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Impact of heat and mass transfer on the peristaltic mechanism of Jeffery fluid in a non-uniform porous channel with variable viscosity and thermal conductivity

  • G. Manjunatha
  • C. Rajashekhar
  • Hanumesh VaidyaEmail author
  • K. V. Prasad
  • K. Vajravelu
Article

Abstract

The present examination emphasizes the effects of heat and mass transfer on the peristaltic flow of Jeffery fluid through a non-uniform channel with variable viscosity and thermal conductivity. The porous walls are considered to make more realistic approximations to the flow characteristics of biological fluids. Further, the convective boundary conditions and wall properties have been employed in the analysis. The mathematical formulation is established on the grounds of low Reynolds number and long wavelength approximations. Perturbation solution is obtained for the resulting nonlinear differential equation of energy for small values of variable thermal conductivity, whereas the exact solution is found for the velocity and concentration fields. The MATLAB software is utilized to generate the graphical representation of the variables used in the model. From the examination, it is seen that a rise in the value of variable viscosity upgrades the velocity, Nusselt number, and temperature fields, though the contrary conduct is seen for concentration profiles. Besides, the rise in volume of the trapped bolus is noticed for an increase in the value of porous and Jeffery parameters.

Keywords

Biot number Porous parameter Schmidt number Soret number Wall properties 

List of symbols

g

Acceleration due to gravity

xy

Axial and radial coordinates

Bi

Biot number

Br

Brinkman number

D

Coefficient of mass diffusivity

Da

Darcy number

Ec

Eckert number

\(E_2\)

Mass characterization

\(T_\mathrm{m}\)

Mean fluid temperature

Nu

Nusselt number

Pr

Prandtl number

p

Pressure

a

Radius of the channel

Re

Reynolds number

\(E_4\)

Rigidity parameter

Sc

Schmidt number

Sr

Soret number

k

Thermal conductivity

\(k_\mathrm{T}\)

Thermal diffusivity

t

Time

uv

Velocity components

\(E_3\)

Wall damping parameter

\(E_5\)

Wall elastic parameter

\(E_1\)

Wall tension parameter

b

Wave amplitude

c

Wave speed

Greek letters

\(\sigma \)

Concentration

\(\rho \)

Density

\(\tau _{\rm xx},\tau _{\rm xy},\tau _{\rm yy}\)

Extra stress components

\(\lambda _1\)

Jeffrey parameter

\(\beta \)

Partial velocity slip parameter

\(\delta \)

Specific heat at constant volume

\(\psi \)

Streamlines

\(\theta \)

Temperature

\(\alpha _1\)

Variable viscosity

\(\gamma \)

Variable thermal conductivity

\(\alpha \)

Velocity slip parameter

\(\mu \)

Viscosity

\(\lambda \)

Wavelength

Notes

Acknowledgements

The authors appreciate the constructive comments of the reviewers which led to a definite improvement in the paper.

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Manipal Institute of TechnologyManipal Academy of Higher EducationManipalIndia
  2. 2.Department of MathematicsVijayanagara Srikrishnadevaraya UniversityBallariIndia
  3. 3.Department of MathematicsUniversity of Central FloridaOrlandoUSA

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