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  1. 3 Open Physics

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  1. 2 2011

  2. 1 2010

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  1. 3 Gorder R.

  2. 3 Vajravelu K.

  3. 1 Sweet E.

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Nonlinear dispersion of a pollutant ejected into a channel flow

100%
Gorder R., Vajravelu K.
Open Physics
|
2011
|
vol. 9
|
issue 5
1182-1194
EN
In this paper, we study the nonlinear coupled boundary value problem arising from the nonlinear dispersion of a pollutant ejected by an external source into a channel flow. We obtain exact solutions for the steady flow for some special cases and an implicit exact solution for the unsteady flow. Additionally, we obtain analytical solutions for the transient flow. From the obtained solutions, we are able to deduce the qualitative influence of the model parameters on the solutions. Furthermore, we are able to give both exact and analytical expressions for the skin friction and wall mass transfer rate as functions of the model parameters. The model considered can be useful for understanding the polluting situations of an improper discharge incident and evaluating the effects of decontaminating measures for the water bodies.
2
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Comment on “Series solution of hydromagnetic flow and heat transfer with hall effect in a second grade fluid over a stretching sheet”

100%
Gorder R., Vajravelu K.
Open Physics
|
2010
|
vol. 8
|
issue 3
514-515
EN
In a recently accepted paper of M. Ayub, H. Zaman and M. Ahmad [Cent. Eur. J. Phys. 8, 135 (2010)] the authors claim that the governing similarity equations of Vajravelu and Roper [Int. J. Nonlin. Mech. 34, 1031 (1999)] are incorrect; without any justification, the authors Ayub et al. simply mention that the equation is “found to be incorrect in the literature” (though no reference supporting this assertion is provided in the citations). We show that this assertion of Ayub et al. is wrong, and that the similarity equation of Vajravelu and Roper is indeed correct.
3
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Analytical solutions for the unsteady MHD rotating flow over a rotating sphere near the equator

81%
Sweet E., Vajravelu K., Gorder R.
Open Physics
|
2011
|
vol. 9
|
issue 1
167-175
EN
In this paper we investigate the three-dimensional magnetohydrodynamic (MHD) rotating flow of a viscous fluid over a rotating sphere near the equator. The Navier-Stokes equations in spherical polar coordinates are reduced to a coupled system of nonlinear partial differential equations. Self-similar solutions are obtained for the steady state system, resulting from a coupled system of nonlinear ordinary differential equations. Analytical solutions are obtained and are used to study the effects of the magnetic field and the suction/injection parameter on the flow characteristics. The analytical solutions agree well with the numerical solutions of Chamkha et al. [31]. Moreover, the obtained analytical solutions for the steady state are used to obtain the unsteady state results. Furthermore, for various values of the temporal variable, we obtain analytical solutions for the flow field and present through figures.
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