Comment on Rooman et al. Entropy Optimization on Axisymmetric Darcy–Forchheimer Powell–Eyring Nanofluid over a Horizontally Stretching Cylinder with Viscous Dissipation Effect. Coatings 2022, 12, 749

Asterios Pantokratoras

doi:10.3390/coatings15020211

Introduction

The concentration shown in Equation (4) in [1] is given as follows:

w \frac{\partial C}{\partial r} + u \frac{\partial C}{\partial z} = D_{B} (\frac{\partial^{2} C}{\partial r^{2}} + \frac{1}{r} \frac{\partial C}{\partial r}) + \frac{D_{T}}{T_{\infty}} (\frac{\partial^{2} T}{\partial r^{2}} + \frac{1}{r} \frac{\partial T}{\partial r})

(1)

In a physics equation, all terms must have the same units. The above equation in units is given as follows:

\begin{array}{l} w (m s^{- 1}) \frac{\partial C (\dim ensionless)}{\partial r (m)} + u (m s^{- 1}) \frac{\partial C (\dim ensionless)}{\partial z (m)} = \\ D_{B} (m^{2} s^{- 1}) (\frac{\partial^{2} C (\dim ensionless)}{\partial r^{2} {(m)}^{2}} + \frac{1}{r (m)} \frac{\partial C (\dim ensionless)}{\partial r (m)}) \\ + \frac{D_{T} (m^{2} s^{- 1})}{T_{\infty} (K)} (\frac{\partial^{2} T (K)}{\partial r^{2} {(m)}^{2}} + \frac{1}{r (m)} \frac{\partial T (K)}{\partial r (m)}) \end{array}

(2)

s^{- 1} + s^{- 1} = s^{- 1} + s^{- 1}

Equation (2) and, consequently, Equation (1) are correct only when the concentration C is dimensionless.

The entropy generation Equation (16) in [1] is as follows:

\begin{array}{l} S_{g} = \frac{k_{n f}}{T_{\infty}^{2}} (1 + \frac{16 σ^{*} T^{3}}{3 k^{*} k_{n f}}) {(\frac{\partial T}{\partial r})}^{2} + \frac{1}{T_{\infty}} (μ_{n f} {(\frac{\partial u}{\partial r})}^{2} + \frac{1}{β c} {(\frac{\partial u}{\partial r})}^{2} - \frac{1}{6 β c^{3}} {(\frac{\partial u}{\partial r})}^{4}) \\ + \frac{R D}{T_{\infty}} (\frac{\partial T}{\partial r} \frac{\partial C}{\partial r}) + \frac{R D}{C_{\infty}} {(\frac{\partial C}{\partial r})}^{2} \end{array}

(3)

In Equation (3),

R (m)

is the cylinder radius (Equation (6) in [1]) and

D (m^{2} s^{- 1})

is a diffusion coefficient.

The units of the term

\frac{k_{n f}}{T_{\infty}^{2}} {(\frac{\partial T}{\partial r})}^{2}

are given as follows:

\frac{k_{n f} (k g m s^{- 3} K^{- 1})}{T_{\infty}^{2} {(K)}^{2}} {(\frac{\partial T (K)}{\partial r (m)})}^{2} = k g m^{- 1} s^{- 3} K^{- 1}

(4)

The units of the term

\frac{1}{T_{\infty}} (μ_{n f} {(\frac{\partial u}{\partial r})}^{2})

are as follows:

\frac{1}{T_{\infty} (K)} (μ_{n f} (k g m^{- 1} s^{- 1}) {(\frac{\partial u (m s^{- 1})}{\partial r (m)})}^{2}) = k g m^{- 1} s^{- 3} K^{- 1}

(5)

The units of the term

\frac{R D}{T_{\infty}} (\frac{\partial T}{\partial r} \frac{\partial C}{\partial r})

are as follows:

\frac{R (m) D (m^{2} s^{- 1})}{T_{\infty} (K)} (\frac{\partial T (K)}{\partial r (m)} \frac{\partial C (\dim ensionless)}{\partial r (m)}) = m s^{- 1}

(6)

The units of the term

\frac{R D}{C_{\infty}} {(\frac{\partial C}{\partial r})}^{2}

are as follows:

\frac{R (m) D (m^{2} s^{- 1})}{C_{\infty} (\dim ensionless)} {(\frac{\partial C (\dim ensionless)}{\partial r (m)})}^{2} = m s^{- 1}

(7)

It is clear that the units of the terms in Equation (3) are different, and for that reason, entropy in Equation (3) is wrong, and all results concerning entropy in [1] are incorrect.

Conflicts of Interest

The author declares no conflict of interest.

Reference

Rooman, M.; Jan, M.A.; Shah, Z.; Vrinceanu, N.; Ferrándiz Bou, S.; Iqbal, S.; Deebani, W. Entropy Optimization on Axisymmetric Darcy–Forchheimer Powell–Eyring Nanofluid over a Horizontally Stretching Cylinder with Viscous Dissipation Effect. Coatings 2022, 12, 749. [Google Scholar] [CrossRef] [Scilit]

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

© 2025 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

Article Metrics

Citations

Article Access Statistics

Journal Statistics

Multiple requests from the same IP address are counted as one view.