Flow of High Prandtl Number Fluid under Varying Axial Magnetic Field

In this paper, the vertical vibration influence on the surface velocity of a 5cSt silicone oil liquid bridge has been investigated numerically. The Navier-Stokes equations coupled with the energy conservation equation are solved on a staggered grid, and the two-phase surface is captured by using the mass conserving level set method. The present results indicate that the axial and radial surface velocities of the liquid bridge are suppressed by the external vertical vibration.

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Thermocapillary Convection of Low Prandtl Number Fluids under Uniform Magnetic Fields

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.580-583.2970 ◽

2014 ◽

Vol 580-583 ◽

pp. 2970-2973 ◽

Cited By ~ 1

Author(s):

Ru Quan Liang ◽

Di Bei ◽

Fu Sheng Yan ◽

Dian Qiao Geng

Keyword(s):

Magnetic Field ◽

Uniform Magnetic Field ◽

Thermocapillary Convection ◽

Stokes Equations ◽

Fluid Velocity ◽

Conservation Equation ◽

Staggered Grid ◽

Navier Stokes ◽

Constant Frequency ◽

Energy Conservation Equation

Numerical simulations on thermocapillary convection of low Pr number molten tin under uniform magnetic field have been conducted under microgravity. The Navier-Stokes equations coupled with the energy conservation equation are solved on a staggered grid, and the free surface is captured by using the level set method. The present results show that the transverse uniform magnetic field can restrain the thermocapillary convection, and the fluid velocity at the hot corner fluctuates with a constant frequency at the steady state.

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Flow Characteristics for High Prandtl Number Fluid under Zero Gravity

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.353-356.3611 ◽

2013 ◽

Vol 353-356 ◽

pp. 3611-3614

Author(s):

Ru Quan Liang ◽

Shuo Yang ◽

Jun Hong Ji ◽

Ji Cheng He

Keyword(s):

Free Surface ◽

Flow Velocity ◽

Liquid Bridge ◽

Surface Deformation ◽

Stokes Equations ◽

Conservation Equation ◽

Staggered Grid ◽

Vortex Center ◽

Zero Gravity ◽

Two Phase

This paper investigated the flow structure in liquid bridge of high Pr Number fluid under zero gravity condition. The free surface deformation and the effects of gas phase around liquid bridge were considered. Navier-Stokes equations coupled with the energy conservation equation were solved on a staggered grid. The two-phase surface was captured by using the mass conserving level set method. The results indicated that location of vortex center move gradually toward the free surface due to thermocapillary convection. The flow velocity nearby the surface of liquid bridge is faster than the internal flow velocity, and the overall velocity level tends to decline with time evolution.

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Combined Marangoni and buoyancy convection in a porous annular cavity filled with Ag-MgO/water hybrid nanofluid

Current Nanoscience ◽

10.2174/1573413717666210928153741 ◽

2021 ◽

Vol 17 ◽

Author(s):

B. Kanimozhi ◽

M. Muthtamilselvan ◽

Qasem M. Al-Mdallal ◽

Bahaaeldin Abdalla

Keyword(s):

Magnetic Field ◽

Stokes Equations ◽

Volume Fraction ◽

Axial Magnetic Field ◽

Vertical Wall ◽

Navier Stokes ◽

Hybrid Nanofluid ◽

Radial Magnetic Field ◽

Navier Stokes Equations ◽

Buoyancy Convection

Background: This article numerically examines the effect of buoyancy and Marangoni convection in a porous enclosure formed by two concentric cylinders filled with Ag-MgO water hybrid nanofluid. The inner wall of the cavity is maintained at a hot temperature and the outer vertical wall is considered to be cold. The adiabatic condition is assumed for other two boundaries. The effect of magnetic field is considered in radial and axial directions. The Brinkman-extended Darcy model has been adopted in the governing equations. Methods: The finite difference scheme is employed to work out the governing Navier-Stokes equations. The numerically simulated outputs are deliberated in terms of isotherms, streamlines, velocityand average Nusselt number profiles for numerous governing parameters. Results: Except for a greater magnitude of axial magnetic field, our results suggest that the rate of thermal transport accelerates as the nanoparticle volume fraction grows.Also, it is observed that there is an escalation in the profile of average Nusselt numberwith an enhancement in Marangoni number. Conclusion: Furthermore, the suppression of heat and fluid flow in the tall annulus is mainly due to the radial magnetic field whereas in shallow annulus, the axial magnetic field profoundly affects the flow field and thermal transfer.

