Question

The heat transfer surface area of a fin is equal to the sum of all surfaces of the fin exposed to the surrounding medium, including the surface area of the fin tip. Under what conditions can we neglect heat transfer from the fin tip?

Short answer

Answer: We can neglect heat transfer from the fin tip if the fin tip's surface area is much smaller compared to the total surface area of the fin, and the temperature difference between the fin tip and the surrounding medium is minimal due to a significant temperature drop along the fin's length.

Step-by-step solution

Understand the factors affecting heat transfer from a fin

Heat transfer from a fin mainly depends on its surface area, the temperature difference between the fin and the surrounding medium, and the thermal conductivity of the fin material. As we increase the surface area, better heat transfer can occur, and thermal conductivity determines how efficiently the heat can be transferred through the material.

Identify the role of the fin tip in heat transfer

The fin tip is one of the surfaces where heat transfer occurs, as it is exposed to the surrounding medium. However, the fin tip's contribution to total heat transfer depends on multiple factors, such as surface finish, width, and temperature distribution along the fin length.

Consider the fin tip surface area relative to the entire surface area

In cases where the surface area of the fin tip is much smaller than the total surface area (for example, in long fins with uniform small thickness), its contribution to overall heat transfer from the fin can be considered as negligible.

Evaluate the temperature distribution along the fin

Another factor that influences the heat transfer from the fin tip is the temperature distribution along the fin's length. If the temperature of the fin decreases substantially as we move from the base towards the tip, the fin tip's temperature will be lower. Consequently, the temperature difference between the fin tip and the surrounding medium will be less, and so will the heat transfer.

Determine the conditions under which we can neglect heat transfer from the fin tip

We can neglect heat transfer from the fin tip in the following conditions: 1. The fin tip's surface area is much smaller compared to the total surface area of the fin. 2. The temperature difference between the fin tip and the surrounding medium is minimal, owing to a significant temperature drop along the fin's length. If these conditions are met, the heat transfer from the fin tip will be insignificant compared to the total heat transfer from the entire fin, and it can be neglected in calculations.