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Unsteady MHD Natural Convective Flow of a Rotating Walters’-B Fluid Over an Oscillating Plate with Fluctuating Wall Temperature and Concentration

Published online by Cambridge University Press:  10 April 2017

J. K. Singh ,
N. Joshi  and
P. Rohidas
J. K. Singh*
Affiliation:
Department of MathematicsVijayanagara Sri Krishnadevaraya UniversityBallari, India
N. Joshi
Affiliation:
Department of MathematicsVijayanagara Sri Krishnadevaraya UniversityBallari, India
P. Rohidas
Affiliation:
Department of MathematicsVijayanagara Sri Krishnadevaraya UniversityBallari, India
*
*Corresponding author ([email protected])
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Abstract

In the present study, unsteady MHD boundary layer flow of a rotating Walters’-B fluid (viscoelastic fluid) over an infinite vertical porous plate embedded in a uniform porous medium with fluctuating wall temperature and concentration taking Hall and ion-slip effects into consideration is discussed. The MHD flow in the rotating fluid system is induced due to the non-torsional oscillations of the plate in its own plane and the buoyancy forces arises from temperature and concentration differences in field of gravity. The partial differential equations governing the fluid motion are solved analytically by using regular perturbation and variable separable methods by assuming very small viscoelastic parameter. Solution for velocity field in the case when natural frequency due to rotation and Hall current is equals to the frequency of oscillations i.e. in the case of resonance is also obtained. In order to note the influences of various system parameters and to discuss the important flow characteristics, the numerical results for fluid velocity in the non-resonance case, temperature and species concentration are computed and depicted graphically versus boundary layer parameter whereas skin friction, Nusselt number and Sherwood number at the plate are computed and presented in tabular form. An interesting observation recorded that there arises flow reversal in the primary flow direction due to high rotation. When natural frequency is greater than the frequency of oscillations the fluid velocity in the primary flow direction is maximum at the plate whereas incase when natural frequency is smaller than the frequency of oscillations, it is maximum in the neighborhood of the plate.

Keywords

Walters’-B fluidNatural convectiveRotationHall and ion-slip effects
Type
Research Article
Information
Journal of Mechanics , Volume 34 , Issue 4 , August 2018 , pp. 519 - 532
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2018 

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