1st error
Within the abstract of the above paper, in the mathematical modeling, in Table 1 and in the concluding remarks, it is clearly mentioned that the base fluid in [1] is engine oil and ALL results have been produced for Prandtl number Pr = 6.2.
The Prandtl numbers of engine oil are presented in page 630 in [2]. The Pr number in [2] varies between 144500 up to 155. The results in [1] for Pr = 6.2 do not correspond to engine oil but to water (page 626 in [2]) and all the results in [1] are wrong.
2nd error
In the section ‘Outcomes and discussion’in [1], it is written that the value of $\lambda $ is $\lambda =0.2$ and the value of c = 0.01.
At the cylinder surface is
$\begin{eqnarray*}f\mbox{'}(c)=\lambda /2.\end{eqnarray*}$
Far away from the cylinder is $\begin{eqnarray*}f\mbox{'}(\eta )=(1-\lambda )/2\,{\rm{as}}\,\eta \to \infty .\end{eqnarray*}$
This means that at the cylinder surface $f\mbox{'}(0.01)=0.1$ and far away $f\mbox{'}(\infty )=0.40$.However in figures 2, 6 and 8 in [1], it is valid $f\mbox{'}(0.01)=0.15$ and $f\mbox{'}(\infty )=0.35$.
3rd error
In equation (7) in [1] the following equation appears1 ) in units is as follows:
$\begin{eqnarray}{T}_{w}+\lambda \displaystyle \frac{{k}_{hnf}}{{k}_{f}}\displaystyle \frac{\partial T}{\partial R}=T(X,R).\end{eqnarray}$
Equation ( $\begin{eqnarray*}{T}_{w}({\rm{K}})+\lambda ({\rm{m}})\displaystyle \frac{{k}_{{hnf}}}{{k}_{f}}\displaystyle \frac{{\rm{\partial }}T({\rm{K}})}{{\rm{\partial }}R({\rm{m}})}=T(X,R)({\rm{K}}),\end{eqnarray*}$
$\begin{eqnarray*}{\rm{Kelvin}}+{\rm{Kelvin}}={\rm{Kelvin}}.\end{eqnarray*}$
In a Physics equation, all terms must have the same units and this means that equation (1 ) is correct only when the units of $\lambda $ are in meters (length). However in equation (13), in [1] the parameter $\lambda $ is dimensionless.
4th error
From the energy equation (3) in [1], it is found that the units of parameter ${\lambda }_{1}$ are $\sec $ in order that the units of the third term in equation (3) are ${\sec }^{-1}{\rm{Kelvin}}$. From the dimensionless parameter ${\gamma }_{T}={\lambda }_{1}a$ (equation (14) in [1]), it is found that the units of $a$ are ${\sec }^{-1}$. Thus the dimensionless similarity parameter $\eta =\tfrac{{V}_{0}{R}^{2}}{a{\nu }_{f}X}$ is wrong because it is dimensional with units $\sec ({\rm{time}})$.
5th error
The parameters $\sigma $ and ${B}_{0}$ are absent from Nomenclature. However, the official units of electrical conductivity $\sigma $ and magnetic field ${B}_{0}$ are ${{\rm{m}}}^{-1}{{\rm{\Omega }}}^{-1}$ and ${\rm{t}}{\rm{e}}{\rm{s}}{\rm{l}}{\rm{a}}\,={{\rm{kg}}}^{1/2}{{\rm{m}}}^{-1}{\sec }^{-1/2}{{\rm{\Omega }}}^{1/2}$, respectively.
Thus the dimensionless magnetic parameter $M=\tfrac{\sigma {B}_{0}^{2}}{2{V}_{0}{\rho }_{bf}}$ is wrong because it is dimensional with units ${{\rm{m}}}^{-1}{({\rm{length}})}^{-1}$.
