The Rayleigh Problem for a Third Grade Electrically Conducting Fluid in a Magnetic Field

Tasawar Hayat Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan E-mail: [email protected]

Herman Mambili-Mamboundou Centre for Differential Equations, Continuum Mechanics and Applications, School of Computational and Applied Mathematics, University of the Witwatersrand, Johannesburg, Private Bag 3, Wits, 2050, South Africa E-mail: [email protected]@wits.ac.za

Ebrahim Momoniat Centre for Differential Equations, Continuum Mechanics and Applications, School of Computational and Applied Mathematics, University of the Witwatersrand, Johannesburg, Private Bag 3, Wits, 2050, South Africa E-mail: [email protected]@wits.ac.za

Fazal M Mahomed Centre for Differential Equations, Continuum Mechanics and Applications, School of Computational and Applied Mathematics, University of the Witwatersrand, Johannesburg, Private Bag 3, Wits, 2050, South Africa E-mail: [email protected]@wits.ac.za

Abstract

The influence of a magnetic field on the flow of an incompressible third grade electrically conducting fluid bounded by a rigid plate is investigated. The flow is induced due by the motion of a plate in its own plane with an arbitrary velocity. The solution of the equations of conservation of mass and momentum balance are obtained analytically. We also present numerical solutions with particular choices of the magnetic field and boundary conditions. Emphasis has been given to the study of the effects of the magnetic field and non-Newtonian fluid parameters.

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The Rayleigh Problem for a Third Grade Electrically Conducting Fluid in a Magnetic Field

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