Linear stability analysis and dynamic simulations of free convection in a differentially heated cavity in the presence of a horizontal magnetic field and a uniform heat source

2006 ◽  
Vol 18 (3) ◽  
pp. 034101 ◽  
Author(s):  
Nikos A. Pelekasis
Keyword(s):  
Magnetic Field ◽  
Stability Analysis ◽  
Heat Source ◽  
Free Convection ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Dynamic Simulations ◽  
Horizontal Magnetic Field ◽  
Uniform Heat

scholarly journals Linear Stability Analysis of Thermal Convection in an Infinitely Long Vertical Rectangular Enclosure in the Presence of a Uniform Horizontal Magnetic Field

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Takashi Kitaura ◽  
Toshio Tagawa
Keyword(s):  
Magnetic Field ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Thermal Convection ◽  
Vertical Channel ◽  
Numerical Code ◽  
Convection Flow ◽  
Horizontal Magnetic Field ◽  
Direction Parallel

Stability of thermal convection in an infinitely long vertical channel in the presence of a uniform horizontal magnetic field applied in the direction parallel to the hot and cold walls was numerically studied. First, in order to confirm accuracy of the present numerical code, the one-dimensional computations without the effect of magnetic field were computed and they agreed with a previous study quantitatively for various values of the Prandtl number. Then, linear stability analysis for the thermal convection flow in a square horizontal cross section under the magnetic field was carried out for the case of Pr = 0.025. The thermal convection flow was once destabilized at certain low Hartmann numbers, and it was stabilized at high Hartmann numbers.

Rayleigh–Bénard instability in a vertical cylinder with a vertical magnetic field

2002 ◽  
Vol 469 ◽  
pp. 189-207 ◽  
Author(s):  
B. C. HOUCHENS ◽  
L. MARTIN WITKOWSKI ◽  
J. S. WALKER
Keyword(s):  
Magnetic Field ◽  
Stability Analysis ◽  
Numerical Solution ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Hartmann Number ◽  
Critical Rayleigh Number ◽  
Vertical Wall ◽  
Vertical Cylinder ◽  
Vertical Magnetic Field

This paper presents two linear stability analyses for an electrically conducting liquid contained in a vertical cylinder with a thermally insulated vertical wall and with isothermal top and bottom walls. There is a steady uniform vertical magnetic field. The first linear stability analysis involves a hybrid approach which combines an analytical solution for the Hartmann layers adjacent to the top and bottom walls with a numerical solution for the rest of the liquid domain. The second linear stability analysis involves an asymptotic solution for large values of the Hartmann number. Numerically accurate predictions of the critical Rayleigh number can be obtained for Hartmann numbers from zero to infinity with the two solutions presented here and a previous numerical solution which gives accurate results for small values of the Hartmann number.

scholarly journals Linear Stability Analysis of Liquid Metal Flow in an Insulating Rectangular Duct under External Uniform Magnetic Field

Fluids ◽  
2019 ◽  
Vol 4 (4) ◽  
pp. 177 ◽  
Author(s):  
Tagawa
Keyword(s):  
Magnetic Field ◽  
Stability Analysis ◽  
Liquid Metal ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Uniform Magnetic Field ◽  
Metal Flow ◽  
Rectangular Duct ◽  
Liquid Metal Flow ◽  
External Uniform Magnetic Field

Linear stability analysis of liquid metal flow driven by a constant pressure gradient in an insulating rectangular duct under an external uniform magnetic field was carried out. In the present analysis, since the Joule heating and induced magnetic field were neglected, the governing equations consisted of the continuity of mass, momentum equation, Ohm’s law, and conservation of electric charge. A set of linearized disturbance equations for the complex amplitude was decomposed into real and imaginary parts and solved numerically with a finite difference method using the highly simplified marker and cell (HSMAC) algorithm on a two-dimensional staggered mesh system. The difficulty of the complex eigenvalue problem was circumvented with a Newton—Raphson method during which its corresponding eigenfunction was simultaneously obtained by using an iterative procedure. The relation among the Reynolds number, the wavenumber, the growth rate, and the angular frequency was successfully obtained for a given value of the Hartmann number as well as for a direction of external uniform magnetic field.

Linear stability analysis of a Newtonian ferrofluid cylinder surrounded by a Newtonian fluid

2021 ◽  
Vol 927 ◽  
Author(s):  
Romain Canu ◽  
Marie-Charlotte Renoult
Keyword(s):  
Magnetic Field ◽  
Stability Analysis ◽  
Dispersion Relation ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Density Ratio ◽  
Bond Number ◽  
Wire Radius ◽  
Azimuthal Magnetic Field ◽  
Relative Magnetic Permeability

We performed a linear stability analysis of a Newtonian ferrofluid cylinder surrounded by a Newtonian non-magnetic fluid in an azimuthal magnetic field. A wire is used at the centre of the ferrofluid cylinder to create this magnetic field. Isothermal conditions are considered and gravity is ignored. An axisymmetric perturbation is imposed at the interface between the two fluids and a dispersion relation is obtained allowing us to predict whether the flow is stable or unstable with respect to this perturbation. This relation is dependent on the Ohnesorge number of the ferrofluid, the dynamic viscosity ratio, the density ratio, the magnetic Bond number, the relative magnetic permeability and the dimensionless wire radius. Solutions to this dispersion relation are compared with experimental data from Arkhipenko et al. (Fluid Dyn., vol. 15, issue 4, 1981, pp. 477–481) and, more recently, Bourdin et al. (Phys. Rev. Lett., vol. 104, issue 9, 2010, 094502). A better agreement than the inviscid theory and the theory that only takes into account the viscosity of the ferrofluid is shown with the data of Arkhipenko et al. (Fluid Dyn., vol. 15, issue 4, 1981, pp. 477–481) and those of Bourdin et al. (Phys. Rev. Lett., vol. 104, issue 9, 2010, 094502) for small wavenumbers.

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