Typographical errors
1st error
Anzeige
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 \(\frac{{\sigma B_{0}^{2} }}{{1 + m_{1}^{2} }}\left( {m_{1} (u + c) + \upsilon } \right)\).
Anzeige
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 followswhere 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.
$$Q = q + 2cd\eta (x)$$
(2)
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.
Declarations
Conflict of interest
The author states that there is no conflict of interest.
Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.