Takahiko Tanahashi

Natural convection of a magnetic fluid in a cubic enclosure

Abstract Laminar natural convection heat transfer of a magnetic fluid in a cubic enclosure is examined experimentally. Wall-temperature distributions are visualized by thermosensitive liquid crystal sheets. The effect of the magnetic field on the transient temperature distributions, and the local and averaged Nusselt numbers are discussed.

Natural convection of a magnetic fluid in concentric horizontal annuli under nonuniform magnetic fields

Abstract Natural convection of a magnetic fluid in concentric annuli was investigated experimentally. Two concentric cylinders were made of copper and placed horizontally. The temperature of the outer cylinder was kept at 15°C, and the inner cylinder was rapidly heated from 15°C to 25°C and held there. A thermosensitive liquid crystal was utilized for temperature visualization instead of flow visualization; temperatures on a central cross-section were also measured by thermocouples. A magnetic field was applied to the cylinders using a permanent magnet. The test liquid was a magnetic fluid with a 33% weight concentration of fine magnetic particles in a water carrier. Several kinds of experiments were carried out to clarify the influences of direction and the intensity of magnetic fields on the natural convection. When there was no magnetic field, ordinary natural convection was observed. When a magnetic field gradient was applied in the same direction as the gravity, a wall-temperature distribution was observed, as if an apparent gravity had increased; however, the clear influence of the magnetic field was not found. When a magnetic field gradient was applied in the opposite direction of the gravity, the reverse natural convection was observed. Consequently, even if the intensity of the applied magnetic field was small, it played an important role in natural convection and heat transfer of a magnetic fluid. It was recognized that natural convection of a magnetic fluid could be controlled by the application of a magnetic field.

Three-Dimensional Simulation of Silicon Melt Flow in Electromagnetic Czochralski Crystal Growth

The three-dimensional silicon melt flow in Electromagnetic Czochralski (EMCZ) growth without crucible rotation was numerically investigated using the finite element method. Due to the interaction of an axial magnetic with a constant electric current passing through the melt from the growing crystal to an electrode attached to the melt surface, an electromagnetic force (EMF) was generated. The EMF significantly suppressed the buoyant convection, and created a large axially elongated vortex in the bulk melt and a small one near the electrode. In EMCZ growth, the heat and mass transfers are thus controlled mostly through the axially elongated vortex driven by the local electromagnetic force.The feature of the melt flow is in qualitative agreement with experimental observation.

Propagation of surface waves of magnetic fluids in travelling magnetic fields

Abstract Propagation of waves on the free surface of magnetic fluid is experimentally investigated. It is found that the surface velocity of the magnetic fluid depends on the intensity and frequency of traveling magnetic fields, and depth of the channel contained with the magnetic fluid. Theoretical investigation is also carried out in order to clarify the phenomena.

Nonequilibrium Theory of Viscoelastic Magnetic Fluids

A new complete set of equations for magnetic fluids is derived using the thermodynamical method and micropolar theory. The present constitutive equations, which take consideration of both viscoelasticity and internal freedom, satisfy the principle of material frame indifference. It is shown that the constitutive equations of magnetization is related to the magnetic field, its change in time and angular velocity of suspended particles. Furthermore, it is made clear that the electromagnetic pressure is independent of the dissipative parts of the magnetization and the electric polarization.

Parallel Iterative Solvers with Localized ILU Preconditioning

It has been well-known that ILU(0) factorization is very effective preconditioning method when large-scale linear sparse systems in scientific and engineering computations are solved iteratively. But its also well-known that this method requires global data dependency and this is not the optimal way on parallel computers where locality is of utmost importance. In this paper, ”Localized” ILU(0) preconditioning method has been implemented to various type of iterative solvers. In this method. ILU(0) factorization is carried out for each processor by zeroing out the matrix components whose column numbers are outside the processor domain. This method provides data locality on each processor and good parallelization effect. Developed system performance has been also evaluated on simulated parallel processors by workstation cluster with PVM.

Lateral sloshing of a magnetic fluid in a container

Abstract The dynamic behavior of a magnetic fluid in a laterally oscillating rectangular container was experimentally studied. A vertical non-uniform magnetic field was applied to the container. The resonant frequency of the fluid-container system moved toward the high frequency region with the magnetic field intensity. An experiment was also carried out for a two-phase liquid of magnetic fluid and kerosene.

AN APPLICATION OF GSMAC-FEM TO ELECTRICALLY CONDUCTING FLUID FLOWS DRIVEN BY LORENTZ FORCE

ABSTRACT A new finite element method for incompressible, electrically conducting fluid flow is presented. This method satisfies the conservation laws of mass, magnetic flux and electric current. The main algorithm of the GSMAC (generalized simplified marker and cell) method is employed in order to satisfy the solenoidal conditions of both magnetic and electric current fields. The flow between two parallel plates, driven by electromagnetic forces are calculated to verify this new method. Numerical results obtained here agree with other numerical results or exact solutions. M-shape axial velocity profiles are clearly simulated by GSMAC—FEM near the electrode between two parallel plates as shown in Figure 1.

Two-dimensional flow of magnetic fluid between two parallel plates

Abstract Two-dimensional flows of magnetic fluid between two parallel plates in the transverse and longitudinal magnetic fields are investigated experimentally. The increasing rate of resistance coefficient is obtained and discussed with respect to the magnetic field length and Reynolds number.

Application of the GSMAC-CIP Method to Incompressible Navier-Stokes Equations at High Reynolds Numbers

The conventional shape function for the finite-element method (FEM) is linear, and it is thus inadequate for analyzing numerically complex flows at high Reynolds numbers. In this study, we propose a new scheme, GSMAC-CIP, using the third-order shape function, which requires continuity of the value of the function and its first space derivative in the whole space and is formulated by a finite element method for the cubic interpolated pseudo-particle (CIP) method. We verified the effectiveness of this new scheme by analyzing the forced-driven convection in a square cavity at Re = 1000, 5000 and 10000. The numerical results obtained by the present scheme are compared with those of GSMAC-FEM using coarser meshes, and it is shown that the present scheme is superior to GSMAC-FEM in terms of space accuracy. Moreover, it is shown that the numerical results obtained by the present scheme using fine meshes were in precise agreement with those obtained by Ghia et al.