Bidirectional temperature gradients coexist virtually in surface tension driven flows. However, the simulations have been performed to the flow with only one temperature gradient. A series of 3 D numerical simulations are conducted to investigate the Marangoni‐thermocapillary flow of silicon melt in a thin annular layer with bidirectional temperature gradients. The temperature gradients are produced by the temperature difference ΔT between walls and the constant heat flux q on the bottom, respectively. When changing q, the melt presents different state evolutions at different ΔT. Furthermore, two critical q are found, one makes the minimum melt temperature higher than the crystallization temperature and the other makes the flow unsteady. Both of the critical heat fluxes decrease with increasing ΔT. q contributes more to the elevation of the melt temperature, while ΔT contributes more to the enhancement of the melt instability. In addition, the melt on the free surface flows mainly along the radial direction.

The surface tension driven convection with the bidirectional temperature differences plays a very important role in many natural processes. However, most of the previous researches have focused only on the convection induced by a unidirectional temperature difference. In this paper, under the coexistence of bidirectional temperature differences, we conduct a series of numerical simulations to investigate the effect of horizontal temperature difference on the Marangoni-thermocapillary convection in a shallow annular pool. The critical values of bottom heat flux Qcri for transition from an axisymmetric steady flow to a three-dimensional unsteady flow at different values of Ma are determined. The result shows the horizontal temperature difference has a negative effect on the stability of Marangoni-thermocapillary convection. The simulation predicts two new state evolutions which do not appear in the convection with a unidirectional temperature difference. When Q is less than the Qcri value of 2.4×10-3, the Marangoni convection without horizontal temperature difference is steady and axisymmetric. When a small horizontal temperature difference is imposed, the convection called basic flow keeps steady and axisymmetric. When the value of Ma exceeds a certain threshold value Macri, the convection becomes a three-dimensional unsteady flow. After this unsteady flow happens, with the increase of Ma, the surface temperature fluctuation evolves from a punctate wave to a hydrothermal wave, and finally to a chaotic wave. Accordingly, the temperature oscillation with time is a periodically regular oscillation at first, then turns into a chaotic mess. When Q is larger than the corresponding Qcri value of 2.4×10-3, without a horizontal difference, the convection is unsteady and no basic flow exists in the variation process of Ma. With the increase of Ma, the surface temperature fluctuation evolves from a double hydrothermal wave to a single hydrothermal wave, and finally to a chaotic wave. The vertical heat transfer and horizontal temperature difference have different effects on the fluid, and their separate roles in driving fluid are determined. The bottom heat flux causes the surface fluid to flow in two opposite radial directions as the highest surface temperature is located in the middle region, while the horizontal temperature difference induces the surface fluid to flow in a single radial direction as the highest surface temperature appears at the hot wall. The combined action of these two forces generates different flows. The increase of horizontal temperature difference leads to the highest surface temperature, which originally appears in the middle region due to the bottom heat flux, and moves toward the hot wall. In this process, the horizontal temperature difference has a positive effect on the enhancement of flow near inner wall but it has a negative effect on the flow near outer wall.

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