Conduction, convection, and radiation are the three main modes of heat transfer. Each mode has its own unique characteristics and is applicable in different scenarios. In the given options, the correct answer is option 'C', which states that heat is mainly transferred by conduction, convection, and radiation in boiler furnaces. Let's understand why this is the correct answer in detail:

Conduction:
- Conduction is the transfer of heat through direct contact between particles of a substance.
- In boiler furnaces, heat is transferred through conduction as the hot gases come into direct contact with the walls of the furnace.
- The walls of the furnace absorb the heat energy from the hot gases, and this heat energy is conducted through the solid material of the furnace walls.

Convection:
- Convection is the transfer of heat through the movement of fluids (liquids or gases) due to temperature differences.
- In boiler furnaces, heat is transferred through convection as the hot gases rise due to their lower density and are replaced by cooler gases.
- This creates a circulation of gases within the furnace, allowing the heat to be distributed throughout the furnace.

Radiation:
- Radiation is the transfer of heat through electromagnetic waves.
- In boiler furnaces, heat is transferred through radiation as the hot gases emit thermal radiation.
- This radiation travels in straight lines and can be absorbed by the walls and other surfaces within the furnace.

Overall, the combination of conduction, convection, and radiation ensures efficient heat transfer in boiler furnaces. Conduction allows heat to be transferred through direct contact, convection facilitates the movement of hot gases to distribute heat, and radiation ensures that heat is emitted and absorbed by surrounding surfaces. This comprehensive heat transfer mechanism is crucial for the efficient operation of boiler furnaces.