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Variable viscosity in peristalsis of Sisko fluid

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Abstract

This paper aims to examine variable viscosity effects on peristalsis of Sisko fluids in a curved channel with compliant characteristics. Viscous dissipation in a heat transfer is studied. The resulting problems are solved using perturbation and numerical schemes to show qualitatively similar responses for velocity and temperature. A streamline phenomenon is also considered.

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Abbreviations

V :

velocity, m/s

\(\bar \upsilon ,\bar u\) :

radial and axial velocity components, m/s

\(\bar x\) :

axial coordinate, m

\(\bar r\) :

radial coordinate, m

\(\bar t\) :

time, s

c :

speed of wave, m/s

\(\bar d\) :

half channel width, m

ρ :

fluid density, kg/m3

\( \pm \bar \eta \) :

displacement of walls, m

a,b :

shear rate viscosities, kg/(m·s)

υ :

kinematic viscosity, m2/s

c p :

specific heat, m2/s2

λ :

wavelength, m

k 1 :

thermal conductivity, W/(K·m)

\(\bar S\) :

extra stress tensor, kg/(m·s2)

\({\bar S_{ij}}\) :

stress components, i = 1, 2, j = 1, 2

p :

pressure, N/m2

\(\bar \varepsilon \) :

amplitude of wave, m

τ:

stress tensor, kg/(m·s2)

n :

fluid parameter

β T :

thermal expansion coefficient, 1/K

R*:

inner radius of curved channel, m

T :

temperature, K

T 0 :

temperature at wall, K

μ(r):

variable viscosity, kg/(m·s)

τ*:

elastic tension, kg/s2

d′:

viscous damping coefficient, kg/(m2·s)

m 1 :

mass per unit area, kg/m2

ψ :

stream function

u, θ :

dimensionless velocity and temperature

Z :

heat transfer rate

ϵ:

amplitude ratio parameter

Br :

Brinkman number

Re :

Reynolds number

δ :

wave number

Pr :

Prandtl number

k :

curvature parameter

Ec :

Eckert number

E 1,E 2,E 3 :

elasticity parameters

α :

variable viscosity parameter

n :

fluid parameter

β*:

material fluid parameter

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Authors and Affiliations

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

    A. Tanveer & T. Hayat

  2. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    T. Hayat & A. Alsaedi

Authors
  1. A. Tanveer
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  2. T. Hayat
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  3. A. Alsaedi
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Correspondence to A. Tanveer.

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Tanveer, A., Hayat, T. & Alsaedi, A. Variable viscosity in peristalsis of Sisko fluid. Appl. Math. Mech.-Engl. Ed. 39, 501–512 (2018). https://doi.org/10.1007/s10483-018-2313-8

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  • DOI: https://doi.org/10.1007/s10483-018-2313-8

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