}_{j}+\bigg{(}\overline{\overline{\tau_{eff}}}\cdot \overrightarrow{V}\bigg{)}\bigg{]}+S_{h} \tag{4}\]  
In Equation (4), E is the total energy, which is the sum of internal and kinetic energy, \(k_{off}\) is the effective thermal conductivity (\(k_{off}=k+k_{i}\), where \(k_{i}\) is the thermal conductivity of the turbulent process, as determined by the turbulence model), \(T\) is the temperature, and \(h_{j}\) and \(\overrightarrow{J}_{j}\) are the enthalpy and diffusion fluxes of the components \(j\), respectively. The first three terms on the right-hand side of Equation (4) represent the energy transfer due to thermal conductivity, component diffusion, and viscous dissipation, respectively, and \(S_{h}\) represents the energy source term, which can be either a heat generation or heat absorption process in various chemical processes, an energy conversion in a multiphase flow, or another defined type of heat source.