\(\eta=y\sqrt{\frac{U}{\text{υx}}}=\frac{y}{x}\sqrt{Re_{x}}\ ;\ \ \frac{u}{U}=f^{{}^{\prime}}\ ;\ \ v=\frac{1}{2}\sqrt{\frac{\text{Uυ}}{x}}\ \left(\eta f^{{}^{\prime}}-f\right)\ ;\) (8a)
\(\theta\left(\eta\right)=\frac{T-T_{\infty}}{T_{w}-T_{\infty}}\ ;\ \ \ \phi\left(\eta\right)=\frac{C-C_{\infty}}{C_{w}-C_{\infty}},\) (8b)