Introduction:
Heat transfer surfaces are commonly used in various engineering applications to enhance heat transfer between a solid surface and the surrounding fluid. Fins are one of the most effective methods to increase the heat transfer area and efficiency of a surface. The provision of fins on a heat transfer surface can significantly improve the heat transfer rate.

Explanation:
The provision of fins on a heat transfer surface can be optimized based on several factors, including the number and thickness of the fins. Let's discuss each option and understand why option 'C' is the correct answer.

a) Fewer number of thick fins:
- Having a few number of thick fins reduces the total surface area available for heat transfer, as thick fins take up more space on the heat transfer surface.
- Additionally, thick fins may lead to increased pressure drop and flow resistance, which can affect the overall heat transfer performance.
- Therefore, having fewer number of thick fins may not be the most efficient way to enhance heat transfer.

b) Fewer number of thin fins:
- Similar to the previous option, having fewer number of fins reduces the total surface area available for heat transfer.
- However, thin fins have a higher surface area-to-volume ratio compared to thick fins, which makes them more effective in transferring heat.
- Therefore, having fewer number of thin fins can still provide some improvement in heat transfer compared to thick fins, but it may not be as efficient as having a large number of fins.

c) Large number of thin fins:
- This option is the correct answer because it combines the advantages of thin fins and a large number of fins.
- Large number of fins increases the total surface area available for heat transfer, which enhances the overall heat transfer rate.
- Thin fins, on the other hand, have a higher surface area-to-volume ratio, which improves heat transfer efficiency.
- Therefore, having a large number of thin fins provides the maximum heat transfer enhancement as it maximizes the surface area and utilizes the high surface area-to-volume ratio of thin fins.

d) Large number of thick fins:
- Having a large number of thick fins may increase the total surface area, but it also increases the volume of material used for the fins.
- Thick fins have a lower surface area-to-volume ratio, which reduces the heat transfer efficiency compared to thin fins.
- Therefore, a large number of thick fins may not provide significant improvement in heat transfer compared to a large number of thin fins.

Conclusion:
To summarize, the provision of fins on a heat transfer surface will be more effective when there is a large number of thin fins. This combination maximizes the surface area available for heat transfer and utilizes the high surface area-to-volume ratio of thin fins, resulting in enhanced heat transfer performance.