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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