Question

The fin efficiency is defined as the ratio of the actual heat transfer from the fin to (a) The heat transfer from the same fin with an adiabatic tip (b) The heat transfer from an equivalent fin which is infinitely long (c) The heat transfer from the same fin if the temperature along the entire length of the fin is the same as the base temperature (d) The heat transfer through the base area of the same fin (e) None of the above

Short answer

Answer: Fin efficiency is defined as the ratio of the actual heat transfer from the fin to the heat transfer from the same fin if the temperature along the entire length of the fin is the same as the base temperature.

Step-by-step solution

Understanding the Definition of Fin Efficiency

Fin efficiency is defined as the ratio of the actual heat transfer from the fin (Q_actual) to the maximum heat transfer possible if the entire fin were to be at the base temperature (Q_max). This can be written as: Fin efficiency = \(\frac{Q_{actual}}{Q_{max}}\) Now, let's evaluate each option.

Analyzing Each Option

(a) The heat transfer from the same fin with an adiabatic tip. Not correct. An adiabatic tip means no heat transfer occurs at the tip, which influences the actual heat transfer, but the ratio is not related only to this condition. (b) The heat transfer from an equivalent fin which is infinitely long. Not correct. The heat transfer from an infinitely long fin would be greater than that from a fin of finite length, but it is not the maximum heat transfer achievable by the actual fin. (c) The heat transfer from the same fin if the temperature along the entire length of the fin is the same as the base temperature. Correct! This option matches the definition of fin efficiency. If the entire fin is at the base temperature, it would maximize the heat transfer (Q_max) for the given situation. (d) The heat transfer through the base area of the same fin. Not correct. The heat transfer through the base area doesn't account for the conductive heat transfer along the length of the fin, which should be considered in determining fin efficiency. (e) None of the above. Not correct. Option (c) correctly represents the definition of fin efficiency.

Selecting the Correct Answer

After analyzing each option, we can conclude that the correct answer is: Fin efficiency is defined as the ratio of the actual heat transfer from the fin to: (c) The heat transfer from the same fin if the temperature along the entire length of the fin is the same as the base temperature.