Numerical Simulation of Magneto-Rheological Fluids

This work pertains to modern interdisciplinaryresearch trends in nanomaterials. The author presentsa novel method with major potential for variousapplications such as ferromagnetic brakes and valves;nanosized shock absorbers and in the medical fieldheart valves and medical nanorobots. A mathematicalmodel is constructed with numerical solutionsproposed for the system of equations describing themodel. The underlying assumption is that aferromagnetic suspension can be regarded as acontinuous medium. Such an assumption was originallysuggested in Peskin's Immersed Boundary (IB) method.The IB method is coupled with Chorin's Projectionmethod to construct a finite differences scheme forsolving a boundary value case. The application andthe calculations are done to a first orderapproximation hence fluid flow is treated as aStokes flow. The integration of the rheologicalbehavior is implicit through the force densityfield. This method can easily extend to an entireclass of Newtonian and non-Newtonian ferromagneticreal fluids whose shear viscosity depend upon themagnetic field and upon the modulus of the strainrate tensor.