scholarly journals Rotating magnetic field effect on convection and its stability in a horizontal cylinder subjected to a longitudinal temperature gradient

2010 ◽  
Vol 664 ◽  
pp. 108-137 ◽  
Author(s):  
D. V. LYUBIMOV ◽  
A. V. BURNYSHEVA ◽  
H. BENHADID ◽  
T. P. LYUBIMOVA ◽  
D. HENRY
Keyword(s):  
Magnetic Field ◽  
Temperature Gradient ◽  
Prandtl Number ◽  
Cross Section ◽  
Rotating Magnetic Field ◽  
Shear Mode ◽  
Convective Flows ◽  
Longitudinal Temperature Gradient ◽  
Longitudinal Temperature ◽  
The Cross

A rotating magnetic field (RMF) is used in crystal growth applications during the solidification process in order to improve the crystal quality. Its influence on the convective flows in molten metals and on their stability is studied here in the case of a horizontal infinite cylindrical channel subjected to a longitudinal temperature gradient. The steady convective flows, which correspond to the usual longitudinal counterflow structure, with four vortices in the cross-section for non-zero Prandtl number, Pr, are modified by the RMF (parametrized by the magnetic Taylor number Tam). For zero Prandtl number, the flow in the cross-section corresponds to circular streamlines and the longitudinal flow structure is moved in the direction of the magnetic field rotation, with a decrease in its intensity and an asymptotic variation as 1/Tam. For non-zero Prandtl numbers, depending on the respective values of Tam on one side and Prandtl and Grashof numbers on the other side, different structures ranging from the circular streamlines with transport by rotation of the longitudinal velocity and the temperature field, to the more usual counterflow structure almost insensitive to the RMF with four cross-section vortices, can be obtained. The decrease in the flow intensity with increasing Tam is also delayed for non-zero Pr, but the same asymptotic limit is eventually reached. The stability analysis of these convective flows for Tam = 0 shows a steep increase of the thresholds around Pr = Prt,0 ≈ 3 × 10−4, corresponding to the transition between the usual counterflow shear mode and a new sidewall shear mode. This transition is still present with an RMF, but it occurs for smaller Pr values as Tam is increased. Strong stabilizing effects of the rotating magnetic field are found for Pr < Prt,0, particularly for Pr = 0 where an exponential increase of the threshold with Tam is found. For Pr > Prt,0 (i.e. in the domain where the sidewall instability is dominant), in contrast, the stabilization by the RMF is weak.

scholarly journals Stability of convection in a horizontal channel subjected to a longitudinal temperature gradient. Part 1. Effect of aspect ratio and Prandtl number

2009 ◽  
Vol 635 ◽  
pp. 275-295 ◽  
Author(s):  
T. P. LYUBIMOVA ◽  
D. V. LYUBIMOV ◽  
V. A. MOROZOV ◽  
R. V. SCURIDIN ◽  
H. BEN HADID ◽  
...  
Keyword(s):  
Temperature Gradient ◽  
Aspect Ratio ◽  
Prandtl Number ◽  
Cross Section ◽  
Horizontal Channel ◽  
Channel Cross Section ◽  
Instability Mode ◽  
Channel Axis ◽  
Longitudinal Temperature Gradient ◽  
Longitudinal Temperature

The paper deals with the numerical investigation of the steady convective flow in a horizontal channel of rectangular cross-section subjected to a uniform longitudinal temperature gradient imposed at the walls. It is shown that at zero Prandtl number the solution of the problem corresponds to a plane-parallel flow along the channel axis. In this case, the fluid moves in the direction of the imposed temperature gradient in the upper part of the channel and in the opposite direction in the lower part. At non-zero values of the Prandtl number, such solution does not exist. At any small values of Pr all three components of the flow velocity differ from zero and in the channel cross-section four vortices develop. The direction of these vortices is such that the fluid moves from the centre to the periphery in the vertical direction and returns to the centre in the horizontal direction. The stability of these convective flows (uniform along the channel axis) with regard to small three-dimensional perturbations periodical in the direction of the channel axis is studied. It is shown that at low values of the Prandtl number the basic state loses its stability due to the steady hydrodynamic mode related to the development of vortices at the boundary of the counter flows. The growth of the Prandtl number results in the strong stabilization of this instability mode and, beyond a certain value of the Prandtl number depending on the cross-section aspect ratio, a new steady hydrodynamic instability mode becomes the most dangerous. This mode is characterized by the localization of the perturbations near the sidewalls of the channel. At still higher values of the Prandtl number, the spiral perturbations (rolls with axis parallel to the temperature gradient) become the most dangerous modes, at first the oscillatory spiral perturbations and then the Rayleigh-type steady spiral perturbations. The influence of the channel width on these different instabilities is also emphasized.

Magnetic-field dependence of the cross section formJmixing in2P1/2Cs and Rb atoms

1994 ◽  
Vol 49 (6) ◽  
pp. 4540-4548 ◽  
Author(s):  
W. Kedzierski ◽  
Ju Gao ◽  
W. E. Baylis ◽  
L. Krause
Keyword(s):  
Magnetic Field ◽  
Cross Section ◽  
Field Dependence ◽  
Magnetic Field Dependence ◽  
The Cross

scholarly journals Heat and Mass Transport in Carbon Nantubes

2010 ◽  
Author(s):  
Junichiro Shiomi ◽  
Carl Fredrik Carlborg ◽  
Shigeo Maruyama
Keyword(s):  
Molecular Dynamics ◽  
Temperature Gradient ◽  
Mass Transport ◽  
Small Diameter ◽  
Elastic Interaction ◽  
Heat And Mass Transport ◽  
Longitudinal Temperature Gradient ◽  
Longitudinal Temperature ◽  
Argon Matrices ◽  
Dynamics Simulations

We have investigated heat and mass transport in single-walled carbon nanotubes (SWNTs) using molecular dynamics methods. Particular attention was paid on the non-equilibrium dynamics at the interface between SWNT and other materials, which strongly manifests in nanoscale. In the first part, we have investigated the heat transport through the interface between SWNTs and surrounding argon matrices in liquid and solid phases. By analyzing the energy relaxation from SWNT to the matrices using non-stationary molecular dynamics simulations, elastic and inelastic thermal energy transports across the interface were separately quantified. The result reveals that the elastic interaction transports energy much faster than the inelastic one, but carries much smaller energy due to slow intra-SWNT phonon relaxation. In the second part, we have investigated a possibility to utilize nonequilibrium thermal interface to transport water through an SWNT. By applying the longitudinal temperature gradient to the SWNT, it is demonstrated that the water cluster is efficiently driven at average acceleration proportional to the temperature gradient. However, the transport simulations with a junction of two different SWNTs suggest that an angstrom diameter difference may result in a significant drag for small diameter SWNTs.

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