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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.
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.