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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
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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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Convection heat transfer in a Maxwell fluid at a non-isothermal surface

81%
Vajravelu K., Prasad K., Sujatha A.
Open Physics
|
2011
|
vol. 9
|
issue 3
807-815
EN
Analysis is carried out to study the convection heat transfer in an upper convected Maxwell fluid at a non-isothermal stretching surface. This is a generalization of the paper by Sadeghy et al. [21] to study the effects of free convection currents, variable thermal conductivity and the variable temperature at the stretching surface. Unlike in Sadeghy et al., here the governing nonlinear partial differential equations are coupled. These coupled equations are transformed in to a system of nonlinear ordinary differential equations and are solved numerically by a finite difference scheme (known as the Keller-Box method) and the numerical results are presented through graphs and tables for a wide range of governing parameters. The results obtained for the flow and heat transfer characteristics reveal many interesting behaviors that warrant further study of nonlinear convection heat transfer.
4
Content available remote

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.
5
Content available remote

Mathematical model for a Herschel-Bulkley fluid flow in an elastic tube

81%
Vajravelu K., Sreenadh S., Devaki P., Prasad K.
Open Physics
|
2011
|
vol. 9
|
issue 5
1357-1365
EN
The constitution of blood demands a yield stress fluid model, and among the available yield stress fluid models for blood flow, the Herschel-Bulkley model is preferred (because Bingham, Power-law and Newtonian models are its special cases). The Herschel-Bulkley fluid model has two parameters, namely the yield stress and the power law index. The expressions for velocity, plug flow velocity, wall shear stress, and the flux flow rate are derived. The flux is determined as a function of inlet, outlet and external pressures, yield stress, and the elastic property of the tube. Further when the power-law index n = 1 and the yield stress τ 0 → 0, our results agree well with those of Rubinow and Keller [J. Theor. Biol. 35, 299 (1972)]. Furthermore, it is observed that, the yield stress and the elastic parameters (t 1 and t 2) have strong effects on the flux of the non-Newtonian fluid flow in the elastic tube. The results obtained for the flow characteristics reveal many interesting behaviors that warrant further study on the non-Newtonian fluid flow phenomena, especially the shear-thinning phenomena. Shear thinning reduces the wall shear stress.
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