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Optimal Homotopy Asymptotic Solution for Cross-Diffusion Effects on Slip Flow and Heat Transfer of Electrical MHD Non-Newtonian Fluid Over a Slendering Stretching Sheet

  • Gossaye AliyEmail author
  • Naikoti Kishan
Original Paper
  • 37 Downloads

Abstract

In this paper, the problem of cross-diffusion and electric field effects on the MHD Williamson fluid flow across a variable thickness stretching sheet with flow slip is presented. The transformed differential equations are solved by using the optimal homotopy asymptotic method. Comparison of results has been made with the numerical solutions from the literature and an interesting covenant has been observed. Subsequently, the effects of governing parameters on the flow, heat and mass transfer characteristics of the problem are presented graphically and discussed exhaustively. Results reveal that velocity and temperature increase with an increase in the electric field. Finally, we observed that the Dufour and Soret numbers have drifted to control the thermal and concentration boundary layers.

Keywords

OHAM Soret Dufour Electric field Slendering sheet Viscous dissipation 

List of Symbols

\( u, v \)

Velocity components in x and y directions

\( f \)

Dimensionless velocity

\( B \)

Magnetic field vector

\( K \)

Thermal conductivity

\( K_{T} \)

Thermal diffusion ratio

\( T_{m} \)

Mean fluid temperature

\( C_{\infty } \)

Concentration of the fluid in the free stream

\( L_{2}^{*} \)

Dimensional temperature jump parameter

\( r_{1} \)

Maxwell’s reflection coefficient

\( b \)

Physical parameter related to stretching sheet

\( m \)

Velocity power index parameter

\( M \)

Magnetic interaction parameter

\( g \)

Dimensionless temperature

\( Sc \)

Schmidt number

\( L_{1} \)

Dimensionless velocity slip parameter

\( L_{3} \)

Dimensionless concentration jump parameter

\( Nu_{x} \)

Local Nusselt number

\( Re_{x} \)

Local Reynolds number

\( C_{p} \)

Specific heat capacity

\( A \)

Coefficient related to stretching sheet

T

Temperature of the fluid

\( D_{m} \)

Molecular diffusivity

C

Concentration of the fluid

\( T_{\infty } \)

Temperature of the fluid

\( L_{1}^{*} \)

Dimensional velocity slip parameter

\( L_{3}^{*} \)

Dimensional conc. jump parameter

\( a \)

Thermal accommodation coefficient

\( d \)

Concentration accommodation coeff

\( Pr \)

Prandtl number

\( Du \)

Dufour number

\( h \)

Dimensionless concentration

\( Sr \)

Soret number

\( L_{2} \)

Thermal slip parameter

\( C_{f} \)

Skin friction coefficient

\( Sh_{x} \)

Local Sherwood number

Greek Symbols

\( \eta \)

Similarity variable

\( \sigma \)

Electrical conductivity of the fluid

\( \rho \)

Density of the fluid

\( \mu \)

Dynamic viscosity

\( \nu \)

Kinematic viscosity

\( \alpha \)

Wall thickness parameter

\( \xi_{1} \)

Mean free path (constant)

\( \Gamma \)

Positive characteristic time

\( \Lambda \)

Williamson fluid parameter

Notes

Compliance with Ethical Standards

Conflict of interest

The authors declare that there is no conflict of interests concerning the publication of this research paper.

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Copyright information

© Springer Nature India Private Limited 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of GondarGondarEthiopia
  2. 2.Department of MathematicsOsmania UniversityHyderabadIndia

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