**4. Entropy Generation**

The equation of entropy generation in dimensional form is given in reference [34].

$$E\_{g\text{eff}}{}^{\prime\prime} = \frac{k\_{nf}}{T\_f^2} \left[ \left(\frac{\text{d}T}{\text{d}r}\right)^2 + \frac{\text{kg}\,\sigma^\*\text{T}^3}{3k\_{nf}\text{H}^+} \left(\frac{\text{d}T}{\text{d}g}\right)^2 \right] + \frac{\mu\_{nf}}{T\_f} \left(\frac{\text{d}\mu}{\text{d}r}\right)^2 + \frac{\sigma B\_{\alpha}^2}{T\_f}\mu^2 + \frac{\text{g}\Sigma}{T\_{\alpha}} \left(\frac{\text{d}\Sigma}{\text{d}r}\right)^2 + \frac{\text{g}\Sigma}{T\_f} \left(\frac{\text{g}\Sigma}{\text{d}r}\right) \left(\frac{\text{g}\Sigma}{\text{d}r}\right) \tag{22}$$

Equation (22) after applying the requisite transformations takes the following form:

$$N\_{G} = \frac{\varepsilon\_{gw}\prime\prime}{E\_{0}\prime\prime} = \text{Re}\_{x}\left[\frac{k\_{df}}{k\_{f}} + R\_{d}(1+\Pi\theta)^{3}\right]\theta\prime^{2} + \frac{\text{Re}\text{Re}\_{x}}{\Pi^{2}}\left(f\prime\right)^{2} + \frac{\text{Re}\text{Re}\_{x}}{\Pi^{2}}Mf\prime^{2} + \frac{\text{Re}\_{x}\Sigma}{\Pi}\left(h\prime^{2} + \frac{\theta\prime\prime}{\Pi}\right) \tag{23}$$

where

$$\text{Br} = \frac{\mu\_{nf}\mu\_w}{k\_{nf}T\_f}, \text{Re}\_x = \frac{\text{x}^2\text{s}}{\nu\_f}, \sum = \frac{\text{C}\_\infty RD}{k\_{nf}}, \text{ II} = \theta\_w - 1 \tag{24}$$
