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Effects of Variable Viscosity on Asymmetric Flow of Non-Newtonian Fluid Driven Through an Expanding/Contracting Channel Containing Porous Walls

  • Research Article-Mechanical Engineering
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Abstract

Flow in porous channel or pipe has attained significant attention in biophysics, especially when the walls are contracting or expanding. The purpose of this work is to explore the effects of variable viscosity on the asymmetric laminar flow of Casson fluid (CF) with thermal radiation in an expanding/contracting channel having porous walls. The flow equations, by using appropriate transformations, are reduced to ordinary differential equations (ODEs). The method of homotopy analysis (HAM) is used to obtain the expressions for the velocity field along with the temperature profile. Graphs are portrayed for different parametric values and analyzed in detail for the consequent dynamic attributes, especially the viscosity-dependent parameter, CF parameter, and the expansion ratio. CF parameter escalates the velocity of the fluid near the lower wall, but after mid-way, it starts decreasing. The fluid velocity due to temperature-dependent (TD) viscosity parameter is more noteworthy for Newtonian fluid (NF) relative to non-Newtonian (NN) fluid. As anticipated, the radiation parameter causes the fluid to heat up.

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Abbreviations

u, v :

Velocity components in the x- and y-directions [ms−1]

x, y :

Spatial coordinates [m]

t :

Time [s]

T f :

Fluid temperature [K]

T0, Tw :

Fluid temperature at walls [K]

B 0 :

Magnetic field intensity,

p * :

Fluid pressure [kg m−1 s−2]

Pr :

Prandtl number [–]

e ij :

(i,j)th components deformation rate

p y :

Yield stress of Casson fluid

C p :

Specific heat

q :

Dimensionless temperature

q r :

Radiative heat flux

K :

Thermal conductivity [Wm−1 K−1]

A0, A1 :

Both wall permeabilities

A :

Ratio parameter [–]

l1, l2 :

Linear operator

p :

Embedding parameter

K * :

Mean adsorption coefficient

Nr :

Radiation parameter [–]

b :

Half-width of the channel [m]

R0, R1 :

Permeation Reynolds numbers

N1, N2 :

Nonlinear operator

\(\alpha\) :

Wall expansion ratio

\(\mu \left( {T_{f} } \right)\) :

Temperature-dependent viscosity [= \(\mu_{0} \mu \left( q \right)\)]

\(\rho\) :

Fluid density [kg m−3]

\(\beta\) :

Casson fluid parameter [–]

\(\delta\) :

Electric conductivity [sm−1]

\(\beta_{0}\) :

Magnetic field intensity [T]

\(\mu_{0}\) :

Plastic dynamic viscosity of the non-Newtonian fluid [kg m−1 s−1]

\(\eta\) :

Transformed coordinate

\(\varepsilon\) :

Viscosity variation parameter [–]

\(\alpha\) :

Expansion ratio

\(\pi\) :

Product of the components of deformation rate with itself

\(\sigma^{*}\) :

Stefan–Boltzmann constant

\(\pi_{c}\) :

Critical value of this product

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Acknowledgements

Thanks to anonymous reviewers for useful remarks on manuscript improvement.

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Authors and Affiliations

  1. Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur, 63100, Pakistan

    S. Rafiq & Z. Abbas

  2. Department of Mathematics, University of Sialkot, Sialkot, 51310, Pakistan

    M. Sheikh

  3. Department of Computer Sciences, Bahria University Islamabad Campus, Islamabad, 44100, Pakistan

    J. Hasnain

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  1. S. Rafiq
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Rafiq, S., Abbas, Z., Sheikh, M. et al. Effects of Variable Viscosity on Asymmetric Flow of Non-Newtonian Fluid Driven Through an Expanding/Contracting Channel Containing Porous Walls. Arab J Sci Eng 45, 9471–9480 (2020). https://doi.org/10.1007/s13369-020-04798-8

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