*4.1. Momentum Equations*

The Equation (2) regulate the boundary layer into non-dimensional ordinary differential equations which can be written in the following way,

$$\begin{aligned} f''' - (1 - q)^{-2.5} \left( 1 - q \left( \frac{\rho\_s}{\rho\_f} \right) \right) (f' - ff'') + \epsilon^2 &= 0 \text{ (for } Al\_2O\_3 - H\_2O) \\\\ f''' - \left( \frac{1 - q \left( \frac{\rho\_s}{\rho\_f} \right)}{306\rho^2 - 0.19\rho + 1} \right) (f' - ff'') + \epsilon^2 &= 0 \text{ (for } \gamma - Al\_2O\_3 - water) \\\\ f''' - \left( \frac{1 - q \left( \frac{\rho\_s}{\rho\_f} \right)}{123\rho^2 + 7.3\rho + 1} \right) (f' - ff'') + \epsilon^2 &= 0 \text{ (for } \gamma - Al\_2O\_3 - C\_2H\_6O\_2) .\end{aligned} \tag{13}$$

$$f^{\prime\prime\prime} - \left(\frac{1 - \varrho\left(\frac{\rho\_b}{\rho\_f}\right)}{123\varrho^2 + 7.3\varrho + 1}\right) \left(f^{\prime} - ff^{\prime\prime}\right) + \varepsilon^2 = 0 \text{ (for } \gamma - Al\_2O\_3 - \mathbb{C}\_2H\_6O\_2\text{)}. \text{ ) }$$
