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Research Papers: Natural and Mixed Convection

# The Impact of Normal Magnetic Fields on Instability of Thermocapillary Convection in a Two-Layer Fluid System

[+] Author and Article Information
Hulin Huang1

Academy of Frontier Science, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, P.R. Chinahlhuang@nuaa.edu.cn

Xiaoming Zhou

Academy of Frontier Science, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, P.R. China

1

Corresponding author.

J. Heat Transfer 131(6), 062502 (Apr 07, 2009) (7 pages) doi:10.1115/1.3084211 History: Received January 29, 2008; Revised November 09, 2008; Published April 07, 2009

## Abstract

When a temperature gradient is imposed along a liquid-liquid interface, thermocapillary convection is driven by the surface tension gradient. Such flow occurs in many application processes, such as thin-film coating, metal casting, and crystal growth. In this paper, the effect of a normal magnetic field, which is perpendicular to the interface, on the instability of thermocapillary convection in a rectangular cavity with differentially heated sidewalls, filled with two viscous, immiscible, incompressible fluids, is studied under the absence of gravity. In the two-layer fluid system, the upper layer fluid is electrically nonconducting encapsulant $B2O3$, while the underlayer fluid is electrically conducting molten InP. The interface between the two fluids is assumed to be flat and nondeformable. The results show that the two-layer fluid system still experiences a wavelike state when the magnetic field strength $Bz$ is less than 0.04 T. The wave period increases and the amplitude decreases with the increasing of magnetic field strength. However, the convective flow pattern becomes complicated with a variable period, while the perturbation begins to fall into oblivion as the magnetic field intensity is larger than 0.05 T. When $Bz=0.1 T$, the wavelike state does not occur, the thermocapillary convection instability is fully suppressed, and the unsteady convection is changed to a steady thermocapillary flow.

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Copyright © 2009 by American Society of Mechanical Engineers
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## Figures

Figure 1

Physical model

Figure 2

Comparison of temperature oscillation frequency at a monitoring point

Figure 3

Streamlines on y=0.01 m plane in one oscillation period (τp) without MHD: (a) t=τ0, (b) t=τ0+1/4τp, (c) t=τ0+1/2τp, and (d) t=τ0+3/4τp

Figure 4

Temperature fluctuation at the monitoring point P with time without MHD

Figure 5

Temperature temporal perturbation on y=0.01 m plane in one period (τp) without MHD: (a) t=τ0, (b) t=τ0+1/4τp, (c) t=τ0+1/2τp, and (d) t=τ0+3/4τp

Figure 6

Streamlines on y=0.01 m plane in one oscillation period (τp) under Bz=0.04 T: (a) t=τ0, (b) t=τ0+1/4τp, (c) t=τ0+1/2τp, and (d) t=τ0+3/4τp

Figure 7

Temperature perturbation on y=0.01 m plane in one period (τp) under Bz=0.04 T: (a) t=τ0, (b) t=τ0+1/4τp, (c) t=τ0+1/2τp, and (d) t=τ0+3/4τp

Figure 8

Temperature fluctuation at monitoring point P under Bz=0.04 T

Figure 9

Temperature fluctuation at point P under Bz=0.05 T

Figure 10

Temperature fluctuation at point P under Bz=0.08 T

Figure 11

Steady streamlines’ pattern of thermocapillary convection under Bz=0.1 T

Figure 12

Temperature fluctuation at monitoring point under Bz=0.1 T

Figure 13

Oscillatory period and amplitude vary with Ha

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