*2.2. Important Physical Quantities*

The basic physical quantities of interest are the coefficient of friction (*Cf*) and Nusselt number (*Nu*), which are defined by:

$$\mathcal{C}\_f = \frac{2\tau\_{w}}{\rho\_{bf} u\_w^2}, \tau\_w = \mu\_{lnf} \left(\frac{\partial}{\partial r} u\right)\_{r=a} \tag{12}$$

$$Nu = \frac{xQ\_w}{k\_{bf}(T\_w - T\_{\infty})}, \ Q\_w = -k\_{mf} \left(\frac{\partial}{\partial r} T\right)\_{r=a} \tag{13}$$

$$\text{Ssh} = \frac{\text{x}Q\_w}{D\_B(\text{C}\_w - \text{C}\_\text{oc})}, \text{ Q}\_w = -D\_B \left(\frac{\partial}{\partial r} \text{C}\right)\_{r=a} \tag{14}$$

By using the similarity transformations as defined in Equation (7), the dimensionless forms of Equations (13)–(15) are:

$$\mathbb{C}\_{f}\sqrt{\text{Re}} = \frac{\mu\_{\text{lnf}}}{\mu\_{bf}}f''(0), \quad \frac{\text{Nu}}{\sqrt{\text{Re}}} = -2\Big(\frac{k\_{\text{lnf}}}{k\_{bf}}\Big)\theta'(0), \frac{\text{Sh}}{\sqrt{\text{Re}}} = -\phi'(0) \tag{15}$$

In Equation (8), the different constant terms appearing are given by:

$$A\_1 = \frac{\mu\_{\text{lnf}}}{\mu\_{bf}}, A\_2 = \frac{\rho\_{\text{lnf}}}{\rho\_{bf}}, A\_3 = \frac{(\rho\beta)\_{\text{lnf}}}{(\rho\beta)\_{bf}} \tag{16}$$
