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Peristaltic flow of a tangent hyperbolic fluid with convective boundary condition

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Abstract

The present work deals with the peristaltic flow of a tangent hyperbolic fluid in an asymmetric channel. The flow equations have been derived for the tangent hyperbolic fluid. Analysis has been done in the presence of convected boundary condition. The governing nonlinear partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations using similarity transformations and then tackled analytically using the perturbation technique. The main focus has been given to the effects of the Biot number, the power law index and the Weissenberg number. Graphical results for velocity, temperature, pressure rise and trapping are obtained and analyzed in detail.

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Abbreviations

C′:

specific heat

Q 0 :

constant heat absorption parameter

B i :

Biot number

K′:

thermal conductivity

σ :

electrical conductivity

\(\bar S\) :

extra stress tensor

g :

gravitation due to acceleration

M :

Hartmann number

μ ∞ :

infinite shear rate viscosity

μ 0 :

zero shear rate viscosity

φ :

phase difference

Ψ :

stream function

P r :

Prandtl number

c :

wave speed

\(\dot \gamma\) :

shear rate

Γ :

time constant

h f :

convective heat transfer

t :

time

λ:

wavelength

T :

local fluid temperature

T 0, T 1 :

wall temperatures

λ1 :

ratio of relaxation to retardation time

u, v :

velocity along x and y directions

x :

coordinate along the channel

y :

coordinate normal to the channel

n :

Power law index

We :

Weissenberg number

P :

Pressure

∞ :

dimensionless temperature

μ :

fluid viscosity

B r :

Brinkman number

ν :

kinematic viscosity of the fluid

ρ :

fluid density

c p :

effective heat capacity

a 1 and b 1 :

waves amplitudes

h 1, h 2 :

height of the channel

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Authors and Affiliations

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

    Noreen Sher Akbar

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  1. Noreen Sher Akbar
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Correspondence to Noreen Sher Akbar.

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Akbar, N.S. Peristaltic flow of a tangent hyperbolic fluid with convective boundary condition. Eur. Phys. J. Plus 129, 214 (2014). https://doi.org/10.1140/epjp/i2014-14214-0

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  • DOI: https://doi.org/10.1140/epjp/i2014-14214-0

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