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An integral method for the boundary layer of MHD non-Newtonian power-law fluid in the entrance region of channels

Abstract

This paper presents the analytical solutions to laminar flow of MHD Newtonian and non-Newtonian power-law fluids in the entrance region of channels. The boundary layer growth and velocity profile of developing flow in a two-dimensional channel, under the influence of a uniform magnetic field, are investigated. The direction of the magnetic field is assumed perpendicular to the flow. For each case, a novel and useful non-dimensional correlation for computing the magnetic entrance length is proposed, using the integral equations method. In addition, the effect of different parameters on the magnetic entrance length, boundary layer thickness and thus core velocity and pressure loss are studied. It was found that with the increase of the Hartmann number, the entrance length declined. Furthermore, the entrance length decreases while the power-law index and magnetic interaction parameter increase. As well as, the results have shown that the augmentation of the magnetic interaction parameter leads to greater pressure drop in comparison with the hydrodynamic flow.

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Abbreviations

a :

Half width of channel (m)

B :

Total magnetic field (T)

B 0 :

External magnetic field (T)

b :

Induced magnetic field (T)

D :

Distance between the plates (m)

E :

Electric field (N/C)

Ha :

Hartmann number

J :

Density of electric current (A/m2)

K :

Consistency coefficient

n :

Power-law index

N :

Magnetic interaction parameter

P :

Pressure (Pa)

P*:

Dimensionless pressure

Re :

Reynolds number

R :

Generalized Reynolds number

u :

x-Component of the velocity (m/s)

U :

Inlet velocity (m/s)

u c :

Potential core velocity (m/s)

v :

y-Component of the velocity (m/s)

x :

Coordinate in the direction of flow (m)

x/D :

Dimensionless axial distance from the entry (in the x direction)

X/D :

Dimensionless magnetic entrance length

y :

Coordinate in the direction normal to flow (m)

ρ :

Density (kg/m3)

σ :

Electrical conductivity (Ω m)−1

δ :

Boundary layer thickness (m)

υ :

Constant (=K/ρ)

η :

Arbitrary variable

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Correspondence to Morteza Abbasi.

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Technical Editor: Cezar Negrao.

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Taheri, M.H., Abbasi, M. & Khaki Jamei, M. An integral method for the boundary layer of MHD non-Newtonian power-law fluid in the entrance region of channels. J Braz. Soc. Mech. Sci. Eng. 39, 4177–4189 (2017). https://doi.org/10.1007/s40430-017-0887-5

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Keywords

  • Entrance length
  • Integral method
  • MHD channel
  • Power-law fluid