Final answer:
The heat transfer in a beaker of water depicted by the arrows is primarily due to convection, which involves the movement of fluid due to temperature-induced density differences.
Step-by-step explanation:
The process primarily responsible for the transfer of heat in a beaker of water, as indicated by the arrows, is convection. Convection refers to the heat transfer by the macroscopic movement of a fluid, which takes place when hotter, less dense material rises and colder, denser material sinks, causing a transfer of heat. This process is driven by the difference in density that arises from the difference in temperature within the fluid. In contrast, conduction is the direct heat transfer through a substance that occurs when there is a temperature difference between adjoining regions without the movement of the material itself.