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

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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.

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Abbreviations

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

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)

q w :

Wall heat flux

Re x :

Local Reynolds number

α :

Temperature base thermal diffusivity (m2s−1)

η :

Similarity variable

θ :

Dimensionless temperature

υ :

Kinematic viscosity of the fluid

ρ f :

Fluid density (kgm−1)

ρ p :

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)

T w :

Temperature at the stretching sheet (K)

T ∞ :

Ambient temperature (K)

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Authors and Affiliations

  1. Department of Mathematics, Quaid-i-Azam University, Islamabad, 44000, Pakistan

    Mair Khan & M. Y. Malik

  2. Department of Mathematics, Mirpur University of Science and Technology (MUST), Mirpur, 10250, Pakistan

    T. Salahuddin

Authors
  1. Mair Khan
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  2. T. Salahuddin
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  3. M. Y. Malik
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Correspondence to T. Salahuddin.

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Technical Editor: Cezar Negrao, PhD.

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Khan, M., Salahuddin, T. & Malik, M.Y. Impact of enhancing diffusion on Carreau–Yasuda fluid flow over a rotating disk with slip conditions. J Braz. Soc. Mech. Sci. Eng. 41, 78 (2019). https://doi.org/10.1007/s40430-018-1492-y

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  • DOI: https://doi.org/10.1007/s40430-018-1492-y

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