Introduction:
In the field of heat transfer, fins are widely used to enhance heat transfer from a solid surface to the surrounding fluid. Fins are extended surfaces that increase the surface area available for heat transfer. The effectiveness of a fin depends on the mode of heat transfer present in the environment.

Explanation:
The given question states that the effectiveness of a fin will be maximum in an environment with free convection. Let's understand why this is the correct answer.

1. Free Convection:
Free convection is a mode of heat transfer in which heat is transferred through fluid motion caused by density differences. When a solid surface is heated, the surrounding fluid near the surface becomes hotter and less dense, causing it to rise. This upward motion creates a natural circulation of fluid, carrying heat away from the surface. In this mode of heat transfer, fins are highly effective in enhancing heat transfer.

2. Forced Convection:
Forced convection is a mode of heat transfer in which fluid motion is induced by external means such as a fan or pump. In this case, the effectiveness of fins depends on the velocity and direction of the forced flow. Fins can enhance heat transfer in forced convection, but their effectiveness may not be as high as in free convection. The forced flow may disrupt the natural circulation and reduce the effectiveness of the fins.

3. Radiation:
Radiation is a mode of heat transfer that does not require a medium for heat transfer. It occurs through electromagnetic waves. Fins are not very effective in enhancing radiation heat transfer. The effectiveness of fins primarily depends on the convective heat transfer mechanism.

4. Convection and Radiation:
When both convection and radiation are present in the environment, the effectiveness of fins will be influenced by both mechanisms. However, the convective heat transfer still dominates in terms of effectiveness. Fins will enhance the convective heat transfer by increasing the surface area and promoting fluid motion. Therefore, the effectiveness of fins will be higher in this case compared to radiation alone but not as high as in free convection.

Conclusion:
In conclusion, the effectiveness of a fin is maximum in an environment with free convection. Free convection allows for natural fluid motion, which is highly enhanced by fins. While fins can also be effective in forced convection and in environments with both convection and radiation, their effectiveness is highest in free convection due to the natural circulation of fluid.