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Analytical investigation of Jeffery-Hamel flow with high magnetic field and nanoparticle by Adomian decomposition method

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Abstract

In this study, the effects of magnetic field and nanoparticle on the Jeffery-Hamel flow are studied using a powerful analytical method called the Adomian decomposition method (ADM). The traditional Navier-Stokes equation of fluid mechanics and Maxwell’s electromagnetism governing equations are reduced to nonlinear ordinary differential equations to model the problem. The obtained results are well agreed with that of the Runge-Kutta method. The present plots confirm that the method has high accuracy for different α, Ha, and Re numbers. The flow field inside the divergent channel is studied for various values of Hartmann number and angle of channel. The effect of nanoparticle volume fraction in the absence of magnetic field is investigated.

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Abbreviations

A*:

constant parameter

B 0 :

magnetic field (wb·m−2)

F :

general nonlinear operator

Lu :

linear term

Ru :

remained of linear operator

A :

Adomian polynominal

f(η):

dimensionless velocity

Ha :

Hartmann number

P :

pressure term

Re :

Reynolds number

r,θ :

cylindrical coordinates

U max :

maximum value of velocity

u,v :

velocity components along x and y axes, respectively

α :

angle of channel

η :

dimensionless angle

θ :

any angle

ρ :

density

ϕ :

nanoparticle volume fraction

µ :

dynamic viscosity

υ :

kinematic viscosity

β :

constant

∞ :

condition at infinity

nf:

nanofluid

f:

base fluid

s:

nano-solid-particles

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Authors and Affiliations

  1. Faculty of Mechanical Engineering, Babol University of Technology, P. O. Box 484, Babol, Islamic Republic of Iran

    M. Sheikholeslami, D. D. Ganji, H. R. Ashorynejad & H. B. Rokni

Authors
  1. M. Sheikholeslami
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  2. D. D. Ganji
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  3. H. R. Ashorynejad
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  4. H. B. Rokni
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Correspondence to H. B. Rokni.

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Sheikholeslami, M., Ganji, D.D., Ashorynejad, H.R. et al. Analytical investigation of Jeffery-Hamel flow with high magnetic field and nanoparticle by Adomian decomposition method. Appl. Math. Mech.-Engl. Ed. 33, 25–36 (2012). https://doi.org/10.1007/s10483-012-1531-7

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  • DOI: https://doi.org/10.1007/s10483-012-1531-7

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