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Peristaltic mechanism of a Rabinowitsch fluid in an inclined channel with complaint wall and variable liquid properties

  • Hanumesh Vaidya
  • C. Rajashekhar
  • G. ManjunathaEmail author
  • K. V. Prasad
Technical Paper
  • 31 Downloads

Abstract

The present paper emphasizes the impacts of the compliant wall and variable liquid properties on the peristaltic stream of a Rabinowitsch liquid in an inclined channel. The viscosity of the liquid differs over the thickness of the channel, and temperature-dependent thermal conductivity is considered. The perturbation strategy is utilized to solve the governing nonlinear temperature equations. The expressions for the velocity, skin friction coefficient, pressure rise, frictional force, streamline, temperature and coefficient of heat transfer are obtained. The consequences of pertinent parameters on the velocity, temperature, streamline and coefficient of heat transfer for the dilatant, Newtonian and pseudoplastic liquid models are analysed graphically. The results obtained for velocity and temperature reveal that an expansion in the estimation of variable viscosity results in diminishing the velocity and temperature fields for shear thickening liquid. Furthermore, it is noticed that for a large value of thermal conductivity the temperature profile decreases for dilatant, Newtonian and pseudoplastic fluid models.

Keywords

Compliant wall Variable viscosity Thermal conductivity Inclined channel Skin friction 

List of symbols

\(a\)

Undisturbed radius

\(b\)

Amplitude

\(c\)

Wave speed

\(H\)

Spring stiffness

\(t\)

Time

\(x,y\)

Axial and radial coordinates

\(u,v\)

Velocity components

\(g\)

Acceleration due to gravity

\(p\)

Pressure

\(P\)

Pressure gradient

\(k\)

Thermal conductivity

\(F\)

Body force parameter

\(Re\)

Reynolds number

\(Pr\)

Prandtl number

\(Ec\)

Eckert number

\(N\)

Brinkmann number

\(E_{1}\)

Wall tension parameter

\(E_{2}\)

Mass characterizing parameter

\(E_{3}\)

Wall damping parameter

\(E_{4}\)

Wall rigidity parameter

\(E_{5}\)

Wall elastic parameter

\(Z\)

Coefficient of heat transfer

\(C_{\text{f}}\)

Skin friction coefficient

\(\psi\)

Stream function

\(\Delta P\)

Pressure rise

\(F_{1}\)

Frictional force

\(q\)

Flow rate

\(\overline{Q}\)

Time-averaged flow rate

Greek letters

\(\lambda\)

Wavelength

\(\rho\)

Density

\(\tau\)

Shear stress

\(\xi\)

Specific heat at constant pressure

\(\mu\)

Viscosity

\(\alpha\)

Angle of inclination parameter

\(\varepsilon\)

Amplitude ratio

\(\theta\)

Temperature

\(\phi\)

Coefficient of pseudoplasticity

\(\beta\)

Variable viscosity

\(\gamma\)