6th error
The dimensionless parameter $\alpha =\tfrac{N{m}_{d}}{{\rho }_{bf}}$ is wrong because its units are
$\begin{array}{lll}\alpha & = & \displaystyle \frac{{N}({{\rm{kgm}}}^{-2},{\rm{N}}{\rm{o}}{\rm{m}}{\rm{e}}{\rm{n}}{\rm{c}}{\rm{l}}{\rm{a}}{\rm{t}}{\rm{u}}{\rm{r}}{\rm{e}}){{m}}_{d}({{\rm{kgm}}}^{-3},{\rm{N}}{\rm{o}}{\rm{m}}{\rm{e}}{\rm{n}}{\rm{c}}{\rm{l}}{\rm{a}}{\rm{t}}{\rm{u}}{\rm{r}}{\rm{e}})}{{\rho }_{{bf}}({{\rm{kgm}}}^{-3})}\\ & = & {{\rm{kgm}}}^{-2}.\end{array}$
7th error
The dimensionless parameter ${\beta }_{v}=\tfrac{K}{2{V}_{0}{m}_{d}}$ is wrong because its units are:
$\begin{eqnarray*}\begin{array}{rcl}{\beta }_{v} & = & \displaystyle \frac{K({\rm{\Omega }},{\rm{N}}{\rm{o}}{\rm{m}}{\rm{e}}{\rm{n}}{\rm{c}}{\rm{l}}{\rm{a}}{\rm{t}}{\rm{u}}{\rm{r}}{\rm{e}})}{2{V}_{0}({\rm{m}}\,{\sec }^{-1}){{\rm{m}}}_{d}({{\rm{kgm}}}^{-2},{\rm{N}}{\rm{o}}{\rm{m}}{\rm{e}}{\rm{n}}{\rm{c}}{\rm{l}}{\rm{a}}{\rm{t}}{\rm{u}}{\rm{r}}{\rm{e}})}\\ & = & \displaystyle \frac{({\rm{\Omega }})}{({\rm{m}}\,{\sec }^{-1})({{\rm{kgm}}}^{-2})}=\displaystyle \frac{({\rm{\Omega }})}{({\rm{sec}}^{-1})\left({{\rm{kgm}}}^{-1}\right)}\\ & = & {{\rm{kg}}}^{-1}{\rm{m}}\,\sec \,{\rm{\Omega }}.\end{array}\end{eqnarray*}$
8th error
The dimensionless parameter ${\beta }_{T}=\tfrac{1}{2{V}_{0}{\tau }_{T}}$ is wrong because its units are:
$\begin{eqnarray*}\begin{array}{rcl}{\beta }_{T} & = & \displaystyle \frac{1}{2{V}_{0}\left({\rm{m}}\,{\sec }^{-1}\right){\tau }_{T}\left(\sec ,{\rm{N}}{\rm{o}}{\rm{m}}{\rm{e}}{\rm{n}}{\rm{c}}{\rm{l}}{\rm{a}}{\rm{t}}{\rm{u}}{\rm{r}}{\rm{e}}\right)}\\ & = & {{\rm{m}}}^{-1}.\end{array}\end{eqnarray*}$
9th error
Above the section ‘Similarity analysis’in [1], it is written that ${k}_{f}$ is the fluid thermal conductivity. The official units of thermal conductivity are ${\rm{kgm}}\,{\sec }^{-3}{{\rm{Kelvin}}}^{-1}$ and the symbol ${k}_{hnf}$ denotes hybrid nanofluid thermal conductivity with the same units.
The dimensionless heat flux is calculated in equation (15) in [1] as follows:2 ) is wrong.
$\begin{eqnarray}{N}_{{VX}}=-\displaystyle \frac{1}{{k}_{{hnf}}({T}_{w}-{T}_{\infty })}{\left(\displaystyle \frac{{\rm{\partial }}T}{{\rm{\partial }}R}\right)}_{R=c}.\end{eqnarray}$
The units of ${N}_{VX}$ are ${{\rm{kg}}}^{-1}{{\rm{m}}}^{-2}{\sec }^{3}{\rm{Kelvin}}$ and equation (10th error
The parameter N1 appears in equations (3) and (6) in [1] and then disappears.
11th error
The parameter Q appears in equation (3) and then disappears.
12th error
The Hall parameter in Nomenclature is dimensional. The correct version is dimensionless.
13th error
The surface drag force Cf in Nomenclature is dimensional. The correct version is dimensionless.
14th error
The specific heat ratio in Nomenclature is dimensional. The correct version is dimensionless.
15th error
The units of dust particle relaxation time in Nomenclature is Kelvin. The correct version is second.
16th error
The parameter ${\theta }_{r}$ in Nomenclature is dimensional. The correct version is dimensionless.
Conflict of interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Author contribution statement
Asterios Pantokratoras wrote the paper.