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Comment on the paper " Magnetohydrodynamic Flow and Heat Transfer of Nanofluids in Stretchable Convergent/Divergent Channels, Syed Tauseef Mohyud-Din, Umar Khan, Naveed Ahmed and Saleh M. Hassan, Appl. Sci. 2015, 5, 1639-1664; doi:10.3390/app5041639"

Asterios Pantokratoras

School of Engineering, Democritus University of Thrace,

67100 Xanthi – Greece

e-mail:

Abstract

The present comment concerns some doubtful results included in the above paper.

In the above paper the momentum equation (equation 2 in [1]) is as follows

(1)

where is the nano-fluid density, is the radial velocity, and are the radial and tangential coordinates, is the pressure, is the nano-fluid dynamic viscosity, is the nano-fluid electrical conductivity and is the strength of the magnetic field.

The above equation is not correct. The correct form is (page 151 in [2], [3])

(2)

Two of the non-dimensional parameters used in the above paper are the Hartmann number and the Eckert number defined as (page 1643 in [1] )

(3)

(4)

where is a quantity defined as (equation 5 in [1]), is the angle of channel wall, is the specific heat and is the wall temperature. The units of electrical conductivity are (page 417 in [2])

The units of the magnetic field are Tesla (page 207 in [4])

The units of dynamic viscosity are

The units of specific heat are

Therefore the units of are

and the units of are

This means that the Hartmann number and the Eckert number are dimensional not dimensionless as the authors claim. In conclusion the momentum equation and two non-dimensional parameters are wrong in Mohyud-Din et al. [1].

References

[1]. Mohyud-Din, S.T.; Khan, U.; Ahmed, N.; and Hassan, S. M. Magnetohydrodynamic Flow and Heat Transfer of Nanofluids in Stretchable Convergent/Divergent Channels. Appl. Sci. 2015, 5, 1639-1664; doi:10.3390/app5041639.

[2]. Davidson, P. A. An introduction to Magnetohydrodynamics. Cambridge University Press, Cambridge, 2001.

[3]. Pantokratoras, A. A note on MHD Blasius flow. Acta Mechanica, 2015, 226, 1305-1308.

[4]. Ozoe, H. Magnetic Convection. Imperial College Press, London 2005.