Derivation Of Boundary Layer Equations Of Two Special Ferromagnetic Fluid

Ferrofluid is strongly polarized in the presence of a magnetic field. It is astable colloidal liquid, consisting of nano-scale magnetic solid particles, liquidand surface active agent. Electromagnetic fluid is a kind of conductive fluid,such as plasma, liquid metal, and they can generate electricity by cutting themagnetic induction lines. The diflerence between ferrofluid and electromagneticfluid is that electromagnetic fluid does not contain ferromagnetic particles, andwill not be magnetized. A lot of formulas and results about electromagnetic fluidboundary layer equations are given, but there is less work about the boundarylayer equations of ferrofluid .Ferrofluid have wide applications in industrial, med-ical, measurement, and other aspects of aviation: ferrofluid power generation,ferrofluid polishing, the use of ferromagnetic fluid for seamless shaft seal, the useof ferrofluid within magnetic field to remove the tumor and so on. Therefore, it isnecessary to study boundary layer theory and establish boundary layer equationsof ferromagnetic fluid.Based on the boundary layer equations of electromagnetic fluid method,further study of the magnetic fluid boundary layer theory have been done, andunder certain assumptions, this paper established boundary layer equations ofnon-conductive and conductive ferrofluid. In this paper, the magnetic fluid isincompressible, steady and viscous.Firstly, for the non-conductive ferrofliud, this paper derived the decompo-sition form of the ferrohydrodynamic equations, and then gave the expressionof velocity and original velocity according to the boundary conditions. A figuredescribing the dimensionless velocity is given. For the non-conductive Poiseuilleflow, the dimensionless velocity reached to the maximum in the middle of theplate and reached to the minimum on the boundary. For non-conducting Cou-ette flow, the dimensionless velocity reached to the maximum at the one thirdplace of the channel and reached the minimum on the boundary .Secondly, in some special conditions, the ferromagnetic fluid is conductive,in practice, especially in the magnetic fluid power generation experiments, it isnecessary to consider the case of ferromagnetic conductive fluid. Therefore, thispaper derived the decomposition form of the ferrohydrodynamic equations for conductive ferrofluid, and then gave the expression of velocity and original veloc-ity according to the boundary conditions. A figure describing the dimensionlessvelocity is given. For the conductive Poiseuille flow, the paper obtained thatwhen Fa is greater, speed curve is stable, but near the pipe wall the velocitygradient is also greater. The dimensionless velocity reached to the maximum inthe middle of the plate and reached the minimum on the boundary. For the con-ductive Couette flow, when Fa is greater, the speed curve is stable, but near thepipe wall the velocity gradient is also greater. The dimensionless velocity reachedto the minimum on the boundary. Compared to non-conductive magnetic fluid,electromagnetic force is also be considered.