*2.2. Model Assumptions*

Although there is a temperature difference in the flow process of a cooling medium, it is within the allowable range of error. Therefore, it is considered that the density of the cooling medium is fixed. The simulation is carried out in an ideal situation to some extent. A homogeneous heat distribution over the active area of the cell is assumed. For the convenience of calculation, the following assumptions are made:


#### *2.3. Governing Equations*

Assuming that the flow of the cooling liquid in the channel is a three-dimensional steady laminar flow, the continuity equation, momentum equation and energy equation in the reaction process can be expressed as follows:

(a) continuity equation

$$\frac{\partial u\_{\mathbf{x}}}{\partial x} + \frac{\partial u\_{\mathbf{y}}}{\partial y} + \frac{\partial u\_{\mathbf{z}}}{\partial z} = 0 \tag{5}$$

(b) momentum equation

$$-\frac{1}{\rho}\frac{\partial p}{\partial \mathbf{x}} + \upsilon \nabla^2 u\_\mathbf{x} = u\_\mathbf{x}\frac{\partial u\_\mathbf{x}}{\partial \mathbf{x}} + u\_\mathbf{y}\frac{\partial u\_\mathbf{x}}{\partial y} + u\_\mathbf{z}\frac{\partial u\_\mathbf{x}}{\partial z} \tag{6}$$

$$-\frac{1}{\rho}\frac{\partial p}{\partial y} + \upsilon \nabla^2 u\_\text{Y} = u\_\text{x}\frac{\partial u\_\text{y}}{\partial x} + u\_\text{y}\frac{\partial u\_\text{y}}{\partial y} + u\_\text{z}\frac{\partial u\_\text{y}}{\partial z} \tag{7}$$

$$-\frac{1}{\rho}\frac{\partial p}{\partial z} + v\,\nabla^2 u\_{\mathbf{z}} = \mu\_{\mathbf{x}}\frac{\partial u\_{\mathbf{z}}}{\partial \mathbf{x}} + \mu\_{\mathbf{y}}\frac{\partial u\_{\mathbf{z}}}{\partial \mathbf{y}} + \mu\_{\mathbf{z}}\frac{\partial u\_{\mathbf{z}}}{\partial z} \tag{8}$$

(c) energy equation

$$u\_{\mathbf{x}}\frac{\partial t}{\partial \mathbf{x}} + v\frac{\partial t}{\partial y} + w\frac{\partial t}{\partial z} = \frac{\lambda}{\rho c\_{\mathbb{P}}} \left(\frac{\partial^2 t}{\partial x^2} + \frac{\partial^2 t}{\partial y^2} + \frac{\partial^2 t}{\partial z^2}\right) \tag{9}$$

where *u*x,*u*y,*u*z is the velocity component of fluid along the x, y and z axes; *v* is the kinematic viscosity; *<sup>λ</sup> <sup>ρ</sup>c*<sup>p</sup> is the thermal diffusion coefficient.
