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Numerical simulation of effects of Soret and Dufour parameters on the peristaltic transport of a magneto six-constant Jeffreys nanofluid in a non-uniform channel: a bio-nanoengineering model

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Abstract

The effect of the Soret and Dufour parameters on the peristaltic transport of a magneto six-constant Jeffreys nanofluids in a non-uniform channel are examined in this research. The mathematical modeling of six-constant Jeffreys nanofluids with double-diffusivity convection and inclined magnetic field is provided with a detailed description. To simplify partial differential equations that are highly nonlinear in nature, the long wavelength and low approximation of the Reynolds number are used. The reduced differential equations are solved by numerical method. The exact temperature, concentration and nanoparticle solutions are calculated. The importance of the various physical parameters of flow quantities is shown in numerical and graphical data. It is observed that the nanosolid particle concentration drops when large values of Brownian motion parameter and Soret number are considered. Furthermore, random collusions transfer molecular kinetic energy into thermal energy during the micro-mixing process of solid nanoparticles within the nanoliquid, resulting in a rise in fluid temperature.

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Abbreviations

U, V :

Velocities in X and Y directions

\(a_{0},a_{1},a_{2} \) :

Material constants

m :

Non-uniform parameter of channel

\({\tilde{a}}\) :

Half width of channel

p :

Pressure

\(\rho _{\mathrm{f}}\) :

Fluid density

\(\rho _{\mathrm{p}}\) :

Nanoparticle mass density

\(\beta _{\mathrm{T}}\) :

Volumetric thermal expansion

\(( \rho c )_{\mathrm{f}}\) :

Heat capacity of fluid

k :

Thermal conductivity

\(\varTheta \) :

Nanoparticle volume fraction

\(D_{\mathrm{B}}\) :

Brownian diffusion coefficient

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

Solutal diffusively

\(D_{\mathrm{CT}}\) :

Soret diffusively

\(\theta \) :

Dimensionless temperature

\(\gamma \) :

Dimensionless solutal concentration

\(\varOmega \) :

Nanoparticle volume fraction

Re :

Reynolds number

\(\psi \) :

Stream function

\(\lambda _{1}\) :

Relaxation time

\(N_{\mathrm{b}}\) :

Brownian motion parameter

\(\beta \) :

Amplitude ratio

\(\eta \) :

Angle of inclination

\(G_{rT}\) :

Thermal Grashof number

\(\mu \) :

Viscosity of fluid

\(\lambda \) :

Wavelength

c :

Propagation of velocity

\({\tilde{t}}\) :

Time

\(b_{0}\) :

Half width at inlet

\(\rho _{f_{0}}\) :

Fluid density at \(T_{0}\)

g :

Acceleration due to gravity

\(\beta _{C}\) :

Volumetric solutal expansion

\((\rho c)_{p}\) :

Heat capacity of nanoparticle

T :

Temperature

C :

Solutal concentration

\(D_{\mathrm{T}}\) :

Thermophoretic diffusion coefficient

\(D_{\mathrm{TC}}\) :

Dufour diffusively

\(G_{rc}\) :

Solutal Grashof number

\(G_{rF}\) :

Nanoparticle Grashof number

Pr :

Prandtl number

\(\delta \) :

Wave number

M :

Hartmann number

Ln :

Nanofluid Lewis number

\(\lambda _{2}\) :

Delay time

\(N_{\mathrm{t}}\) :

Thermophoresis parameter

\(N_{\mathrm{TC}}\) :

Dufour parameter

\(N_{\mathrm{CT}}\) :

Soret parameter

Le :

Lewis number

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Authors and Affiliations

  1. MCS, National University of Sciences and Technology, Islamabad, Pakistan

    Safia Akram

  2. National University of Modern Languages, Islamabad, Pakistan

    Maria Athar

  3. COMSATS University Islamabad, Islamabad, Pakistan

    Khalid Saeed

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  1. Safia Akram
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  2. Maria Athar
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Correspondence to Safia Akram.

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Akram, S., Athar, M. & Saeed, K. Numerical simulation of effects of Soret and Dufour parameters on the peristaltic transport of a magneto six-constant Jeffreys nanofluid in a non-uniform channel: a bio-nanoengineering model. Eur. Phys. J. Spec. Top. 231, 535–543 (2022). https://doi.org/10.1140/epjs/s11734-021-00348-x

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