Hartmann Flow in a Rotating System in the Presence of Inclined Magnetic Field with Hall Effects

G. S.  Seth; Raj  Nandkeolyar; Md. S.  Ansari

doi:10.6180/jase.2010.13.3.03

Hartmann Flow in a Rotating System in the Presence of Inclined Magnetic Field with Hall Effects

G. S. Seth¹, Raj Nandkeolyar This email address is being protected from spambots. You need JavaScript enabled to view it.¹ and Md. S. Ansari¹

¹Department of Applied Mathematics, Indian School of Mines University, Dhanbad-826004, India

Received: February 20, 2009
Accepted: August 14, 2009
Publication Date: September 1, 2010

Download Citation: ||https://doi.org/10.6180/jase.2010.13.3.03

ABSTRACT

Hartmann flow of a viscous incompressible electrically conducting fluid in a rotating system in the presence of an inclined magnetic field is studied. Solution for the velocity and induced magnetic field, in dimensionless form, contains four pertinent parameters viz. M² (square of Hartmann number), K² (rotation parameter), m (Hall current parameter) and θ (angle of inclination of magnetic field). Asymptotic behavior of this solution is analyzed for small and large values of and to gain some physical insight into the flow-pattern. For large values of K² and M², the flow field is divided into two regions, namely, (1) boundary layer region and (2) central core region. The expressions for the shear stress at the plates of channel due to the primary and secondary flows and mass flow rates in the primary and secondary flow directions are derived. The numerical values of the velocity and induced magnetic field are depicted graphically for various large values of M² and K². It is found that the maxima of velocity profiles occur near the walls of channel which indicates the formation of boundary layers near the walls. The energy equation taking viscous and Joule dissipations into account is solved numerically with the help of MATLAB software and the solution for the fluid temperature T is presented graphically for various values of M², K², m, θ and P_r. It is found that the magnetic field decreases fluid temperature whereas rotation, Hall current, angle of inclination and Prandtl number increase it.

Keywords: Coriolis Force, Hall Current, Modified Hartmann Boundary Layer, Modified Hydromagnetic Ekman Boundary Layer, Viscous and Joule Dissipations

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