Variable thermal conductivity

Notes

Acknowledgements

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

References

  1. 1.
    Hamid AH, Javed T, Ahmad B, Ali N (2017) Numerical study of two-dimensional non-Newtonian peristaltic flow for long wavelength and moderate Reynolds number. J Braz Soc Mech Sci Eng 39:4421–4430CrossRefGoogle Scholar
  2. 2.
    Kavitha A, Reddy RH, Saravana R, Sreenadh S (2017) Peristaltic transport of a Jeffery fluid in contact with a Newtonian fluid in an inclined channel. Ain Shams Eng J 8:683–687CrossRefGoogle Scholar
  3. 3.
    Manjunatha G, Rajashekhar C (2018) Slip effects on peristaltic transport of Casson fluid in an inclined elastic tube with porous walls. J Adv Fluid Mech Therm Sci 43:67–80Google Scholar
  4. 4.
    Rajashekhar C, Manjunatha G, Prasad KV, Divya BB, Vaidya H (2018) Peristaltic transport of two-layered blood flow using Herschel–Bulkley model. Cogent Eng 5:1495592CrossRefGoogle Scholar
  5. 5.
    Javed T, Ahmed B, Hamid AH, Sajid M (2018) Numerical analysis of peristaltic transport of Casson fluid for non-zero Reynolds number in presence of the magnetic field. Nonlinear Eng 7:183–193CrossRefGoogle Scholar
  6. 6.
    Ahmed B, Javed T, Ali N (2018) Numerical study at moderate Reynolds number of peristaltic flow of micropolar fluid through a porous-saturated channel in magnetic field. AIP Adv 8:015319CrossRefGoogle Scholar
  7. 7.
    Wada S, Hayashi H (1971) Hydrodynamic lubrication of journal bearings by Pseudo-Plastic lubricants. Bull JSME 69:268CrossRefGoogle Scholar
  8. 8.
    Akbar NS, Nadeem S (2014) Application of Rabinowitsch fluid model in peristalsis. Zeitschrift für Naturforschung A 69:473–480CrossRefGoogle Scholar
  9. 9.
    Maraj E, Nadeem S (2015) Application of Rabinowitsch fluid model for the mathematical analysis of peristaltic flow in a curved channel. Zeitschrift für Naturforschung A 70:513–520CrossRefGoogle Scholar
  10. 10.
    Hina S, Nadeem S (2017) Analysis of combined convective and viscous dissipation effects for peristaltic flow of Rabinowitsch Fluid model. J Bionic Eng 14:182–190CrossRefGoogle Scholar
  11. 11.
    Oudina FM, Bessaih R (2014) Numerical modelling of MHD stability in a cylindrical configuration. J Frankl Inst 351:667–681CrossRefGoogle Scholar
  12. 12.
    Hayat T, Yasmin H, Alsaedi A (2015) Convective heat transfer analysis for peristaltic flow of power-law fluid in a channel. J Braz Soc Mech Sci Eng 37:463–477CrossRefGoogle Scholar
  13. 13.
    Oudina FM, Bessaih R (2016) Oscillatory magnetohydrodynamic natural convection of liquid metal between vertical coaxial cylinders. J Appl Fluid Mech 9:1655–1665CrossRefGoogle Scholar
  14. 14.
    Oudina FM (2017) Numerical modelling of the hydrodynamic stability in vertical annulus with heat source of different lengths. Eng Sci Technol Int J 20:1324–1333CrossRefGoogle Scholar
  15. 15.
    Ramesh K, Devakar M (2017) Influence of heat transfer on the peristaltic transport of Walter’s B fluid in an inclined annulus. J Braz Soc Mech Sci Eng 39:2571–2584CrossRefGoogle Scholar
  16. 16.
    Wakif A (2018) Boulahia Z Sehaqui, R A, Semi analytical analysis of electro-thermo-hydrodynamic stability in dielectric nanofluids using Buongiorno’s mathematical model together with more realistic boundary conditions. Results Phys 9:1438–1454CrossRefGoogle Scholar
  17. 17.
    Wakif A, Boulahia Z, Ali F, Eid MR, Sehaqui R (2018) Numerical analysis of the unsteady natural convection MHD couette nanofluid flow in the presence of thermal radiation using single and two-phase nanofluid models for Cu–Water nanofluids. Int J Appl Comput Math 4:81MathSciNetCrossRefGoogle Scholar
  18. 18.
    Wakif A, Boulahia Z, Mishra SR, Rashidi MM, Sehaqui R (2018) Influence of a uniform transverse magnetic field on the thermo-hydrodynamic stability in water-based nanofluids with metallic nanoparticles using the generalized Buongiorno’s mathematical model. Eur J Plus 133:181CrossRefGoogle Scholar
  19. 19.
    Oudina FM, Makinde OD (2018) Numerical simulation of Oscillatory MHD natural convection in cylindrical annulus: Prandtl number effect. Defect Diffus Forum 387:417–427CrossRefGoogle Scholar
  20. 20.
    Oudina FM (2019) Convective heat transfer of Titania nanofluids of different base fluids in cylindrical annulus with discrete heat source. Heat Transf Asian Res 48:135–147CrossRefGoogle Scholar
