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Steady MHD Flow of a Dusty Incompressible Non-Newtonian Oldroyd 8-Constant Fluid in a Circular Pipe

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Abstract

The steady magneto-hydrodynamic flow of a dusty incompressible electrically conducting and non- Newtonian Oldroyd 8-constant fluid through a circular pipe is examined considering the Hall effect. A constant pressure gradient is imposed in the axial direction of the pipe while an external uniform magnetic field is applied in the perpendicular direction. A numerical solution for the governing nonlinear momentum equations is obtained using the method of finite differences. The effect of the Hall current, the non-Newtonian fluid characteristics and the particle-phase viscosity on the velocity, the volumetric flow rates, and the skin friction coefficients of both the fluid and the particle phases is investigated.

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Abbreviations

B :

Viscosity ratio

B o :

Magnetic induction (kg s−2 A−1)

Ha :

Hartmann number

J :

Current density (A m−2)

K :

Stokes constant (kg s−1)

p :

Pressure gradient (kg m−2 s−2)

m :

Hall parameter

N :

Number of dust particles per unit volume (m−3)

V :

Velocity component of the fluid phase (m s−1)

V p :

Velocity component of the particle phase (m s−1)

r :

Radial direction (m)

z :

Axial direction (m)

μ :

Viscosity of the fluid (kg m−1 s−1)

μ p :

Viscosity of the dust particles (kg m−1 s−1)

ρ :

Density of the fluid

ρ p :

Mass of dust particles per unit volume of the fluid (kg m−3)

σ :

Electrical conductivity of the fluid (m−2 kg−1 s3 A2)

λ i :

Material parameters (i = 1–7)

α :

Inverse Stokes number

β :

Hall factor

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Authors and Affiliations

  1. Department of Engineering Mathematics and Physics, Faculty of Engineering, El-Fayoum University, El-Fayoum, 63514, Egypt

    Hazem Ali Attia

  2. Faculty of Engineering, Department of Engineering Mathematics and Physics, Cairo University, Giza, 12211, Egypt

    Mostafa A. M. Abdeen

Authors
  1. Hazem Ali Attia
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  2. Mostafa A. M. Abdeen
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Correspondence to Mostafa A. M. Abdeen.

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Attia, H.A., Abdeen, M.A.M. Steady MHD Flow of a Dusty Incompressible Non-Newtonian Oldroyd 8-Constant Fluid in a Circular Pipe. Arab J Sci Eng 38, 3153–3160 (2013). https://doi.org/10.1007/s13369-012-0475-z

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  • DOI: https://doi.org/10.1007/s13369-012-0475-z

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