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Peristaltic transport of non-Newtonian nanofluid through an asymmetric microchannel with electroosmosis and thermal radiation effects

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Abstract

In this paper, we have investigated the electroosmotic-driven flow of Sutterby nanofluid under the peristaltic mechanism with the influence of a magnetic field. The flow of fluid is taken into the undulating asymmetrical microchannel. Using Debye-Hückel linearization approximation, the fluid velocity and temperature profiles were calculated. The nanofluid flow is considered in the static electric field on the horizontal side and the applied external magnetic field in the transversal direction. The flow pattern also considers thermal radiation and the Joule heating parameter. Governing fluid flow equations such as continuity, momentum and temperature equations are reduced in consideration of the long wavelength and the very tiny Reynolds number approximation. The resulting nonlinear equations are resolved numerically with the help of the built-in NDSolve function made available in the computational mathematical software MATHEMATICA. Graphical illustrations of the fluid velocity profile, temperature and Trapping phenomenon (Streamlines) have been explained in detail. It is found that increasing the values of Hartmann number velocity of the nanofluid diminishes, and the temperature of the fluid enhances. Results from the Sutterby nanofluid model might have a broad range of applications, such as cancer tissue destruction, disease diagnosis, etc.

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Abbreviations

\({\mathbf{u}} = \left( {\overline{u}^{\prime } ,\overline{v}^{\prime } } \right)\) :

Velocity vector \(\left[ {{\text{m}}\;{\text{s}}^{ - 1} } \right]\)

\(\left( {\overline{x}^{\prime } ,\overline{y}^{\prime } } \right)\) :

Cartesian coordinate of a point

\(a_{1} ,a_{2}\) :

Wave amplitudes of the walls \([{\text{m}}]\)

\(c\) :

Speed \(\left[ {{\text{m}}\;{\text{s}}^{ - 1} } \right]\)

\(d_{1} ,d_{2,}\) :

Width of the channel walls \([{\text{m}}]\)

\(h_{1}^{{^{\prime } }} ,h_{2}^{{^{\prime } }}\) :

Geometry of the channel walls

\(\overline{t}^{\prime }\) :

Time \([{\text{s}}]\)

\({\mathbf{S}}\) :

Cauchy stress tensor

\(F\) :

Flow rate

\({\mathbf{B}}\) :

Magnetic field vector

\(T\) :

Temperature of fluid

\({\mathbf{J}}\) :

Electric current density

\({\mathbf{E}}\) :

Electric field vector

\({\mathbf{I}}\) :

Identity tensor

\(p\) :

Pressure

\(n_{0}\) :

Bulk concentration

\(e\) :

Electronic charge

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

Boltzmann constant \([{\text{J}}\;{\text{K}}^{ - 1} ]\)

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

Absolute temperature \([{\text{K}}]\)

\(z\) :

Charge balance

\(q_{{\text{r}}}\) :

Radiative heat flux

\(k\) :

Thermal conductivity \(\left[ {{\text{W}}\;{\text{m}}^{ - 1} \;{\text{K}}^{ - 1} } \right]\)

\(c_{p}\) :

Specific heat \(\left[ {{\text{J}}\;{\text{Kg}}^{ - 1} \;{\text{K}}^{ - 1} } \right]\)

\(k^{ * }\) :

Mean absorption coefficient \([{\text{m}}^{2} \;{\text{kg}}^{ - 1} ]\)

\(T_{1}\) :

Temperature at the upper wall \([{\text{K}}]\)

\(T_{0}\) :

Temperature at the lower wall \([{\text{K}}]\)

\({\text{Re}}\) :

Reynolds number of the base fluid

\(\overline{{\text{Re}}}\) :

Reynolds number of the nanofluid

\({\text{Nr}}\) :

Radiation parameter of the base fluid

\(\overline{{{\text{Nr}}}}\) :

Radiation parameter of the nanofluid

\(H\) :

Hartmann number of the base fluid

\(\overline{H}\) :

Hartmann number of the nanofluid

\({\text{Ec}}\) :

Eckert number of the base fluid

\(\overline{{{\text{Ec}}}}\) :

Eckert number of the nanofluid

\(\Pr\) :

Prandtl number of the base fluid

\(\overline{\Pr }\) :

Prandtl number of the nanofluid

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

Joule heating parameter of the base fluid

\(\overline{{S_{{\text{p}}} }}\) :

Joule heating parameter of the nanofluid

\(U_{{{\text{HS}}}}\) :

Helmholtz-Smoluchowski velocity \([ms^{ - 1} ]\)

\(\overline{\varphi }^{\prime }\) :

Phase difference

\(\lambda\) :

Wavelength \([{\text{m}}]\)

\(\mu\) :

Dynamic viscosity \(\left[ {{\text{Kg}}\;{\text{m}}^{ - 1} \;{\text{s}}^{ - 1} } \right]\)

\(\rho\) :

Density \([{\text{Kg}}\;{\text{m}}^{ - 3} ]\)

\(\overline{\xi }\) :

Zeta potential \([{\text{V}}]\)

\(\sigma^{ * }\) :

Stefan–Boltzmann constant \(\left[ {{\text{W}}\;{\text{m}}^{ - 2} \;{\text{K}}^{ - 4} } \right]\)

\(\overline{\varpi }^{\prime }\) :

The solid fractional volume of nanofluid

\(\varepsilon\) :

Dielectric constant \(\left[ {{\text{F}}\;{\text{m}}^{ - 1} } \right]\)

\(\varepsilon_{0}\) :

Permittivity of vacuum \(\left[ {8.854 \times 10^{ - 12} {\text{F}}\;{\text{m}}^{ - 1} } \right]\)

\(\overline{\phi }^{\prime }\) :

Electrical potential \([{\text{V}}]\)

\(\overline{s}^{\prime }\) :

Extra stress tensor

\(\delta\) :

Wave number

\(\Phi\) :

Viscous dissipation factor

\(\sigma\) :

Electrical conductivity \([{\text{S}}\;{\text{m}}^{1} ]\)

\(k_{1}\) :

Debye-Hückel parameter

\(\beta\) :

Mobility of the medium

\(\psi\) :

Stream function \(\left[ {{\text{m}}^{2} \;{\text{s}}^{ - 1} } \right]\)

\({\text{nf}}\) :

Properties of nanofluid

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

Properties of base fluid

\({\text{np}}\) :

Properties of nanoparticles

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Authors and Affiliations

  1. Research Scholar, Research and Development Center, Bharathiar University, Coimbatore, Tamil Nadu, 641 046, India

    J. Kamalakkannan

  2. Department of Science and Humanities, Adhiparasakthi College of Engineering, Kalavai, Tamil Nadu, 632 506, India

    C. Dhanapal

  3. Department of Mathematics, University College of Engineering, Arni, Tamil Nadu, 632 326, India

    M. Kothandapani

  4. Department of Mathematics, Sri Sai Ram Engineering College, West Tambaram, Chennai, Tamil Nadu, 600 044, India

    A. Magesh

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  1. J. Kamalakkannan
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  2. C. Dhanapal
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Kamalakkannan, J., Dhanapal, C., Kothandapani, M. et al. Peristaltic transport of non-Newtonian nanofluid through an asymmetric microchannel with electroosmosis and thermal radiation effects. Indian J Phys 97, 2735–2744 (2023). https://doi.org/10.1007/s12648-023-02636-9

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