Numerical Simulation of Magneto-Rheological Fluids

This work pertains to modern, interdisciplinary§research trends in nanomaterials. The author presents§a novel method with major potential for various§applications such as ferromagnetic brakes and valves;§nanosized shock absorbers, and in the medical field,§heart valves and medical nanorobots. A mathematical§model is constructed with numerical solutions§proposed for the system of equations describing the§model. The underlying assumption is that a§ferromagnetic suspension can be regarded as a§continuous medium. Such an assumption was originally§suggested in Peskin s Immersed Boundary (IB) method.§The IB method is coupled with Chorin s Projection§method to construct a finite differences scheme for§solving a boundary value case. The application and§the calculations are done to a first order§approximation, hence fluid flow is treated as a§Stokes flow. The integration of the rheological§behavior is implicit, through the force density§field. This method can easily extend to an entire§class of Newtonian and non-Newtonian ferromagnetic§real fluids, whose shear viscosity depend upon the§magnetic field, and upon the modulus of the strain§rate tensor.