A Note on the Analytical Treatment in Ferrohydrodynamics

概要

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A new complete set of basic equations for magnetic suspensions is derived on the theory of micropolar fluids developed by Eringen and a solution to these basic equations is obtained analytically for a steady motion of magnetic suspensions in a circular pipe which is placed in a homogeneous magnetic field parallel to the flow direction. A phenomenological treatment is given for the specification of material constants of a micropolar fluid, which are vortex viscosity and spin viscosity. In order to clarify the dynamical flow characteristics in the presence of a magnetic field, six dimensionless parameters to show the magnetic effect, polar effect, wall surface effect and so on are introduced into the solution for the rotational Peclet number Per≪1 and Per≥1. Some discussions are presented on velocity profiles, distribution of microrotations and distribution of vorticities. In particular, the suspension is non-Newtonian even if a magnetic field does not exist.
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