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Analysis of MHD flow characteristics of an UCM viscoelastic flow in a permeable channel under slip conditions

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Abstract

In the present study, the problem of two-dimensional magneto-hydrodynamic (MHD) flow of an upper-convected Maxwell (UCM) fluid has been investigated in a permeable channel with slip at the boundaries. Employing the similarity variables, the basic partial differential equations are reduced to ordinary differential equations with Dirichlet and Neumann boundary conditions which are solved analytically and numerically using the Homotopy Analysis Method and fourth-order Runge–Kutta–Fehlberg method, respectively. The influences of the some physical parameters such as Reynolds number, slip condition, Hartman number and Deborah number on non-dimensional velocity profiles are considered. As an important outcome, comparison between HAM and numerical method shows that HAM is an exact and high-efficient method for solving these kinds of problems. Moreover, it can be found that the velocity profiles are a decreasing function of Hartmann number and Deborah number.

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Abbreviations

Rew :

Reynolds number

M :

Hartman number

k :

Slip parameter

De:

Deborah number

HAM :

Homotopy analysis method

NUM :

Numerical method

ħ :

Auxiliary parameter

\(\mathcal{H}\) :

Auxiliary function

\(\mathcal{L}\) :

Linear operator of HAM

\(\mathcal{N}\) :

Non-linear operator

v * :

Velocity component in y-direction

u * :

Velocity component in x-direction

x :

Dimensionless horizontal coordinate

y :

Dimensionless vertical coordinate

x * :

Distance in x-direction parallel to the plates

y * :

Distance in y-direction parallel to the plates

ρ :

Density of the fluid

λ :

Relaxation time

υ :

Kinematic viscosity

β :

Of sliding friction

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Authors and Affiliations

  1. Department of Mechanical Engineering, Sari Branch, Islamic Azad University, Sari, Iran

    M. Abbasi, M. Khaki & D. D. Ganji

  2. Department of Mechanical Engineering, Shahid Rajaee Teacher Training University (SRTTU), Tehran, Iran

    A. Rahbari

  3. Young researchers Club, Sari Branch, Islamic Azad University, Sari, Iran

    I. Rahimipetroudi

Authors
  1. M. Abbasi
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  2. M. Khaki
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  3. A. Rahbari
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  4. D. D. Ganji
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  5. I. Rahimipetroudi
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Corresponding author

Correspondence to D. D. Ganji.

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Technical Editor: Monica Feijo Naccache.

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Abbasi, M., Khaki, M., Rahbari, A. et al. Analysis of MHD flow characteristics of an UCM viscoelastic flow in a permeable channel under slip conditions. J Braz. Soc. Mech. Sci. Eng. 38, 977–988 (2016). https://doi.org/10.1007/s40430-015-0325-5

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  • DOI: https://doi.org/10.1007/s40430-015-0325-5

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