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Thermal analysis for heat transfer enhancement in electroosmosis-modulated peristaltic transport of Sutterby nanofluids in a microfluidic vessel

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A Correction to this article was published on 12 March 2019

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Abstract

A theoretical study is conducted for magnetohydrodynamic pumping of electroosmotic non-Newtonian physiological nanoliquids through a two-dimensional microfluidic channel. The Sutterby rheological nanofluid model is utilized to characterize the liquid. The normalized two-dimensional conservation equations for mass, longitudinal and transverse momentum, energy and solutal concentration are reduced with lubrication approximations (long wavelength and low Reynolds number assumptions). A coordinate transformation is employed to map the unsteady problem from the wave laboratory frame to a steady problem in the wave frame. Slip and convective conditions are imposed at the channel walls. The emerging boundary value problem is solved numerically using MATLAB software. The flow is effectively controlled by many geometric parameters, viz., electroosmosis, Hartmann and Sutterby fluid parameters. It is observed from the analysis that the rise in magnetic and electroosmosis effects leads to a reduction in the axial velocity field. The radiation parameter decreases the temperature for the positive value of Joule heating parameter and the trend is revered for the negative Joule heating parameter. This study is encouraged by exploring the nanofluid dynamics in peristaltic transport as symbolized by heat transport in biological flows, novel pharmacodynamics pumps and gastrointestinal motility enhancement. The study is also relevant to MHD biomimetic blood pumps.

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Change history

  • 12 March 2019

    The original article was published with typographical errors in the non-dimensionalization and parameters involved in the equations.

Abbreviations

\(A_{1}\) :

Deformation tensor

\(a\) :

Half-width of the channel

\(B_{0}\) :

Uniform transverse magnetic field

\(\bar{B}\) :

External imposed magnetic field

\(b\) :

Wave amplitude of the channel

\(B,\,m\) :

Material constants

\(Bh\) :

Thermal Biot number

\(Bm\) :

Concentration Biot number

\(c\) :

Speed of the wave

\(C\) :

Nanoparticle concentration

\(D\) :

Diffusivity of the chemical species

\(D_{\text{s}}\) :

Solutal diffusivity of the electrolyte

\(D_{\text{ct}}\) :

Soret diffusivity

\(Da\) :

Darcy number

\(D_{\text{tc}}\) :

Dufour diffusivity

\(e\) :

Electronic charge

\(E_{\text{x}}\) :

Applied electrical field

\(Gr_{\text{t}}\) :

Thermal Grashof number

\(Gr_{\text{c}}\) :

Solutal Grashof number

\(g\) :

Gravitation due to the gravity

\(\bar{J}\) :

Current density

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

Thermal conductivity

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

Chemical reaction parameter

\(k^{ * }\) :

Mean absorption coefficient

\(M\) :

Hartmann number

\(N_{\text{tc}}\) :

Dufour thermo-diffusive parameter

\(N_{\text{ct}}\) :

Soret diffuse thermo-parameter

\(P\) :

Pressure in the fixed frame

\(p\) :

Pressure in the wave frame

\(Pe\) :

Ionic Peclet number

\(Pr\) :

Prandtl number

\(Q\) :

Volumetric flow rate in the fixed frame

\(\bar{q}\) :

Velocity vector

\(q\) :

Volumetric flow rate in the wave frame

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

Radioactive heat flux

\(\bar{R}\) :

Modified Darcy resistance

\(Rn\) :

Radiation parameter

\(S\) :

Joule heating parameter

\(\bar{S}\) :

Extra stress tensor for Sutterby fluid model

\(Sc\) :

Schmidt number

\(T\) :

Temperature

\(t\) :

Time

\(U,V\) :

Velocity components in the fixed frame

\(u,v\) :

Velocity components in the wave frame

\(X,Y\) :

Coordinates of the fixed frame

\(x,y\) :

Coordinates of the wave frame

\(Uhs\) :

Helmholtz–Smoluchowski velocity

\(z\) :

Charge balance

\(\lambda\) :

Wavelength

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

Density of the fluid

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

Thermal expansion coefficient

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

Coefficient of expansion with concentration

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

Electrical charge density

\(\left( {\rho c_{\text{p}} } \right)_{\text{f}}\) :

Heat capacity of the nanofluid

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

Electrical conductivity

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

Effective viscosity

\(k\) :

Permeability

\(\phi\) :

Porosity of the medium

\(\sigma^{ * }\) :

Stefan–Boltzmann constant

\(\alpha\) :

Velocity slip parameter

\(\kappa_{\text{h}}\) :

Heat transfer coefficient

\(\kappa_{\text{m}}\) :

Mass transfer coefficient

\(\eta_{\text{h}}\) :

Thermal conductivity coefficient

\(\eta_{\text{m}}\) :

Mass diffusivity coefficient

\(\varPsi\) :

Electric potential

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

Dielectric constant

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

Net charge density of the electrolyte

\(\kappa\) :

Electroosmotic parameter

\(\lambda_{\text{d}}\) :

Characteristic thickness of electrical double layer

\(\beta\) :

Non-dimensional Sutterby nanofluid parameter

\(\varGamma\) :

Dimensionless chemical reaction parameter

\(\alpha\) :

Dimensionless velocity slip parameter

\(\phi\) :

Wave amplitude ratio

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Acknowledgements

The authors are thankful to the reviewers for their useful suggestions and comments which improved the quality of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Symbiosis Institute of Technology, Symbiosis International University, Pune, 412115, India

    K. Ramesh

  2. Department of Mathematics, Srinivasa Ramanujan Center, SASTRA Deemed University, Kumbakonam, Tamilnadu, 612001, India

    J. Prakash

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Ramesh, K., Prakash, J. Thermal analysis for heat transfer enhancement in electroosmosis-modulated peristaltic transport of Sutterby nanofluids in a microfluidic vessel. J Therm Anal Calorim 138, 1311–1326 (2019). https://doi.org/10.1007/s10973-018-7939-7

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