Skip to main content
SpringerLink
Log in

Electroosmotic Peristaltic Pumping of Jeffrey Liquid with Variable Characteristics: An Application to Hemodynamic

  • Original Paper
  • Published:
International Journal of Applied and Computational Mathematics Aims and scope Submit manuscript

Abstract

The current model investigates the electroosmotic characteristics of the Jeffrey fluid's peristaltic transport in a uniform channel to study the impacts of variable viscosity, variable thermal conductivity, slip effects, electroosmotic parameter, Helmholtz–Smoluchowski velocity parameter. The governing equations are simplified by using the long-wavelength and small Reynold’s number approximations. Further, the semi-analytical method (perturbation method) is applied for solving the transformed equations and solutions are obtained for the stream function, velocity, temperature distribution, concentration, and Pressure gradient. Finally, the effects of various parameters assessed numerically are presented through graphs and discussed in detail. The results reveal that increased variable viscosity and electroosmotic parameters enhance the fluid velocity at the centre of the channel. Further, the Helmholtz–Smoluchowski velocity parameter and the variable thermal conductivity parameter slows down the particle motion at the centre of the channel. Furthermore, the size of the trapped bolus enhances with the values of the Electroosmotic parameter and Jeffrey parameter.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

Data Availability

Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.

Abbreviations

\(E_{x}\) :

Axial applied electric field

\(B_{r}\) :

Brinkman number

\(\mu_{0}\) :

Constant viscosity

\(x,\,\,y\) :

Coordinates

\(Ec\) :

Eckert number

E :

Electrical field

g :

Gravitation

\(U_{hs}\) :

Helmholtz–Smoluchowski velocity

D:

Mass diffusivity

\(f\) :

Mean flow rate

Pr:

Prandlt number

P :

Pressure

\(K_{T}\) :

Ratio of thermal diffusion

Re:

Reynolds number

\(Sc\) :

Schmidt number

\(c_{p\,\,}\) :

Specific heat

\(S_{r}\) :

Soret number

S :

Stress component

t :

Time

K(T) :

Variable thermal conductivity

u :

Velocity

b :

Wave amplitude

c :

Wave speed

a :

Width of the channel

\(\varepsilon\) :

Amplitude ratio

\(\overline{n}^{ + } , \overline{n}^{ - }\) :

Cations, anions

\(\alpha\) :

Coefficient of variable viscosity

\(\beta\) :

Coefficient of thermal conductivity

\({\Omega }\) :

Concentration

\(\gamma_{2}\) :

Concentration slip

\({\uplambda }_{D}\) :

Debye length

\(\rho\) :

Density

\(\xi\) :

Dielectric permittivity

\({\Theta }\) :

Dimensionless volume flow rate

\(\rho_{e}\) :

Electrical charge density

\(\phi\) :

Electric potential

\(m_{e}\) :

Electroosmotic term

\(\tau\) :

Shear stress

\(\psi\) :

Stream function

\(\theta\) :

Temperature

\(\gamma_{1}\) :

Temperature slip

\(\mu \left( y \right)\) :

Variable thermal conductivity

\(\gamma\) :

Velocity slip

\(\mu\) :

Viscosity

\(\lambda\) :

Wave length

References

  1. Mernone, A.V., Mazumdar, J.N., Lucas, S.K.: A mathematical study of peristaltic transport of a Casson fluid. Math. Comput. Model. 35(7–8), 895–912 (2002). https://doi.org/10.1016/S0895-7177(02)00058-4

    Article  MathSciNet  MATH  Google Scholar 

  2. Javed, M.: A mathematical framework for peristaltic mechanism of non-Newtonian fluid in an elastic heated channel with hall effect. Multidiscip. Model. Mater. Struct. 17(2), 360–372 (2021). https://doi.org/10.1108/MMMS-11-2019-0200

    Article  MathSciNet  Google Scholar 

  3. Hayat, T., Noreen, S., Alhothuali, M.S., Asghar, S., Alhomaidan, A.: Peristaltic flow under the effects of an induced magnetic field and heat and mass transfer. Int. J. Heat Mass Transf. 55(1–3), 443–452 (2012). https://doi.org/10.1016/j.ijheatmasstransfer.2011.09.044

