Abstract
The unsteady magnetohydrodynamic flow of an electrically conducting viscous incompressible non-Newto- nian Casson fluid bounded by two parallel non-conducting porous plates has been studied with heat transfer considering the Hall effect. The fluid is acted upon by a uniform and exponential decaying pressure gradient. 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 is suddenly set into mo- tion and simultaneously suddenly isothermally heated to a temperature other than the lower plate temperature. Numerical solutions are obtained for the governing momentum and energy equations taking the Joule and viscous dissipations into consideration. The effect of unsteady pressure gradient, the Hall term, the parameter describing the non-Newtonian behavior on both the velocities and temperature distributions have been stud- ied.
Highlights
The study of Couette flow in a rectangular channel of an electrically conducting viscous fluid under the action of a transversely applied magnetic field has immediate applications in many devices such as magnetohydrodynamic (MHD) power generators, MHD pumps, accelerators, aerodynamics heating, electrostatic precipitation, polymer technology, petroleum industry, purification of crude oil and fluid droplets sprays
Channel flows of a Newtonian fluid with heat transfer were studied with or without Hall currents by many authors [1,2,3,4,5,6,7,8,9,10]
Casson fluid is a shear thinning liquid which has an infinite viscosity at a zero rate of shear
Summary
The study of Couette flow in a rectangular channel of an electrically conducting viscous fluid under the action of a transversely applied magnetic field has immediate applications in many devices such as magnetohydrodynamic (MHD) power generators, MHD pumps, accelerators, aerodynamics heating, electrostatic precipitation, polymer technology, petroleum industry, purification of crude oil and fluid droplets sprays. Attia [10] studied the influence of the Hall current on the velocity and temperature fields of an unsteady Hartmann flow of a conducting Newtonian fluid between two infi- nite non-conducting horizontal parallel and porous plates. Attia and Sayed-Ahmed [17] studied the influence of the Hall current on the velocity and temperature fields of an unsteady Couettee flow of a conducting Casson fluid between two infinite non-conducting horizontal parallel plates with constant pressure gradient. The extension of such problem to the case of Couettee flow of non-Newtonian Casson fluid has been done in the present study. The inclusion of unsteady pressure gradient, the Hall current, the suction and injection, and the non-Newtonian fluid characteristics leads to some interesting effects on both the velocity and temperature fields
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