The heat transfer surface area of a fin is equal to the sum...

Name: Problem 121, Chapter 3: Heat and Mass Transfer: Fundamentals and Applications
Uploaded: 2023-10-29T16:34:37-08:00
Duration: 2 min 24 s
Channel: Kratika Bhadauria
Description: 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?

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?

Key Concepts

Extended Surfaces (Fins)

Fins are used in thermal management to increase the heat transfer area beyond that of the basic body. Their analysis involves balancing heat conduction along the fin with convective losses from its surfaces. This concept is crucial for understanding how fins enhance thermal performance by dissipating heat into the surrounding medium.

Geometric Considerations

The geometry of a fin—including its length, thickness, and especially the relative size of the tip area compared to the lateral surface—directly influences its overall heat transfer. When the fin is long and thin, the lateral surface area far exceeds the tip area, making the heat loss from the tip relatively insignificant.

Adiabatic Tip Assumption

In many practical analyses, the tip of a fin can be approximated as adiabatic (i.e., no heat transfer occurs there) if its contribution to the overall heat transfer is negligible. This is typically valid when the tip’s surface area is small or when the convective heat transfer coefficient at the tip is low compared to that on the fin surfaces.

Non-Dimensional Parameters (e.g., mL, Biot Number)

Parameters like the product mL—which derives from the fin parameter m (a function of thermal conductivity, convective coefficient, and geometry) and the fin length L—and the Biot number help quantify the relative significance of conduction in the fin and convection at its surfaces. When these parameters indicate that the tip region's effect on overall heat transfer is minimal, neglecting tip convection is justified.

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