    Article  MATH  Google Scholar 

  4. Das, S., Chakraborty, S.: Analytical solutions for velocity, temperature and concentration distribution in electroosmotic microchannel flows of a non-Newtonian bio-fluid. Anal. Chim. Acta 559(1), 15–24 (2006). https://doi.org/10.1016/j.aca.2005.11.046

    Article  Google Scholar 

  5. Srinivas, S., Gayathri, R., Kothandapani, M.: The influence of slip conditions, wall properties and heat transfer on MHD peristaltic transport. Comput. Phys. Commun. 180(11), 2115–2122 (2009). https://doi.org/10.1016/j.cpc.2009.06.015

    Article  MathSciNet  MATH  Google Scholar 

  6. Akbar, N.S., Butt, A.W.: Heat transfer analysis for the peristaltic flow of Herschel–Bulkley fluid in a nonuniform inclined channel. Zeitschrift für Naturforschung A 70(1), 23–32 (2015). https://doi.org/10.1515/zna-2014-0164

    Article  Google Scholar 

  7. Imran, N., Javed, M., Sohail, M., Thounthong, P., Nabwey, H.A., Tlili, I.: Utilization of hall current and ions slip effects for the dynamic simulation of peristalsis in a compliant channel. Alex. Eng. J. 59(5), 3609–3622 (2020). https://doi.org/10.1016/j.aej.2020.06.006

    Article  Google Scholar 

  8. Makanda, G., Shaw, S., Sibanda, P.: Effects of radiation on MHD free convection of a casson fluid from a horizontal circular cylinder with partial slip in non-Darcy porous medium with viscous dissipation. Bound. Value Prob. 75, 2015 (2015). https://doi.org/10.1186/s13661-015-0333-5

    Article  MathSciNet  MATH  Google Scholar 

  9. Shaw, S., Nayak, M.K., Makinde, O.D.: Transient rotational flow of radiative nanofluids over an impermeable Riga plate with variable properties. Defect Diffus. Forum 387, 640–652 (2018). https://doi.org/10.1002/htj.22320c

    Article  Google Scholar 

  10. Nayak, M.K., Shaw, S., Makinde, O.D., Chamkha, A.J.: Investigation of partial slip and viscous dissipation effects on the radiative tangent hyperbolic nanofluid flow past a vertical permeable Riga plate with internal heating: bungiorno model. J. Nanofluids 8, 51–62 (2019). https://doi.org/10.1166/jon.2019.1576

    Article  Google Scholar 

  11. Nayak, M.K., Prakash, J., Tripathi, D., Pandey, V.S., Shaw, S., Makinde, O.D.: 3D Bioconvective multiple slip flow of chemically reactive Casson nanofluid with gyrotactic micro-organisms. Heat Transf.—Asian Res 49, 135–153 (2020). https://doi.org/10.1002/htj.21603

    Article  Google Scholar 

  12. Bashaga, G., Shaw, S.: Shear augmented solute disersion during drug delivery for three-layer flow through microvessel under stress jump and momentum slip-Darcy model. Appl. Math. Mech. (English Ed.) 42(6), 901–914 (2021). https://doi.org/10.1007/s10483-021-2737-8

    Article  MathSciNet  MATH  Google Scholar 

  13. Sheriff, S., Sadaf, H., Akbar, N.S., Mir, N.A.: Heat and peristaltic propagation of water based nanoparticles with variable fluid features. Phys. Scr. 94(12), 125704 (2019). https://doi.org/10.1088/1402-4896/ab3316

    Article  Google Scholar 

  14. Vaidya, H., Rajashekhar, C., Manjunatha, G., Prasad, K.V.: Peristaltic mechanism of a Rabinowitsch fluid in an inclined channel with complaint wall and variable liquid properties. J. Braz. Soc. Mech. Sci. Eng. 41(3), 52 (2019). https://doi.org/10.1007/s40430-018-1543-4

    Article  Google Scholar 

  15. Chu, Y.M., et al.: Entropy analysis in the Rabinowitsch fluid model through inclined Wavy channel: constant and variable properties. Int. Commun. Heat Mass Transf. 119, 104980 (2020). https://doi.org/10.1016/j.icheatmasstransfer.2020.104980

