Abstract
This work numerically studies the flow pattern of a magnetic fluid filled within an annulus whose inner cylinder is moving at a constant rotational speed, while the outer cylinder is stationary but under the influence of a nonuniform external magnetic field. The magnetic field consists of four basic configurations, that is, completely circular, semicircular, quarter circular, and alternately quarter circular. The strength of the external magnetic field is characterized using a reference Hartmann number. As the reference Hartmann number increases, the fluid elements need to overcome greater resistance to enter the region with magnetic field. Hence, there always exists an apparent recirculation cell within the region without externally applied magnetic field. The strength and size of the recirculation cell depend on the reference Hartmann number, the number and size of the discrete regions without external magnetic field. Only the shear stress on the moving cylinder always increases in magnitude with the reference Hartmann number and the span of the single external magnetic field region. Splitting and separating the external magnetic field may increase the magnitude of the shear stress on the moving inner cylinder but decrease that on the stationary outer cylinder. If the magnitude of the shear stress on the outer cylinder reduces beyond zero, a shear stress in the opposite sense will increase in magnitude with Hartmann number.
Highlights
The study of magnetohydrodynamics MHD has recently become a topic of study which has attracted a lot of attention
The induced electric field interacts with the overall magnetic field to produce Lorentz force that acts on the fluid elements
The purpose of this paper is to numerically study the flow pattern of a magnetic fluid filled within an annulus under the influence of different nonuniform externally applied magnetic field configurations
Summary
The study of magnetohydrodynamics MHD has recently become a topic of study which has attracted a lot of attention. In the 1960s, Papell of NASA mixed very fine magnetite particles below 10 nm with appropriate surfactant so that the nanomagnetite could be effectively dispersed in nonpolar solvents 1. He successfully produced a magnetic fluid which had demonstrated many very distinctive physical behaviors. Under the influence of an external magnetic field, a conducting magnetic fluid in motion will produce an electromotive force that causes an induced electric current to flow. The presence of this induced electric field in turn produces an induced magnetic field. Since the Lorentz force acts to oppose the mechanisms that create it, it generally serves to reduce the magnitude of fluid element velocity field
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