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Combined Free and Forced Convection Couette-Hartmann Flow in a Rotating Channel with Arbitrary Conducting Walls and Hall Effects

Published online by Cambridge University Press:  17 August 2016

G. S. Seth ,
S. Sarkar  and
O. D. Makinde
G. S. Seth
Affiliation:
Department of Applied Mathematics Indian School of Mines Dhanbad, India
S. Sarkar*
Affiliation:
Department of Mathematics School of Applied Sciences KIIT University Bhubaneswar, India
O. D. Makinde
Affiliation:
Faculty of Military Sciences Stellenbosch University Saldanha, South Africa
*
*Corresponding author (ssarkar@iitbbs.ac.in; sarkar.ism@gmail.com)
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Abstract

Combined free and forced convection Couette-Hartmann flow of a viscous, incompressible and electrically conducting fluid in rotating channel with arbitrary conducting walls in the presence of Hall current is investigated. Boundary conditions for magnetic field and expressions for shear stresses at the walls and mass flow rate are derived. Asymptotic analysis of solution for large values of rotation and magnetic parameters is performed to highlight nature of modified Ekmann and Hartmann boundary layers. Numerical solution of non-linear energy equation and rate of heat transfer at the walls are computed with the help of MATHEMATICA. It is found that velocity depends on wall conductance ratio of moving wall and on the sum of wall conductance ratios of both the walls of channel. There arises reverse flow in the secondary flow direction near central region of the channel due to thermal buoyancy force. Thermal buoyancy force, rotation, Hall current and wall conductance ratios resist primary fluid velocity whereas thermal buoyancy force and Hall current favor secondary fluid velocity in the region near lower wall of the channel. Magnetic field favors both the primary and secondary fluid velocities in the region near lower wall of the channel.

Keywords

Couette-Hartmann rotating flowFree and forced convectionArbitrary wall conductanceViscous and Joule Dissipations
Type
Research Article
Information
Journal of Mechanics , Volume 32 , Issue 5 , October 2016 , pp. 613 - 629
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2016 

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