    Article  Google Scholar 

  16. Sheikholeslami, M., Jafaryar, M., Said, Z., Alsabery, A.I., Babazadeh, H., Shafee, A.: Modification for helical turbulator to augment heat transfer behavior of nanomaterial via numerical approach. Appl. Therm. Eng. 182, 115935 (2021). https://doi.org/10.1016/j.applthermaleng.2020.115935

    Article  Google Scholar 

  17. Sheikholeslami, M., Jafaryar, M.: Nanoparticles for improving the efficiency of heat recovery unit involving entropy generation analysis. J. Taiwan Inst. Chem. Eng. (2020). https://doi.org/10.1016/j.jtice.2020.09.033

    Article  Google Scholar 

  18. Sheikholeslami, M., Farshad, S.A.: Numerical simulation of effect of non-uniform solar irradiation on nanofluid turbulent flow. Int. Commun. Heat Mass Transf. 129, 105648 (2021). https://doi.org/10.1016/j.icheatmasstransfer.2021.105648

    Article  Google Scholar 

  19. Ramesh, K., Devakar, M.: Effect of endoscope on the peristaltic transport of a couple stress fluid with heat transfer: application to biomedicine. Nonlinear Eng. 8(1), 619–629 (2019). https://doi.org/10.1515/nleng-2017-0166

    Article  Google Scholar 

  20. Tang, G.H., Li, X.F., He, Y.L., Tao, W.Q.: Electroosmotic flow of non-Newtonian fluid in microchannels. J. Nonnewton. Fluid Mech. 157(1–2), 133–137 (2009). https://doi.org/10.1016/j.jnnfm.2008.11.002

    Article  MATH  Google Scholar 

  21. Jian, Y., Yang, L., Liu, Q.: Time periodic electro-osmotic flow through a microannulus. Phys. Fluids 22(4), 1–9 (2010). https://doi.org/10.1063/1.3358473

    Article  MATH  Google Scholar 

  22. Ferrás, L.L., Afonso, A.M., Alves, M.A., Nóbrega, J.M., Pinho, F.T.: Analytical and numerical study of the electro-osmotic annular flow of viscoelastic fluids. J. Colloid Interface Sci. 420, 152–157 (2014). https://doi.org/10.1016/j.jcis.2013.12.043

    Article  Google Scholar 

  23. Bandopadhyay, A., Tripathi, D., Chakraborty, S.: Electroosmosis-modulated peristaltic transport in microfluidic channels. Phys. Fluids 10(1063/1), 4947115 (2016)

    Google Scholar 

  24. Guo, X., Qi, H.: Analytical solution of electro-osmotic peristalsis of fractional Jeffreys fluid in a micro-channel. Micromachines (2017). https://doi.org/10.3390/mi8120341

    Article  Google Scholar 

  25. Jayavel, P., Jhorar, R., Tripathi, D., Azese, M.N.: Electroosmotic flow of pseudoplastic nanoliquids via peristaltic pumping. J. Braz. Soc. Mech. Sci. Eng. 41(2), 1–18 (2019). https://doi.org/10.1007/s40430-018-1555-0

    Article  Google Scholar 

  26. Noreen, S., Riaz, A., Lu, D.: Soret-dufour effects in electroosmotic biorheological flow of Jeffrey fluid. Heat Transf. 49(4), 2355–2374 (2020). https://doi.org/10.1002/htj.21725

    Article  Google Scholar 

  27. Waheed, S., Noreen, S., Hussanan, A.: Study of heat and mass transfer in electroosmotic flow of third order fluid through peristaltic microchannels. Appl. Sci. (2019). https://doi.org/10.3390/app9102164

    Article  Google Scholar 

  28. Waheed, S., Noreen, S., Tripathi, D., Lu, D.: Electrothermal transport of third-order fluids regulated by peristaltic pumping. J. Biol. Phys. 46(1), 45–65 (2020). https://doi.org/10.1007/s10867-020-09540-x

