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Arabian Journal for Science and Engineering

, Volume 44, Issue 2, pp 873–880 | Cite as

A Numerical Study of Viscous Dissipative Transport of Viscoplastic Fluid Influenced by Induced Magnetic Field

  • Z. Iqbal
  • Zaffar MahmoodEmail author
Research Article - Mechanical Engineering
  • 30 Downloads

Abstract

The present work is a detailed study of a steady two-dimensional stagnation point flow of non-Newtonian fluid toward a linear stretching surface with induced magnetic field. Problem development is accomplished in existence of convective boundary condition. Nonlinear flow analysis is computed with the help of shooting algorithm. Physical characteristics of pertinent parameters have been analyzed through graphs and tables. The main emphasis of the present study is to analyze the impact of induced magnetic field with incorporation of stretching ratio parameter (when \(A<1\) and \(A>1\)) on fluid velocity and temperature profiles. Magnetic and fluid constraints contribute in lowering mass boundary layer thickness for fixed value of stretching ratio parameter. However, magnetic Prandtl number reciprocal, fluid and magnetic parameters contributed in enhancing induced magnetic profile for a fixed value of stretching ratio parameter. Comparison with available results in the literature in limiting sense is achieved. Moreover, heat flux has opposite effects for magnetic and fluid parameters, but has same effects for magnetic Prandtl number.

Keywords

Induced magnetic field Viscous dissipation Stagnation point flow Numerical solution 

List of symbols

\(H_{1}\) and \(H_{2}\)

Magnetic components along x- and y-directions

\(f^{\prime }, g^{\prime }\)

Dimensionless fluid velocity and induced magnetic field

\(\textit{Pr},\textit{Ec}\)

Prandtl number, Eckert number

\(k_\mathrm{w},h_\mathrm{f}\)

Thermal conductivity of fluid, heat transfer coefficient

\(T,T_\mathrm{w},T_{\infty },\)

Fluid, wall and ambient temperatures

\(q_\mathrm{w},H_{0},\epsilon \)

Heat flux, uniform magnetic field, magnetic parameter

\(C_\mathrm{f}, \textit{Nu}, \textit{Re}\)

Skin friction coefficient, local Nusselt, local Reynolds number

\(C_\mathrm{p}\)

Specific heat

uv

Velocity components in x- and y-directions

xy

Cartesian coordinates

\(\textit{Bi}, A\)

Biot number, stretching ratio parameter

Greek symbols

\(\eta ,\theta \)

Dimensionless space variable and temperature

\(\nu ,\mu \)

Kinematic and dynamic viscosities

\(\lambda , \beta \)

Reciprocal magnetic Prandtl number, Casson fluid parameter

Subscripts

\(\mathrm{w}\)

Wall

\(\infty \)

Infinity

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Copyright information

© King Fahd University of Petroleum & Minerals 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of SciencesHITEC UniversityTaxilaPakistan

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