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Numerical study of electroosmosis-induced alterations in peristaltic pumping of couple stress hybrid nanofluids through microchannel

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Abstract

This paper presents a computational modeling approach to analyze the peristaltic pumping of couple stress hybrid nanofluids regulated by the electroosmosis mechanism through a microchannel. The effects of applied magnetic field, Joule heating and buoyancy have also been computed. In this analytical model, water-based titanium dioxide (TiO2) and silver (Ag) hybrid nanofluids have been considered. For more relevant physical problem, the axial velocity slip and thermal slip conditions have also been introduced. The nonlinear differential equations are simplified by considering the Hückel–Debye approximations as well as lubrication theory, and then the equations have been solved numerically by Mathematica 10 software via the NDsolve commands. The pertinent influences of key parameters on the axial velocity, nanoparticle temperature, Nusselt number and streamlines in the microchannel have been visualized graphically. It is observed that an increase in the thermal Grashof number produces a maximum axial velocity, and temperature of nanoparticles for both water–titanium dioxide and water–silver nanofluids. The maximum axial velocity and nanoparticle temperature occur in water–titanium dioxide as compared with water–silver. The outcomes of this model shall be very useful in the designs of smart electro-peristaltic pumps for thermal systems and drug delivery systems.

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Abbreviations

\(B_{0}\) :

Magnetic field strength

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

Specific heat of nanoparticle

\(E_{\xi }\) :

Axially applied electric field

\(k_{\text{B}}\) :

Boltzmann constant

\(\bar{n}_{ + }\) and \(\bar{n}_{ - }\) :

Positive and negative ions having bulk concentration

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

Dimensional pressure

\(n_{0}\) :

Bulk concentration

\(\,\bar{T}\) :

Dimensional temperature

z :

Valence

\(\mu_{\text{eff}}\) :

Effective viscosity

\(\left( {\rho \beta } \right)_{\text{eff}}\) :

Effective thermal expansion of the nanofluid

\(\rho_{\text{f}}\) :

Density of fluid

\(\varphi\) :

Nanoparticle volume fraction

\(\beta_{\text{p}}\) :

Nanoparticle thermal expansion coefficient

\(\bar \kappa_{\text{p}}\) :

Thermal conductivity of nanoparticle

\(\bar{a}\) :

Amplitudes of walls

d :

Width of the channel

\(\rho_{\text{e}}\) :

Net charge density of the electrolyte

Re:

Reynolds number

Gr:

Thermal Grashof number

Pr:

Prandtl number

Br:

Brinkman number

\(\beta\) :

Joule-heating parameter

\(c_{\text{p f}}\) :

Specific heat of fluid

e :

Elementary charge valence

\(g\) :

Acceleration due to gravity

\(n\) :

The shape factor of nanoparticles

\(T_{\text{m}} \left( { = \frac{{T_{0} + T_{1} }}{2}} \right)\) :

Mean temperature

\(\,\bar{t}\) :

Dimensional time

\(T_{\text{v}}\) :

Absolute temperature

\(\bar{u},\,\bar{v}\) :

Velocity along \(\bar{\xi }\) and \(\bar{\eta }\) directions

\(\rho_{\text{eff}}\) :

Effective density

\(\,\sigma\) :

Electrical conductivity

\(\bar\kappa_{\text{eff}}\) :

Effective thermal conductivity and couple stress viscosity

\(\rho_{\text{p}}\) :

Density of nanoparticle

\(\beta_{\text{f}}\) :

Fluid thermal expansion coefficient

\(\bar\kappa_{\text{f}}\) :

Thermal conductivity of fluid

\(\mu_{\text{f}}\) :

Dynamic viscosity of fluid

\(\lambda\) :

Wavelength

\(\varepsilon_{\text{ef}}\) :

Dielectric constant

\(\delta\) :

Wave number

\(\gamma\) :

Couple-stress parameter

H:

Hartmann number

Ec:

Eckert number

Uhs:

Helmholtz–Smoluchowski velocity

\(\psi\) :

Stream function

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology Uttarakhand, Srinagar, 246174, India

    Dharmendra Tripathi

  2. Department of Mathematics, Avvaiyar Government College for Women, Karaikal, Puducherry-U.T., 609 602, India

    J. Prakash

  3. Department of Mathematics, Acharya Nagarjuna University Campus, Ongole, 523 001, India

    M. Gnaneswara Reddy

  4. Department of Mechanical Engineering, Manipal University Jaipur, Jaipur, Rajasthan, 303007, India

    Rakesh Kumar

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  1. Dharmendra Tripathi
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  4. Rakesh Kumar
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Tripathi, D., Prakash, J., Gnaneswara Reddy, M. et al. Numerical study of electroosmosis-induced alterations in peristaltic pumping of couple stress hybrid nanofluids through microchannel. Indian J Phys 95, 2411–2421 (2021). https://doi.org/10.1007/s12648-020-01906-0

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