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Metachronal beating of cilia under influence of Hartmann layer and heat transfer

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Abstract

The propulsion system of cilia motion is investigated considering a viscous fluid model. The problem of the two-dimensional fluid motion in a symmetric channel with ciliated walls is considered. The features of ciliary structures are resolved by the supremacy of viscosity effects over inertial control by the long-wavelength and low-Reynolds-number approximation. Exact solutions for the longitudinal pressure gradient, temperature and velocities are obtained. The pressure gradient and volume flow rate for different values of the flow parameters are also predicted. The flow possessions for the viscous fluid are solved as a function of the cilia and metachronal wave velocity.

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Abbreviations

U, V :

Velocity components

M :

Hartmann number

X, Y :

Coordinates

a :

Wave’s amplitudes

μ :

Viscosity of the fluid

T :

Temperature

Φ :

Cilia length

β :

Slenderness parameter

Re:

Modified Reynolds number

ν :

Kinematic viscosity of the fluid

t :

Time

c :

Wave speed

a :

Stretching parameter

Q :

Flow rate

p y :

Yield stress

α :

Eccentricity of the elliptical motion

B r :

Brinkman number

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Author information

Authors and Affiliations

  1. DBS&H CEME, National University of Sciences and Technology, Islamabad, Pakistan

    Noreen Sher Akbar

  2. School of Mathematical Sciences, Peking University, 100871, Beijing, P.R. China

    Z. H. Khan

  3. Department of Mathematics, University of Malakand, Khyber Pakhtunkhwa, Pakistan

    Z. H. Khan

  4. Department of Mathematics, Quaid-i-Azam University 45320, 44000, Islamabad, Pakistan

    S. Nadeem

Authors
  1. Noreen Sher Akbar
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  2. Z. H. Khan
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  3. S. Nadeem
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Correspondence to S. Nadeem.

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Sher Akbar, N., Khan, Z.H. & Nadeem, S. Metachronal beating of cilia under influence of Hartmann layer and heat transfer. Eur. Phys. J. Plus 129, 176 (2014). https://doi.org/10.1140/epjp/i2014-14176-1

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  • DOI: https://doi.org/10.1140/epjp/i2014-14176-1

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