Dear Editor,

These comments demonstrate some wrong and misleading results presented in the paper by Sudarsana Reddy et al. [1]. The momentum and energy equations in [1] are defined as follows, for a non-Newtonian fluid:

$$ \begin{aligned} u\frac{\partial u}{\partial r} - \frac{{v^{2} }}{r} + w\frac{\partial u}{\partial z} + \lambda_{1} \left( {v^{2} \frac{{\partial^{2} u}}{{\partial z^{2} }} + u^{2} \frac{{\partial^{2} u}}{{\partial r^{2} }} + 2uv\frac{{\partial^{2} u}}{\partial r\partial z}} \right) & = \frac{ - 1}{{\rho_{\text{nf}} }}\frac{\partial p}{\partial r} + \frac{{\mu_{\text{nf}} }}{{\rho_{\text{nf}} }}\left( {\frac{{\partial^{2} u}}{{\partial r^{2} }} + \frac{1}{r}\frac{\partial u}{\partial r} - \frac{u}{{r^{2} }} + \frac{{\partial^{2} u}}{{\partial z^{2} }}} \right) \\ & \quad + \frac{{\sigma_{\text{nf}} }}{{\rho_{\text{nf}} }}B_{0}^{2} \left( { - u - \lambda_{1} v\frac{\partial u}{\partial z}} \right), \\ \end{aligned} $$
(1)
$$ \begin{aligned} u\frac{\partial v}{\partial r} + \frac{uv}{r} + w\frac{\partial v}{\partial z} + \lambda_{1} \left( {v^{2} \frac{{\partial^{2} u}}{{\partial z^{2} }} + u^{2} \frac{{\partial^{2} u}}{{\partial r^{2} }} + 2uv\frac{{\partial^{2} u}}{\partial r\partial z}} \right) & = \frac{ - 1}{{\rho_{\text{nf}} }}\frac{\partial p}{\partial z} + \frac{{\mu_{\text{nf}} }}{{\rho_{\text{nf}} }}\left( {\frac{{\partial^{2} v}}{{\partial r^{2} }} + \frac{1}{r}\frac{\partial v}{\partial r} - \frac{v}{{r^{2} }} + \frac{{\partial^{2} v}}{{\partial z^{2} }}} \right) \\ & \quad + \frac{{\sigma_{\text{nf}} }}{{\rho_{\text{nf}} }}B_{0}^{2} \left( { - v - \lambda_{1} u\frac{\partial v}{\partial z}} \right), \\ \end{aligned} $$
(2)
$$ u\frac{\partial w}{\partial r} + w\frac{\partial w}{\partial z} = \frac{ - 1}{{\rho_{\text{nf}} }}\frac{\partial p}{\partial r} + \frac{{\mu_{\text{nf}} }}{{\rho_{\text{nf}} }}\left( {\frac{{\partial^{2} w}}{{\partial r^{2} }} + \frac{1}{r}\frac{\partial w}{\partial r} + \frac{{\partial^{2} w}}{{\partial z^{2} }}} \right), $$
(3)
$$ u\frac{\partial T}{\partial r} + w\frac{\partial T}{\partial z} = \frac{{k_{\text{nf}} }}{{\left( {\rho c_{p} } \right)_{\text{nf}} }}\left( {\frac{{\partial^{2} T}}{{\partial r^{2} }} + \frac{1}{r}\frac{\partial T}{\partial r} + \frac{{\partial^{2} T}}{{\partial z^{2} }}} \right) - \frac{1}{{\left( {\rho c_{p} } \right)_{\text{nf}} }}\frac{{\partial q_{r} }}{\partial z}. $$
(4)

Sudarsana Reddy et al. [1] considered the flow of a Maxwell nanofluid with single- and multi-wall carbon nanotubes as nanoparticles. However, Table 1 in Ref. [1] shows the thermophysical properties for pure water (base fluid), which is Newtonian (viscous). Therefore, the authors have not used the properties of a non-Newtonian Maxwell fluid in their calculations. For example, Pr was considered equal to 6.2, and the graphical results in Ref. [1] were presented for water–carbon nanotubes. Consequently, the results are not correct. Further, the skin friction coefficient in Ref. [1] does not involve the relaxation time \( \lambda_{1} \). As a result, there is no difference between the skin friction coefficient for viscous and Maxwell nanofluids.

Thus, in view of the above discussion, it is concluded that the published work in Ref. [1] is unreliable and incorrect for further research work.