Hydromagnetic Couette flow between two vertical semi-infinite permeable plates

Abstract

In the present study, a hydromagnetic Couette flow between two vertical semi-infinite permeable plates with uniform injection/suction while considering Joule heating has been investigated. The plate where injection takes place is stationary while the other plate moves with a time dependant velocity in the x-direction. Also, a constant magnetic field is applied perpendicular to the stationary plate. The study involves an electrically conducting fluid flow that is incompressibe, viscous and unsteady. The equations that govern the flow which are continuity equation, momentum equation and energy equation were formed and then non-dimensionalised. Due to the non-linear nature of the equations, they cannot be solved analytically and therefore, the method of solution was the finite difference numerical technique because it is more stable and accurate. The results were analyzed and presented graphically. It was established that various non-dimensional parameters such as Joule Heating parameter, Prandtl Number, Eckert Number and other non-dimensional parameters had effects on temperature and velocity profiles which were discussed into details. The effects of varying these parameters led to either increase, decrease or no effect on flow variables. The findings of this study shall be applied in areas such as the design of cooling systems with liquid metal, electrostatic precipitation, purification of crude oil, petroleum industry, aerodynamic heating, polymer technology, accelerators and many others