Introduction:
Heat dissipation is an important aspect in the design of fins, which are commonly used in various heat transfer applications. Fins are extended surfaces that enhance heat transfer by increasing the surface area available for convection. In order to achieve maximum heat dissipation, the design of the fin should consider various factors, including the lateral surface area distribution along the length of the fin.

Explanation:
1. Maximum lateral surface at the root side of fin:
The root side of the fin refers to the base or bottom part of the fin, where it is connected to the heat source. Designing fins with maximum lateral surface at the root side is beneficial for heat dissipation because:
- The root side is in direct contact with the heat source, and therefore, has a higher temperature compared to the tip side of the fin. By maximizing the lateral surface area at the root side, more heat can be transferred from the heat source to the fin.
- The increased surface area at the root side allows for improved convection heat transfer. Convection is the process of heat transfer through the movement of fluid (liquid or gas) over a surface. Increasing the lateral surface area at the root side enhances the contact between the fluid and the fin surface, resulting in enhanced heat transfer.

2. Other options:
- Maximum lateral surface towards the tip side of fin: This option is not ideal because the tip side of the fin is typically cooler compared to the root side. Therefore, maximizing the lateral surface area towards the tip side would not effectively transfer heat from the fin to the surrounding environment.
- Maximum lateral surface near the center of the fin: This option is also not optimal as the center of the fin is typically located away from the heat source. Therefore, maximizing the lateral surface area near the center would not efficiently transfer heat from the heat source to the fin.
- Minimum lateral surface near the center of the fin: This option is not desirable as it reduces the overall surface area available for heat transfer. By minimizing the lateral surface area near the center, the heat dissipation capacity of the fin would be compromised.

Conclusion:
In conclusion, in order to achieve maximum heat dissipation, the fin should be designed with maximum lateral surface at the root side. This design allows for efficient heat transfer from the heat source to the fin and enhances the convection heat transfer process.