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

  • I. L. AnimasaunEmail author
  • B. Mahanthesh
  • O. K. Koriko
Original Paper


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.


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

List of symbols


Dimensional concentration of the bulk fluid

b and A

Thickness parameters


Characteristics of Eyring–Powell


Skin friction coefficient


Mass diffusivities

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

Dimensionless velocity

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

Concentration of the bulk fluid


Buoyancy parameter


Acceleration due to gravity

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

Concentration of the catalyst


Strength of homogeneous reaction

\(\kappa _{nf}\)

Thermal conductivity of nanofluid

\(\kappa _{bf}\)

Thermal conductivity of the base fluid


Rosseland mean absorption coefficient


Chemical rate coefficients


Velocity power index


Local Nusselt number


Prandtl number


Radiative heat flux


Radiation parameter


Temperature of the fluid


Wall temperature

\(T_{\infty }\)

Free stream temperature


Velocity component in x-direction


Velocity component in y-direction


Distance along the surface


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 \([0,\infty )\)


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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