# Comments on the paper “Flow and heat transfer analysis of carbon nanotubes‐based Maxwell nanofluid flow driven by rotating stretchable disks with thermal radiation” by P. Sudarsana Reddy· K. Jyothi, M. Suryanarayana Reddy; Journal of the Brazilian Society of Mechanical Sciences and Engineering (2018) 40:576

Letter to the Editor

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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: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.

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

(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)

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.

## Notes

## Reference

- 1.Sudarsana Reddy P, Jyothi K, Suryanarayana Reddy M (2018) Flow and heat transfer analysis of carbon nanotubes-based Maxwell nanofluid flow driven by rotating stretchable disks with thermal radiation. J Braz Soc Mech Sci Eng 40:576CrossRefGoogle Scholar

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© The Brazilian Society of Mechanical Sciences and Engineering 2019