Abstract
A mathematical model for magnetohydrodynamic (MHD) three-dimensional Couette flow of an incompressible Maxwell fluid is developed and analyzed theoretically. The application of transverse sinusoidal injection at the lower stationary plate and its equivalent removal by suction through the uniformly moving upper plate lead to three-dimensional flow. Approximate solutions for velocity field, pressure, and skin friction are obtained. The effects of flow parameters such as Hartmann number, Reynolds number, suction/injection parameter, and the Deborah number on velocity components, skin friction factors along main flow direction and transverse direction, and pressure through parallel porous plates are discussed graphically. It is noted that Hartmann number provides a mechanism to control the skin friction component along the main flow direction.
Highlights
In recent years, the problem of LFC has gained considerable importance due to its importance in the reduction of drag and in improving the vehicle power by a considerable amount
Singh [3] studied the effect of transpiration cooling in the presence of the transverse sinusoidal suction/injection velocity
Chaudhary et al [4] analyzed three-dimensional Couette flow in the presence of transpiration cooling between the plates and reported the effects of suction/injection velocity on the flow field, skin friction, and heat transfer
Summary
The problem of LFC (laminar flow control) has gained considerable importance due to its importance in the reduction of drag and in improving the vehicle power by a considerable amount. In the design of heat exchangers and pumps and flow meters, thermal protection, control, and reentry, in space propulsion and so Mathematical Problems in Engineering forth, MHD principle is used by engineers It has been proven theoretically and experimentally that the transition from laminar to turbulent flow which causes the drag coefficient to increase may be prevented/delayed by suction of the fluid by the application of transverse magnetic field and by heat and mass transfer from the boundary layer to the wall. Das [12] studied three-dimensional MHD Couette flow of a viscous incompressible fluid with heat transfer through a porous plate and reported effects of constant suction and sinusoidal injection on the flow. The article is organized as follows: Section 2 presents description of the problem, Section 3 gives formulation of the problem, Section 4 approximates solutions, and Section 5 incorporates results and discussion, while Section 6 includes conclusion
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