On the integro-differential general solution for the unsteady micropolar Stokes flow of a conducting ferrofluid

The three–dimensional (3–D) unsteady creeping motion, corresponding to Stokes flow, of a non–conductive colloidal suspension of ferromagnetic particles, which are embedded within an otherwise electrically conducting, viscous and incompressible, carrier liquid, is considered in this contribution. This group of micropolar conducting ferrofluids comprises a novel class of engineering materials that respond in the presence of a general externally applied magnetic field, which is arbitrarily orientated in the three–dimensional domain of practical interest. Therein, an induced magnetic field of minor importance is created, while the effective viscosity of the fluid is increasing and an additional magnetic pressure appears. In order to be compatible with the principles of both ferrohydrodynamics and magnetohydrodynamics, we readily include the magnetization and the electrical conductivity of the magnetic fluid, respectively into the governing partial differential equations of the particular physical system. Employing the potential representation theory, we fabricate a new integro–differential general solution for the situation under investigation, which provides the time–dependent velocity and total pressure fields in a 3–D spaced closed form and in terms of easy–to–find potentials, via a semi–analytical shape. This generalized representation is proved to be complete, whilst it is valid for any non–axisymmetric geometry. We demonstrate the applicability of our analytical approach, by introducing a basic degenerate case of the aforementioned method to simulate the time–dependent creeping flow of a micropolar fluid with conductive properties inside a circular duct.