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A New Model and Analysis for Peristalsis of Carreau–Yasuda (CY) Nanofluid Subject to Wall Properties

  • Research Article-Mechanical Engineering
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Abstract

Peristaltic movement of non-Newtonian nanofluid obeying Carreau–Yasuda (CY) model across a complaint wall channel is formulated through a different approach. Unlike past researches, we consider the well-known Buongiorno’s model without relying on conventional assumption of constant diffusion coefficients. However, the considered model assumes long wavelength of channel walls compared with the channel width. Lower channel wall is heated by providing convection from hot fluid at temperature Tf. The developed system is coupled and nonlinear which seems difficult to be solved exactly. Hence, numerical computations are made by adopting shooting method-based package NDSolve of MATHEMATICA. A considerable effect of wall slip and rheology on the solution profiles is apparent from the computational results. Moreover, the computed results are aimed at predicting the role of Brownian diffusion and thermophoresis in peristalsis especially when wall elastic effects are present.

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Abbreviations

x, y :

Cartesian coordinates

u, v :

Velocity components

d 1 :

Channel width

a 1 :

Wave amplitude

Bi:

Biot number

D B :

Brownian diffusion coefficient

D T :

Thermophoretic diffusion

B 0 :

Magnetic flux density

C :

Wave speed

M :

Hartmann number

C nf :

Effective heat capacity

K nf :

Effective thermal conductivity

ne :

Number of free electrons

Br:

Brinkman number

Pr:

Prandtl number

Ec:

Eckert number

Re:

Reynolds number

We:

Weissenberg number

T :

Time

L :

Heat transfer coefficient

N b :

Brownian motion parameter

N t :

Thermophoresis parameter

N :

Power law index

T :

Local temperature

C :

Local concentration

E 1 :

Wall tension parameter

E 2 :

Mass characterizing parameter

E 3 :

Wall damping parameter

M :

Hall parameter

\(\mu_{0}\) :

Zero shear rate viscosity

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

Effective electrical conductivity

\(\psi\) :

Stream function

\(\delta\) :

Wave number

\(\theta\) :

Non-dimensional temperature

\(\varepsilon\) :

Amplitude ratio

\(\beta\) :

Viscosity ratio parameter

\(\lambda\) :

Wavelength

\(\nu\) :

Kinematic viscosity

\(\dot{\gamma }\) :

Shear rate

\(\mu_{\infty }\) :

Infinite shear rate viscosity

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

Nanofluid density

\(\beta_{1}\) :

Velocity slip parameter

\(\mu \left( {\dot{\gamma }} \right)\) :

Apparent viscosity

\(\varGamma\) :

Material fluid parameter

\(\phi\) :

Nanoparticle concentration

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Authors and Affiliations

  1. Department of Mathematical Sciences, Fatima Jinnah Women University, The Mall, Rawalpindi, 46000, Pakistan

    Sana Maryam Kayani & S. Hina

  2. School of Natural Sciences (SNS), National University of Sciences and Technology (NUST), Islamabad, 44000, Pakistan

    M. Mustafa

Authors
  1. Sana Maryam Kayani
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  2. S. Hina
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  3. M. Mustafa
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Correspondence to S. Hina.

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Kayani, S.M., Hina, S. & Mustafa, M. A New Model and Analysis for Peristalsis of Carreau–Yasuda (CY) Nanofluid Subject to Wall Properties. Arab J Sci Eng 45, 5179–5190 (2020). https://doi.org/10.1007/s13369-020-04359-z

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