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Three Dimensional Effect of Axial Magnetic Field to Suppress Convection in the Solvent of Ge0.98Si0.02 Grown By the Traveling Solvent Method

10.32920/ryerson.14657451 ◽

2021 ◽

Author(s):

Leily Abidi

Keyword(s):

Magnetic Field ◽

Stokes Equations ◽

Axial Magnetic Field ◽

Three Dimensional ◽

Maximum Velocity ◽

Navier Stokes ◽

Growth Interface ◽

Navier Stokes Equations ◽

Solvent Method ◽

Element Technique

A three dimensional numerical simulation of the effect of an axial magnetic field on the fluid flow, heat and mass transfer within the solvent of GE0.98Si0.02 grown by the travelling solvent method is presented. The full steady state Navier-Stokes equations, as well as the energy, continuity and the mass transport equations, were solved numerically using the finite element technique. It is found that a strong convective flow exists in the solvent, which is known to be undesirable to achieve a uniform crystal. An external axial magnetic field is applied to suppress this convection. By increasing the magnetic induction, it is observed that the intensity of the flow at the centre of the crucible reduces at a faster rate than near the wall. This phenomenon creates a stable and flat growth interface and the silicon distribution in the horizontal plane becomes relatively homocentric. The maximum velocity is found to obey a power law with respect to the Hartmann number Umax Ha⁻⁷/⁴

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Three Dimensional Effect of Axial Magnetic Field to Suppress Convection in the Solvent of Ge0.98Si0.02 Grown By the Traveling Solvent Method

10.32920/ryerson.14657451.v1 ◽

2021 ◽

Author(s):

Leily Abidi

Keyword(s):

Magnetic Field ◽

Stokes Equations ◽

Axial Magnetic Field ◽

Three Dimensional ◽

Maximum Velocity ◽

Navier Stokes ◽

Growth Interface ◽

Navier Stokes Equations ◽

Solvent Method ◽

Element Technique

A three dimensional numerical simulation of the effect of an axial magnetic field on the fluid flow, heat and mass transfer within the solvent of GE0.98Si0.02 grown by the travelling solvent method is presented. The full steady state Navier-Stokes equations, as well as the energy, continuity and the mass transport equations, were solved numerically using the finite element technique. It is found that a strong convective flow exists in the solvent, which is known to be undesirable to achieve a uniform crystal. An external axial magnetic field is applied to suppress this convection. By increasing the magnetic induction, it is observed that the intensity of the flow at the centre of the crucible reduces at a faster rate than near the wall. This phenomenon creates a stable and flat growth interface and the silicon distribution in the horizontal plane becomes relatively homocentric. The maximum velocity is found to obey a power law with respect to the Hartmann number Umax Ha⁻⁷/⁴

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Mathematical Modelling of Thermo-Hydro-Mechanical Behaviour for Concrete under Elevated Temperature

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.670-671.355 ◽

2014 ◽

Vol 670-671 ◽

pp. 355-364

Author(s):

Shao Bo Zhang ◽

Xiao Chun Wang ◽

Xin Pu Shen

Keyword(s):

Elevated Temperature ◽

Stokes Equations ◽

Constitutive Relations ◽

Gaseous Mixture ◽

Mass Conservation ◽

Momentum Conservation ◽

Conservation Equation ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Energy Conservation Equation

A hydro-thermo-mechanical model was presented for concrete at elevated temperature. Three phases of continuum were adopted in this model: gaseous mixture of water vapor and dry air, liquid water, and solid skeleton of concrete. Mass conservation equations, linear momentum conservation equation, and energy conservation equation were derived on the basis of the macroscopic Navier-Stokes equations for a general continuum, along with assumptions made for the purpose of simplification. Mathematical relationships between selected primary variables and secondary variables were given with existing data from references. Specifications of the constitutive relations were made for the kinetic variables and their conjugate forces.

