Final answer:
The movement of water in the described scenario is due to convection, as the warmer water rises and the cooler water sinks, forming a current.
Step-by-step explanation:
When a small container is filled with water, a candle flame placed under one end, and ice cubes placed under the opposite end, the water will begin to move in a current. This movement of water is a result of convection, which is a method of heat transfer where thermal energy is carried by the movement of a fluid. In the scenario described, the water near the candle flame becomes less dense and rises, while the colder water near the ice sinks, forming a convection current within the container.