    Article  Google Scholar 

  29. Reddy, K.V., Reddy, M.G., Makinde, O.D.: Heat and mass transfer of a peristaltic electro-osmotic flow of a couple stress fluid through an inclined asymmetric channel with effects of thermal radiation and chemical reaction. Period. Polytech. Mech. Eng. 65(2), 151–162 (2021). https://doi.org/10.3311/ppme.16760

    Article  Google Scholar 

  30. Hayat, T., Ali, N., Asghar, S.: An analysis of peristaltic transport for flow of a Jeffrey fluid. Acta Mech. 193(1–2), 101–112 (2007). https://doi.org/10.1007/s00707-007-0468-2

    Article  MATH  Google Scholar 

  31. Hussain, Q., Asghar, S., Hayat, T., Alsaedi, A.: Heat transfer analysis in peristaltic flow of MHD Jeffrey fluid with variable thermal conductivity. Appl. Math. Mech. (English Ed.) 36(4), 499–516 (2015). https://doi.org/10.1007/s10483-015-1926-9

    Article  MathSciNet  Google Scholar 

  32. Selvi, C.K., Haseena, C., Srinivas, A.N.S., Sreenadh, S.: The effect of heat transfer on peristaltic flow of Jeffrey fluid in an inclined porous stratum. IOP Conf. Ser. Mater. Sci. Eng. (2017). https://doi.org/10.1088/1757-899X/263/6/062027

    Article  Google Scholar 

  33. Tripathi, D., Jhorar, R., Beg, O.A., Shaw, S.: Electroosmosis Modulated peristaltic biorheological flow through an asymmetric microchannel mathematical model. Meccanica 53, 2079–2090 (2018). https://doi.org/10.1007/s11012-017-0795-x

    Article  MathSciNet  Google Scholar 

  34. Manjunatha, G., Rajashekhar, C., Vaidya, H., Prasad, K.V., Makinde, O.D., Viharika, J.U.: Impact of variable transport properties and slip effects on MHD Jeffrey fluid flow through channel. Arab. J. Sci. Eng. 45(1), 417–428 (2020). https://doi.org/10.1007/s13369-019-04266-y

    Article  Google Scholar 

  35. Divya, B.B., Manjunatha, G., Rajashekhar, C., Vaidya, H., Prasad, K.V.: The hemodynamics of variable liquid properties on the MHD peristaltic mechanism of Jeffrey fluid with heat and mass transfer. Alex. Eng. J. 59(2), 693–706 (2020). https://doi.org/10.1016/j.aej.2020.01.038

    Article  Google Scholar 

  36. Sen, S.S.S., Das, M., Shaw, S.: Thermal dispersed homogeneous-heterogeneous reaction within MHD flowof a Jeffrey fluid in the presence of Newtonian cooling and nonlinear thermal radiation. Heat Transf. (2021). https://doi.org/10.1002/htj.22146

    Article  Google Scholar 

Download references

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

Author information

Authors and Affiliations

  1. Department of Mathematics, B.L.D.E.A.’s V.P. Dr. P. G. Halakatti College of Engineering and Technology, Vijayapura, Karnataka, India

    P. Nagathan, Asha. Patil & S. C. Desai

  2. Department of Mathematics, Manipal Institute of Technology Bengaluru, Manipal Academy of Higher Education, Manipal, Karnataka, India

    C. Rajashekhar

  3. Department of Mechanical Engineering, University of West Attica, 12244, Athens, Greece

    I. Sarris

  4. Department of Mathematics, Vijayanagara Sri Krishnadevaraya University, Ballari, Karnataka, India

    H. Vaidya & K. V. Prasad

Authors
  1. P. Nagathan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Asha. Patil
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. C. Desai
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. C. Rajashekhar
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. I. Sarris
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. H. Vaidya
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. K. V. Prasad
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to C. Rajashekhar or I. Sarris.

Ethics declarations

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nagathan, P., Patil, A., Desai, S.C. et al. Electroosmotic Peristaltic Pumping of Jeffrey Liquid with Variable Characteristics: An Application to Hemodynamic. Int. J. Appl. Comput. Math 8, 151 (2022). https://doi.org/10.1007/s40819-022-01284-7

Download citation

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s40819-022-01284-7

Keywords

Search

Navigation