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: Fin Efficiency Explained.
For a fin with an insulated tip, the fin efficiency depends on its thermal conductivity, length, and heat transfer characteristics. The equation to calculate this efficiency is:\[\eta = \frac{\tanh(ml)}{ml}\]Here, \( m \) depends on thermal conductivity and cross-sectional area, while \( l \) represents the fin's length.Step 2: Summary.
The fin efficiency formula for a fin with an insulated tip is indeed \( \frac{\tanh(ml)}{ml} \). Final Answer: \[ \boxed{\frac{\tanh(ml)}{ml}} \]