*4.1. Parameter Definition*

The Nusselt number (*Nu*), Reynolds number (Re), Prandtl number (Pr), Colburn factor (*j*), and friction factor (*f*) are employed to describe the thermal and flow characteristics of the oil channel and are defined as

$$Nu = \frac{h\_c D}{\lambda\_o} \tag{6}$$

$$\mathrm{Re} = \frac{\rho\_o \mu D}{\mu} \tag{7}$$

$$\text{Pr} = \frac{\mathbb{C}\_p \mu}{\lambda\_o} \tag{8}$$

$$j = \frac{Nu}{\mathrm{RePr}^{\frac{1}{3}}}\tag{9}$$

$$f = \frac{2\Delta PD}{\rho\_o u^2 L} \tag{10}$$

where Δ*P* is the pressure drop between the inlet and outlet of the test model.

In order to evaluate the overall performance considering both maximum temperature and fluid characteristics, the dimensionless number *R*, is improved in the study based on Zhou's [14] research. The *R* is defined as

$$R = \frac{T\_0}{T\_1} \times \frac{\frac{\dot{f}}{f\_0}}{\frac{\dot{f}}{f\_0}} \tag{11}$$

where *T*<sup>0</sup> represents the maximum temperature of the coil without vortex generators, while *T*<sup>1</sup> represents the maximum temperature of the coil with different dislocations of vortex generators. Based on the dimensionless number *R*, the larger *R* is, the better the comprehensive performance will be.