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Numerical Study of the Internal Flow Field of a Centrifugal Impeller

Volume 1: Turbomachinery ◽

10.1115/94-gt-357 ◽

1994 ◽

Cited By ~ 2

Author(s):

Mou-jin Zhang ◽

Chuan-gang Gu ◽

Yong-miao Miao

Keyword(s):

Flow Field ◽

Stokes Equations ◽

Numerical Study ◽

Three Dimensional ◽

Simple Algorithm ◽

Internal Flow ◽

Staggered Grid ◽

Navier Stokes ◽

Centrifugal Impeller ◽

High Reynolds

The complex three-dimensional flow field in a centrifugal impeller with low speed is studied in this paper. Coupled with high–Reynolds–number k–ε turbulence model, the fully three–dimensional Reynolds averaged Navier–Stokes equations are solved. The Semi–Implicit Method for Pressure–Linked Equations (SIMPLE) algorithm is used. And the non–staggered grid arrangement is also used. The computed results are compared with the available experimental data. The comparison shows good agreement.

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An Improved Three-Dimensional Level Set Method for Gas-Liquid Two-Phase Flows

Journal of Fluids Engineering ◽

10.1115/1.1777232 ◽

2004 ◽

Vol 126 (4) ◽

pp. 578-585 ◽

Cited By ~ 14

Author(s):

Hiroyuki Takahira ◽

Tomonori Horiuchi ◽

Sanjoy Banerjee

Keyword(s):

Level Set Method ◽

Level Set ◽

Stokes Equations ◽

Interpolation Method ◽

Density Ratio ◽

Three Dimensional ◽

Mass Conservation ◽

Staggered Grid ◽

Two Phase ◽

Level Set Function

For the present study, we developed a three-dimensional numerical method based on the level set method that is applicable to two-phase systems with high-density ratio. The present solver for the Navier-Stokes equations was based on the projection method with a non-staggered grid. We improved the treatment of the convection terms and the interpolation method that was used to obtain the intermediate volume flux defined on the cell faces. We also improved the solver for the pressure Poisson equations and the reinitialization procedure of the level set function. It was shown that the present solver worked very well even for a density ratio of the two fluids of 1:1000. We simulated the coalescence of two rising bubbles under gravity, and a gas bubble bursting at a free surface to evaluate mass conservation for the present method. It was also shown that the volume conservation (i.e., mass conservation) of bubbles was very good even after bubble coalescence.

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Effect of Axial Magnetic Field Strengths on Radial Velocity Field in Liquid Bridge under Microgravity

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.256-259.1670 ◽

2012 ◽

Vol 256-259 ◽

pp. 1670-1673

Author(s):

Ru Quan Liang ◽

Shuo Yang ◽

Jun Hong Ji ◽

Ji Cheng He

Keyword(s):

Magnetic Field ◽

Liquid Bridge ◽

Axial Magnetic Field ◽

Phase Interface ◽

Mass Conservation ◽

Inhibitory Effect ◽

Two Phase ◽

Conservation Level ◽

The Magnetic Field ◽

Field Strengths

This article studies on the effect of magnetic field strengths on the flow field in a liquid bridge under zero gravity. The mass conservation level set method is used to track the two-phase interface. The results show that inhibitory effect of additional axial magnetic field on thermocapillary convection within liquid bridge is obvious, and this kind of inhibitory effect increasing as the magnetic field strength is strengthened.

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