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Impact of enhancing diffusion on Carreau–Yasuda fluid flow over a rotating disk with slip conditions

  • Mair Khan
  • T. SalahuddinEmail author
  • M. Y. Malik
Technical Paper
  • 33 Downloads

Abstract

The present study is devoted to acquire non-similar solutions for the behavior of slip conditions on the steady MHD Carreau–Yasuda fluid flow over a rotating disk. In order to examine the heat transfer phenomena, superior form of Fourier’s law is used and the conductivity of the fluid is assumed to be changeable. The nonlinear partial differential equations leading the flow and thermal field are written in the non-dimensional ordinary differential form by using suitable transformations. The non-dimensional set of coupled ordinary differential equations is solved using the RK method. The impact of various non-dimensional physical parameters on velocity and temperature fields is explored. The numerical results of resistant force in terms of the skin friction coefficient are revealed graphically for various physical parameters involved in the problem.

Keywords

MHD Slip conditions Generalized Fourier’s law Variable thermal conductivity Carreau–Yasuda fluid model Rotating disk Shooting method 

List of symbols

\(C_{f} ,C_{g}\)

Skin friction coefficient

We

Weissenberg number

d

Fluid parameter

n

Power law index

\(\varGamma^{d}\)

Time constant

f(η)

Dimensionless stream function

κ

Thermal conductivity (Wm−1K−1)

\(\tau\)

Extra tensor

\(\mu_{0}\)

Zero shear rate viscosity

\(\mu_{\infty }\)

Infinite shear rate viscosity

\(k_{f}\)

Generally supposed to be constant

Pr

Prandtl number

ρ

Fluid pressure

(ρC)f

Heat capacity of the fluid (Jm−3K−1)

(ρC)p

Effective heat capacity of the nanoparticle material (Jm−3K−1)

qw

Wall heat flux

Rex

Local Reynolds number

α

Temperature base thermal diffusivity (m2s−1)

η

Similarity variable

θ

Dimensionless temperature

υ

Kinematic viscosity of the fluid

ρf

Fluid density (kgm−1)

ρp

Nanoparticle mass density (kgm−1)

σ

Electrical conductivity of the fluid

λ

Velocity slip parameter

Ha

Hartmann number

\(\delta_{t}\)

Thermal relaxation parameter

ψ

Stream function (m2s−1)

Condition at the free stream

w

Condition of the surface

\(\lambda_{1}\)

Tangential slip parameter

T

Fluid temperature (K)

Tw

Temperature at the stretching sheet (K)

T

Ambient temperature (K)

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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  1. 1.Department of MathematicsQuaid-i-Azam UniversityIslamabadPakistan
  2. 2.Department of MathematicsMirpur University of Science and Technology (MUST)MirpurPakistan

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