Question

For an insulated tip, the fin efficiency is given by

• A. \( \frac{\cosh(ml)}{ml} \)
• B. \( \frac{\sinh(ml)}{ml} \)
• C. \( \frac{\tanh(ml)}{l} \)
• D. \( \frac{\tanh(ml)}{ml} \)

Hint:

Fin efficiency depends on the thermal properties and geometry of the fin, and is expressed using the \( \tanh \) function for an insulated tip.

Answer 1

The Correct Option is D

Step 1: Understand fin efficiency.
For an insulated tip, the fin efficiency is a function of the thermal conductivity, length of the fin, and heat transfer. The formula for fin efficiency with an insulated tip is: \[ \eta = \frac{\tanh(ml)}{ml} \] Where \( m \) is a function of the thermal conductivity and cross-sectional area, and \( l \) is the length of the fin. Step 2: Conclusion.
The correct formula for fin efficiency for an insulated tip is \( \frac{\tanh(ml)}{ml} \). Final Answer: \[ \boxed{\frac{\tanh(ml)}{ml}} \]