Comment on the paper “A couple stress of peristaltic motion of Sutterby micropolar nanofluid inside a symmetric channel with a strong magnetic field and Hall currents effect, Nabil T. M. El-Dabe, Galal M. Moatimid, Mona A. A. Mohamed, Yasmeen M. Mohamed, Archive of Applied Mechanics (2021) 91:3987–4010”

Abstract

Some errors exist in the above paper.

Typographical errors

1st error

The term $\frac{{\mu \sigma B_{0}^{2} }}{{1 + m_{1}^{2} }}\left( {(u + c) - m_{1} \upsilon } \right)$ in Eq. (22) in [1] is wrong. The correct is $\frac{{\sigma B_{0}^{2} }}{{1 + m_{1}^{2} }}\left( {(u + c) - m_{1} \upsilon } \right)$.

2nd error

The term $\frac{{\mu \sigma B_{0}^{2} }}{{1 + m_{1}^{2} }}\left( {m_{1} (u + c) + \upsilon } \right)$ in Eq. (23) in [1] is wrong.

The correct is $\frac{{\sigma B_{0}^{2} }}{{1 + m_{1}^{2} }}\left( {m_{1} (u + c) + \upsilon } \right)$.

3rd error

The dimensionless parameter $\beta_{1} = \frac{{Q_{0} d^{2} }}{{K_{c} c_{f} }}$ in Eq. (32) in [1] is wrong. The correct is $\beta_{1} = \frac{{Q_{0} d^{2} }}{{\mu c_{f} }}$.

4th error

In the caption of Figs. 14, 15, 16 and 17 in [1] it is written “versus y”. The correct is “versus $\Theta$”.

5th error

In the caption of Figs. 18 and 19 it is written “versus y”. The correct is “versus x”.

6th error

In Nomenclature the parameter $\Gamma$ represents material constants but this parameter is absent from the problem formulation.

7th error

In Nomenclature the parameter $\alpha_{1}$ is defined as non-dimensional slip parameter. However this parameter is dimensional.

8th error

In Nomenclature the mean absorption coefficient is defined as $\beta_{1}$ and $K_{R}$.

Serious errors

1st error

In a Physics equation all terms must have the same units and from Eqs. (22) and (23) in [1] it is found that the units of K₁ are kgm⁻¹ s⁻¹. From Eq. (24) in [1] it is found that the units of j are m³ s⁻¹. The dimensionless parameter $J_{1} = \frac{j}{{d^{2} }}$ in Eq. (32) in [1] is wrong because it is dimensional with units m s⁻¹.

2nd error

In Eq. (25) in [1] appears the term

$$\left[ {N.N - N\left( {\frac{\partial \upsilon }{{\partial x}} - \frac{\partial u}{{\partial y}}} \right) + \gamma_{m} \left[ {\left( {\frac{\partial N}{{\partial x}}} \right)^{2} + \left( {\frac{\partial N}{{\partial y}}} \right)^{2} } \right]} \right]$$

(1)

From the dimensionless parameter $\vec{\gamma }_{m} = \frac{{\gamma_{m} }}{{\mu d^{2} }}$ it is found that the units of $\gamma_{M}$ are kgm s⁻¹. The units of $N.N$ and $N\left( {\frac{\partial \upsilon }{{\partial x}} - \frac{\partial u}{{\partial y}}} \right)$ are s⁻² whereas the units of $\gamma_{m} \left[ {\left( {\frac{\partial N}{{\partial x}}} \right)^{2} + \left( {\frac{\partial N}{{\partial y}}} \right)^{2} } \right]$ are kgm⁻¹ s⁻³. In Physics it is not allowed to add quantities with different units and the above term (1) is wrong.

3rd error

The Eq. (67) in [1] is as follows

$$Q = q + 2cd\eta (x)$$

(2)

where Q is non-dimensional and the units of $cd\eta (x)$ are m² s⁻¹. In a Physics equation all terms must have the same units and for that reason the Eq. (2) is wrong.

4th error

In the momentum Eqs. (22) and (23) in [1] appears the Hall parameter m₁. The Hall MHD is a well known field in plasma Physics which is concentrated in the subatomic world and studies the interaction between electrons and ions with a strong magnetic field. Generally speaking, the theory is applicable to phenomena occurring on length scales shorter than an ion inertial length, and time scales shorter than an ion cyclotron period. The momentum equation in Hall MHD does not include any influence of Hall term. In [2] it is written “Aside from the magnetic field induction, the Hall term only enters the energy equation. Thus, the Hall term is a transport mechanism for the magnetic field but not for mass or momentum”. In [3] the Hall parameter H is included in the magnetic transport Eq. (2.5b) and is absent from the momentum Eq. (2.5a).

Thus the Hall parameter m₁ in Eqs. (22), (23) and (36) in [1] must be zero.