Abstract
The well-known problem of unidirectional plane flow of a fluid in a non-porous half-space due to the impulsive motion of the rigid plane wall it rests upon is discussed in the context of an unsteady MHD third-grade fluid in presence of Hall currents. The governing non-linear partial differential equations describing the problem are converted to a system of non-linear ordinary differential equations by using the similarity transformations. The complex analytical solution is found by using the homotopy analysis method (HAM). The existing literature on the topic shows that it is the first study regarding the effects of Hall current on flow of an unsteady MHD third-grade fluid over an impulsively moving plane wall. The convergence of the obtained complex series solutions is carefully analyzed. The effects of dimensionless parameters on the velocity are illustrated through plots and the effects of the pertinent parameters on the local skin friction coefficient at the surface of the wall are presented numerically in tabular form.
Highlights
Almost every student of fluid mechanics is familiar with Stokes’ first problem [1], the flows over a plane wall which is initially at rest and is suddenly set into motion in its own plane with a constant velocity is termed as Stokes’ first problem [2] [3]
Stokes’ first problem for Oldroyd-B and second grade fluid in a porous half space is studied by Tan and Masuoka [12] [13]
The effects of the material parameters of the third-grade fluid, Hall parameter, Hartmann number and homotopy parameter on the velocity and its time series are investigated for the impulsive motion of the wall
Summary
Almost every student of fluid mechanics is familiar with Stokes’ first problem [1], the flows over a plane wall which is initially at rest and is suddenly set into motion in its own plane with a constant velocity is termed as Stokes’ first (or Rayleigh-type) problem [2] [3]. How to cite this paper: Zaman, H., et al (2014) Stokes First Problem for an Unsteady MHD Third-Grade Fluid in a NonPorous Half Space with Hall Currents. Stokes’ first problem for Oldroyd-B and second grade fluid in a porous half space is studied by Tan and Masuoka [12] [13]. Hayat et al [18] presented numerical solution of Stokes’ first problem for a third grade fluid in a porous half space. The present investigation is to analyze the Stokes first problem for an unsteady MHD third-grade fluid in a non-porous half space with Hall currents. The effects of the material parameters of the third-grade fluid, Hall parameter, Hartmann number and homotopy parameter on the velocity and its time series are investigated for the impulsive motion of the wall. Sometimes our graphs for real and imaginary parts of velocity look likes that they are not satisfying boundary conditions, but it is not true because we are not plotting the complete solution, we are taking either real part or imaginary part of the solution
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
