The Effect of Hall Current on Unsteady MHD Free Convective Couette Flow of a Bingham Fluid with Thermal Radiation
S. Harisingh Naik1, K. Rama Rao2, M. V. Ramana Murthy3
1S. Harisingh Naik, Department of Mathematics and Computer Science University College of Science, Osmania University, Hyderabad, (Andhra Pradesh), India.
2K. Rama Rao, Department of Mathematics, Chaithanya Bharathi Institute of Technology (C. B. I. T), Gandipet, Hyderabad, (Andhra Pradesh), India.
3M. V. Ramana Murthy, Department of Mathematics and Computer Science University College of Science, Osmania University, Hyderabad, (Andhra Pradesh), India.
Manuscript received on July 28, 2014. | Revised Manuscript received on August 14, 2014. | Manuscript published on August 30, 2014. | PP: 1-16 | Volume-3 Issue-6, August 2014. | Retrieval Number: F3259083614/2013©BEIESP
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Abstract: The objective of this study to find the numerical solution of unsteady magneto hydrodynamic flow of an electrically conducting viscous incompressible non – Newtonian Bingham fluid bounded by two parallel non – conducting porous plates is studied with thermal radiation considering the Hall Effect. An external uniform magnetic field is applied perpendicular to the plates and the fluid motion is subjected to a uniform suction and injection. The lower plate is stationary and the upper plate moves with a constant velocity and the two plates are kept at different but constant temperatures. The fluid is considered to be a gray, absorbing emitting but non – scattering medium and the Roseland approximation is used to describe the radioactive heat flux in the energy equation. Numerical solutions are obtained for the governing momentum and energy equations taking the Joule and viscous dissipations into consideration. The dimensionless governing coupled, non – linear boundary layer partial differential equations are solved by an efficient, accurate, and extensively validated and unconditionally stable finite difference scheme of the Crank – Nicolson method. The effects of the Hall term, the parameter describing the non – Newtonian behavior, thermal radiation parameter and the velocity of suction and injection on both the velocity and temperature distributions are studied through graphs and tabular form.
Keywords: Couette flow, Thermal radiation, Bingham fluid, Hall Effect and Finite difference method.