  21. 21.
    Srinivas S, Gayathri R, Kothandapani M (2009) The influence of slip conditions, wall properties and heat transfer on MHD peristaltic transport. Comput Phys Commun 180:2115–2122MathSciNetCrossRefGoogle Scholar
  22. 22.
    Mustafa M, Hina S, Hayat T, Alsaedi A (2012) Influence of wall properties on the peristaltic flow of a nanofluid: analytic and numerical solutions. Int J Heat Mass Transf 55:4871–4877CrossRefGoogle Scholar
  23. 23.
    Javed M, Hayat T, Mustafa M, Ahmad B (2016) Velocity and thermal slip effects on peristaltic motion of Walters-B fluid. Int J Heat Mass Transf 96:210–217CrossRefGoogle Scholar
  24. 24.
    Bhatti MM, Zeeshan A (2017) Heat and mass transfer analysis on peristaltic flow of a Prandtl-fluid suspension with slip effects. J Mech Med Biol 17:1750028CrossRefGoogle Scholar
  25. 25.
    Saravana R, Vajravelu K, Sreenadh S (2018) Influence of compliant walls and heat transfer on the peristaltic transport of a Rabinowitsch fluid in an inclined channel. Zeitschrift für Naturforschung A 73:833–843CrossRefGoogle Scholar
  26. 26.
    Hanumesh V, Manjunatha G, Rajashekhar C, Prasad KV (2018) Role of slip and heat transfer on peristaltic transport of Herschel-Bulkley fluid through an elastic tube. Multidiscip Modell Mater Struct 14:940–959Google Scholar
  27. 27.
    Khan AA, Tariq H (2018) Influence of wall properties on the peristaltic flow of dusty Walter’s B fluid. J Braz Soc Mech Sci Eng 40:368CrossRefGoogle Scholar
  28. 28.
    Devaki P, Sreenadh S, Vajravelu K, Prasad KV, Hanumesh V (2018) Wall properties and slip consequences on peristaltic transport of a Casson liquid in a flexible channel with heat transfer. Appl Math Nonlinear Sci 3:277–290MathSciNetCrossRefGoogle Scholar
  29. 29.
    Abbasi FM, Hayat T, Ahmad B (2015) Numerical analysis for peristaltic transport of Carreau–Yasuda fluid with variable thermal conductivity and convective conditions. J Cent South Univ 22:4467–4475CrossRefGoogle Scholar
  30. 30.
    Prasad KV, Vajravelu K, Vaidya H, Basha NZ, Umesh V (2018) Thermal and species concentration of MHD Casson fluid at a vertical sheet in the presence variable fluid properties. Ain Shams Eng J 9:1763–1779CrossRefGoogle Scholar
  31. 31.
    Prasad KV, Vaidya H, Vajravelu K, Rashidi MM (2017) Effects of variable fluid properties on MHD Flow and heat transfer over a stretching sheet with variable thickness. J Mech 33:501–512CrossRefGoogle Scholar
  32. 32.
    Prasad KV, Vajravelu K, Chiu-On N, Vaidya H (2017) MHD squeeze flow and heat transfer of a nanofluid between parallel disks with variable fluid properties and transpiration. Int J Mech Mater Eng 12:9CrossRefGoogle Scholar
  33. 33.
    Rajashekhar C, Manjunatha G, Vaidya H, Divya BB, Prasad KV (2018) Peristaltic flow of Casson liquid in an inclined porous tube with convective boundary conditions and variable liquid properties. Front Heat Mass Transf 11:35Google Scholar
  34. 34.
    Hayat T, Ali N (2008) Effect of variable viscosity on the peristaltic transport of a Newtonian fluid in an asymmetric channel. Appl Math Model 32:761–774MathSciNetCrossRefGoogle Scholar
  35. 35.
    Lachiheb M (2016) On the effect of variable viscosity on the peristaltic transport of a Newtonian fluid in an asymmetric channel. Can J Phys 94:320–327CrossRefGoogle Scholar
  36. 36.
    Awais M, Bukhari U, Ali A, Yasmin H (2017) Convective and peristaltic viscous fluid flow with variable viscosity. J Eng Thermophys 26:69–78CrossRefGoogle Scholar
  37. 37.
    Awati VB, Jyoti M, Prasad KV (2017) Series analysis for the flow between two stretchable disks. Eng Sci Technol Int J 20:1211–1219CrossRefGoogle Scholar
  38. 38.
    Awati VB, Jyoti M, Bujurke NM (2018) Series solution of steady viscous flow between two porous disks with stretching motion. J Nanofluids 7:982–994CrossRefGoogle Scholar

Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  1. 1.Department of MathematicsSSA Government First Grade College (Autonomous)BallariIndia
  2. 2.Department of Mathematics, Manipal Institute of TechnologyManipal Academy of Higher EducationManipalIndia
  3. 3.Department of MathematicsVijayanagara Srikrishnadevaraya UniversityBallariIndia

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