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Numerical Study of Carreau Nanofluid Flow Under Slips

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Abstract

The numerical exploration of three dimensional Carreau magneto Nanofluid flow through a stretching sheet has been bestowed with considering nonlinear thermal radiation, velocity, thermal and mass slips. The heat and mass transfer attributes have been reported under the existing important variables in this work. The elementary equations which influence flow are remoulded to a system through the similarity transmutations. The remoulded system together with the boundary restrictions are procured deploying Runge–Kutta 4th order process and Shooting approach numerically. The impacts of involving physical variables on heat and mass transfer features are examined. The impacts of the important variables on skin friction factors have been tackled via tables. The Nusselt number’s estimates and Sherwood number’s estimates have been obtained and tackled via graphs and tables. This study predicts that the velocity distribution is suppressed by greater values of Hartmann number. The temperature profile and concentration profile both upgrade with uplifted estimates of thermophoresis parameter, while they decay with augmented values of thermal slip parameter. The skin friction coefficients improve with hiking estimates of permeability parameter, while depreciate with the ratio of infinite shear rate viscosity to the zero shear rate viscosity. Mounting estimates of Lewis number enhance the temperature distribution.

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Abbreviations

\( a \) :

Positive fixed number

\( b \) :

Positive fixed number

\( B_{0} \) :

Constant magnetic field

\( C \) :

Fluid concentration

\( (C_{p} )_{f} \) :

Specific heat at constant pressure

\( Cf_{x} \) :

Skin friction coefficient along x-direction

\( Cf_{y} \) :

Skin friction coefficient along y-direction

\( C_{\infty } \) :

Ambient fluid concentration

\( C_{W} \) :

Wall surface concentration

\( D_{B} \) :

Brownian diffusion coefficient

\( D_{T} \) :

Thermophoretic diffusion coefficient

\( f \) :

Boundary-layer stream function

\( g \) :

Gravitational acceleration

\( k^{*} \) :

Mean absorption coefficient

\( K_{p} \) :

Permeability of the porous medium

\( K_{r} \) :

Chemical reaction factor

\( K_{1} \) :

Permeability parameter

\( Le \) :

Lewis number

\( M \) :

Hartmann number

\( n \) :

Power law index

\( N^{*} \) :

Concentration to thermal buoyancy forces ratio

\( Nb \) :

Brownian motion parameter

\( N_{R} \) :

The nonlinear radiation parameter

\( Nt \) :

Thermophoresis parameter

\( Nu_{{\bar{x}}} \) :

Local Nusselt number

\( N_{1} \) :

Velocity slip factor for the u velocity component

\( N_{2} \) :

Thermal slip factor

\( N_{3} \) :

Mass slip factor

\( \Pr \) :

Prandtl number

\( q_{r} \) :

Radiative heat flux

\( \text{Re}_{x} \) :

Local Reynolds number in x-direction

\( \text{Re}_{y} \) :

Local Reynolds number in y-direction

\( Sh_{{\bar{x}}} \) :

Local Sherwood number

\( T \) :

Fluid temperature

\( T_{W} \) :

Cone surface temperature

\( T_{\infty } \) :

Free stream temperature

\( u \) :

Component of velocity along x direction

\( U_{w} ,\,V_{w} \) :

Stretching velocities of the surface

\( v \) :

Component of velocity along y direction

\( w \) :

Component of velocity along z direction

\( We \) :

The local Weissenberg number

\( x,\,y,\,z \) :

Coordinate axes

\( \alpha \) :

Thermal diffusivity

\( \alpha^{*} \) :

Ratio of stretching sheet

\( \alpha_{1}^{ * } \) :

Mixed convection parameter

\( \beta^{ * } \) :

The ratio of infinite shear rate viscosity to the zero shear rate viscosity

\( \beta_{c} \) :

Nonlinear convection parameter due to concentration

\( \delta_{c} \) :

Mass slip parameter

\( \delta_{t} \) :

Thermal slip parameter

\( \delta_{u} \) :

Tangential slip parameter

\( \eta \) :

Similarity variable

\( \gamma \) :

Local Biot number

\( \mu_{f} \) :

Dynamic viscosity

\( \mu_{0} \) :

Zero shear rate viscosity

\( \mu_{\infty } \) :

Infinite shear rate viscosity

\( \nu_{f} \) :

Kinematic viscosity

\( \lambda_{0} \) :

Ratio of thermal expansion coefficient

\( \lambda_{1} ,\,\lambda_{2} \) :

Ratio of concentration expansion coefficients

\( \phi \) :

Boundary-layer concentration

\( \rho_{f} \) :

Density of the fluid

\( \sigma \) :

Electrical charge density

\( \sigma * \) :

Stefan Boltzmann constant

\( \theta \) :

Boundary-layer temperature

\( \theta_{w} \) :

Temperature ratio parameter

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Authors and Affiliations

  1. Koneru Lakshmaiah Education Foundation, Vaddeswaram, Guntur, A.P, India

    Penumudi Naga Santoshi

  2. Department of Mathematics, Koneru Lakshmaiah Education Foundation, Vaddeswaram, Guntur, A.P, India

    Gurrampati Venkata Ramana Reddy

  3. Department of Mathematics, Government Degree College, Yellandu, Bhadradri Kothagudem, Telangana, India

    Polarapu Padma

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  1. Penumudi Naga Santoshi
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Naga Santoshi, P., Venkata Ramana Reddy, G. & Padma, P. Numerical Study of Carreau Nanofluid Flow Under Slips. Int. J. Appl. Comput. Math 5, 122 (2019). https://doi.org/10.1007/s40819-019-0706-z

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