The three methods by which transfer of heat energy takes place is:

Heat energy transfer occurs through three primary mechanisms: convection, conduction, and radiation, making the correct answer the one that lists all three.

Conduction is the transfer of heat through a solid material due to the interaction of molecules at different energy levels. It takes place when molecules are in direct contact, allowing heat to move from the hotter region to the cooler region without any movement of the material as a whole.

Convection involves the transfer of heat in fluids (liquids and gases) through the movement of the fluid itself. As the fluid is heated, it becomes less dense and rises, while cooler, denser fluid descends. This movement creates a circulation pattern that effectively transfers heat throughout the fluid.

Radiation is the transfer of heat in the form of electromagnetic waves. This process can occur in a vacuum, as it does not require a medium for heat transfer. For example, the heat from the sun reaches Earth through radiation.

Each of these mechanisms plays a crucial role in various heating systems and the general understanding of thermodynamics. The other options do not correctly identify all three primary methods of heat transfer, which is why they do not provide a complete answer.