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Thermophoresis on boundary layer heat and mass transfer flow of Walters-B fluid past a radiate plate with heat sink/source

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Abstract

The Walters-B liquid model is employed to simulate medical creams and other rheological liquids encountered in biotechnology and chemical engineering. This rheological model introduces supplementary terms into the momentum conservation equation. The combined effects of thermal radiation and heat sink/source on transient free convective, laminar flow and mass transfer in a viscoelastic fluid past a vertical plate are presented by taking thermophoresis effect into account. The transformed conservation equations are solved using a stable, robust finite difference method. A parametric study illustrating the influence of viscoelasticity parameter (Γ), thermophoretic parameter (τ), thermal radiation parameter (F), heat sink/source (ϕ), Prandtl number (Pr), Schmidt number (Sc), thermal Grashof number (Gr), solutal Grashof number (Gm), temperature and concentration profiles as well as local skin-friction, Nusselt and Sherwood number is conducted. The results of this parametric study are shown graphically and inform of table. The study has applications in polymer materials processing.

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Abbreviations

x, y:

Coordinates along the plate generator and normal to the generator respectively

u, v:

Velocity components along the x- and y-directions respectively

g:

Gravitational acceleration

t′:

Time

t:

Dimensionless time

Gr :

Thermal Grashof number

Gm:

Solutal Grashof number

F:

Radiation parameter

k 0 :

Walters-B viscoelasticity parameter

NuX :

Non-dimensional local Nusselt number

Pr:

Prandtl number

T′:

Temperature

T:

Dimensionless temperature

C′:

Concentration

C:

Dimensionless concentration

D:

Mass diffusion coefficient

N:

Buoyancy ration number

U, V:

Dimensionless velocity components along the X- and Y-directions respectively

X, Y:

Dimensionless spatial coordinates along the plate generator and normal to the generator respectively

Sc:

Schmidt number

ShX :

Non-dimensional local Sherwood number

α:

Thermal diffusivity

β:

Volumetric thermal expansion coefficient

β * :

Volumetric concentration expansion coefficient

Γ:

Viscoelastic parameter

τ :

Thermophoretic parameter

Φ:

Heat sink/source parameter

ν :

Kinematic viscosity

Δt :

Dimensionless time-step

ΔX :

Dimensionless finite difference grid size in X-direction

ΔY :

Dimensionless finite difference grid size in Y-direction

τ X :

Dimensionless local skin-friction

w :

Condition on the wall

∞:

Free stream condition

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Acknowledgments

The authors are grateful to reviewers for their constructive comments which have helped to improve the present article. One of the authors (B. Vasu) is thankful to the Motilal Nehru National Institute of Technology Allahabad, India for the necessary support.

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Authors and Affiliations

  1. Department of Mathematics, Motilal Nehru National Institute of Technology, Allahabad, 211004, India

    B. Vasu

  2. Department of Mechanical and Civil Engineering, Purdue University Northwest, Westville, IN, 46391, USA

    Rama Subba Reddy Gorla

  3. Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, India

    P. V. S. N. Murthy

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  1. B. Vasu
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  3. P. V. S. N. Murthy
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Correspondence to Rama Subba Reddy Gorla.

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Vasu, B., Gorla, R.S.R. & Murthy, P.V.S.N. Thermophoresis on boundary layer heat and mass transfer flow of Walters-B fluid past a radiate plate with heat sink/source. Heat Mass Transfer 53, 1553–1570 (2017). https://doi.org/10.1007/s00231-016-1917-z

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