\begin{align}
    \frac{\partial B_y}{\partial t} = - \left[ \frac{\partial }{\partial x} (v_x B_y) 
- \frac{\partial }{\partial x} \left( \eta \frac{\partial B_y}{\partial x} + \alpha_2 \frac{\partial B_y}{\partial x} 
- \eta \frac{\partial B_x}{\partial y} - \alpha_2 \frac{\partial B_x}{\partial y} \right) \\
- \frac{\partial }{\partial z} \left( \eta \frac{\partial B_y}{\partial z} + \alpha_2 \frac{\partial B_y}{\partial z} 
- \eta \frac{\partial B_z}{\partial y} - \alpha_2 \frac{\partial B_z}{\partial y} \right) 
+ B_y \frac{\partial v_z}{\partial z} \right]