Journal of Thermal Analysis and Calorimetry

, Volume 139, Issue 2, pp 1213–1228 | Cite as

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


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.


Biot number Porous parameter Schmidt number Soret number Wall properties 

List of symbols


Acceleration due to gravity


Axial and radial coordinates


Biot number


Brinkman number


Coefficient of mass diffusivity


Darcy number


Eckert number


Mass characterization


Mean fluid temperature


Nusselt number


Prandtl number




Radius of the channel


Reynolds number


Rigidity parameter


Schmidt number


Soret number


Thermal conductivity


Thermal diffusivity




Velocity components


Wall damping parameter


Wall elastic parameter


Wall tension parameter


Wave amplitude


Wave speed

Greek letters

\(\sigma \)


\(\rho \)


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

Extra stress components

\(\lambda _1\)

Jeffrey parameter

\(\beta \)

Partial velocity slip parameter

\(\delta \)

Specific heat at constant volume

\(\psi \)


\(\theta \)


\(\alpha _1\)

Variable viscosity

\(\gamma \)

Variable thermal conductivity

\(\alpha \)

Velocity slip parameter

\(\mu \)


\(\lambda \)




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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