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On the Motion of Non-Newtonian Eyring–Powell Fluid Conveying Tiny Gold Particles Due to Generalized Surface Slip Velocity and Buoyancy

  • I. L. Animasaun
  • B. Mahanthesh
  • O. K. Koriko
Original Paper
  • 33 Downloads

Abstract

In the painting industry, space science and biomedical science, the nature of relaxation in the flow of non-Newtonian fluid (i.e. blood) containing gold (Ag) suits the characteristics of Eyring–Powell fluid flow induced by generalized surface slip velocity and buoyancy. However, flow of various non-Newtonian fluids on the horizontal surface of a slanted paraboloid of revolution objects (i.e. rocket, as in space science), over a bonnet of a car and over a pointed surface of an aircraft is of importance to experts in all these fields. In this article, the analysis of the motion within the thin layer formed on a horizontal object which is neither a perfect horizontal nor vertical and neither an inclined surface nor a cone/wedge is presented. The transformed governing equations which model the flow was non-dimenzionalized, parameterized and solved numerically using a well-known Runge–Kutta integration procedure along with shooting technique. The influence of increasing the magnitude of major parameters on the temperature distribution, local heat transfer rate, concentration of the fluid, local skin friction coefficient and velocity of the flow are illustrated graphically and discussed. Velocity slip parameter is found to be a decreasing function of temperature distribution across the flow. Heat transfer rate \((Nu_{x}Re_{x}^{-1/2})\) at the wall (\(\xi = 0\)) is an increasing function of velocity slip parameter. Maximum coefficient of concentration of homogeneous bulk fluid at the wall exists at larger values of the emerged velocity slip and volume fraction parameters.

Keywords

Paraboloid of revolution Eyring–Powell fluid Homogeneous–heterogeneous reactions Nonlinear thermal radiation Quartic autocatalysis Chemical reaction 

List of symbols

a

Dimensional concentration of the bulk fluid

b and A

Thickness parameters

c

Characteristics of Eyring–Powell

\(C_{f}\)

Skin friction coefficient

\(D_{A},D_{B}\)

Mass diffusivities

\(f(\eta )\) and \(F(\varsigma )\)

Dimensionless velocity

\(g(\eta )\) and \(G(\xi )\)

Concentration of the bulk fluid

\(G_r\)

Buoyancy parameter

g

Acceleration due to gravity

\(h(\eta )\) and \(H(\xi )\)

Concentration of the catalyst

K

Strength of homogeneous reaction

\(\kappa _{nf}\)

Thermal conductivity of nanofluid

\(\kappa _{bf}\)

Thermal conductivity of the base fluid

\(k^{*}\)

Rosseland mean absorption coefficient

\(k_{1},k_{s}\)

Chemical rate coefficients

m

Velocity power index

\(Nu_{x}\)

Local Nusselt number

\(P_{r}\)

Prandtl number

\(q_{r}\)

Radiative heat flux

R

Radiation parameter

T

Temperature of the fluid

\(T_{w}\)

Wall temperature

\(T_{\infty }\)

Free stream temperature

u

Velocity component in x-direction

v

Velocity component in y-direction

x

Distance along the surface

y

Distance normal to the surface

Greek Symbols

\(\alpha , \aleph \)

Eyring–Powell fluid parameters

\(\beta _j\)

Eyring–Powell parameter

\(\beta _{ep}\)

Vol. coefficients of thermal expansion

\(\delta \)

Ratio of diffusion coefficients

\(\eta \)

Similarity variable \([\chi ,\infty )\)

\(\theta (\eta )\) and \(\Theta (\xi )\)

Dimensionless temperature

\(\vartheta _{nf}\)

Kinematics viscosity of the nanofluid

\(\hbar \)

Generalized slip parameter

\(\Lambda \)

Strength of the heterogeneous reaction

\(\theta _w\)

Temperature parameter

\(\mu _{nf}\)

Viscosity of Erying–Powell nanofluid

\(\mu _{bf}\)

Viscosity of basefluid (blood)

\(\rho \)

Fluid density

\(\ell \)

Dimensional concentration of the catalyst

\(\sigma ^*\)

Stefan–Boltzmann constant

\(\chi \)

Wall thickness parameter

\(\psi (x,y)\)

Stream function

\(\xi \)

Dimensionless distance \([0,\infty )\)

Notes

Compliance with Ethical Standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

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© Springer Nature India Private Limited 2018

Authors and Affiliations

  1. 1.Department of Mathematical SciencesFederal University of TechnologyAkureNigeria
  2. 2.Department of MathematicsChrist UniversityBangaloreIndia

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