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Comment on the Paper “Onset of Marangoni-Bénard Ferroconvection with Temperature Dependent Viscosity, C. E. Nanjundappa, I. S. Shivakumara, R. Arunkumar, Microgravity Sci. Technol. (2013) 25:103–112”
Comment on the Paper “Onset of Marangoni-Be´ nard Ferroconvection with Temperature Dependent Viscosity, C. E. Nanjundappa, I. S. Shivakumara, R. Arunkumar, Microgravity Sci. Technol. (2013) 25:103-112”
Asterios Pantokratoras 0
0 School of Engineering, Democritus University of Thrace , 67100, Xanthi , Greece
The present comment concerns some doubtful results included in the above paper. The effect of temperature dependent viscosity on the onset of Marangoni-Be´nard ferroconvection under microgravity conditions in a horizontal ferrofluid layer in the presence of a uniform vertical magnetic field has been studied in the above paper. The viscosity is considered to be varying exponentially with temperature. The lower rigid and the upper horizontal free boundaries were considered to be perfectly insulated to temperature perturbations. The non-dimensional velocity boundary condition at the lower plate is as follows (Eq. 27 in Nanjundappa et al. 2013)
W = DW = 0
z = 0
where W is the non-dimensional vertical velocity, D is
the differential operator D = d /d z and z is the
nondimensional vertical distance (z = 0 at the lower plate and
z = 1 at the upper plate).
According to above boundary condition (1) velocity
profiles should approach the lower rigid plate with zero
gradient. However, the above boundary conditions is not satisfied
in Fig. 6 presented by Nanjundappa et al. (2013). In Fig. 1 of
the present work we show a real dimensionless velocity
profile from Nanjundappa et al. (2013) taken from their Fig. 6
and a second velocity profile proposed by the present author
(sketch). The quantity Rm is the magnetic Rayleigh
number and the quantity B is the viscosity parameter. It is seen
that the velocity profile presented by Nanjundappa et al.
(2013) meets the lower plate with a steep angle with
nonzero gradient (DW = d W /d z = 0) violating the boundary
conditions DW = d W /d z = 0. The proposed velocity
profile is in agreement with the boundary condition (1) of the
All profiles in Fig. 6 of Nanjundappa et al. (2013) do not
comply with the boundary condition (1) and are wrong.
Fig. 1 The existing dimensionless velocity profile is given by
Nanjundappa et al. (2013, Fig. 6) for B = 5. The proposed velocity profile
is in agreement with the boundary condition (1) of the present work
Microgravity Sci. Technol.
Nanjundappa , C.E. , Shivakumara , I.S. , Arunkumar , R.: Onset of marangoni-be´nard ferroconvection with temperature dependent viscosity . Microgravity Sci. Technol . 25 , 103 - 112 ( 2013 )