Question

Provision of fins on a heat transfer surface will be more effective if the number and size of fins are

• A. Fewer and thick
• B. Large and thick
• C. Large and thin
• D. Fewer and thin

Hint:

Extended Surface Fin Design: Fins are most effective when they are LARGE IN NUMBER AND THIN (provides maximum surface area with high fin effectiveness $\epsilon = \sqrt{kP/hA_c}$).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Extended surface fin optimization in heat exchangers: fin effectiveness ($\epsilon_{ ext{fin}} = \sqrt{ rac{P k}{h A_c}}$) is maximized by employing a large number of closely spaced, thin fins (small cross-sectional area $A_c$, high perimeter-to-area ratio $P/A_c$, and high surface area).
Key Formula or Approach:
\[ \text{Fin Effectiveness } (\epsilon_{\text{fin}}) = \sqrt{\frac{h k P}{h^2 A_c}} = \sqrt{\frac{k P}{h A_c}} \quad \implies \quad \mathbf{\text{Maximized by Large Number of Thin Fins (High } P/A_c)} \]

Step 2: Detailed Explanation:
In extended surface heat transfer engineering (refrigeration condensers, milk chillers, air heaters):
- Extended surfaces (fins) are attached to heat transfer walls to enhance convective heat dissipation when the outer film heat transfer coefficient ($h$) is low (e.g., gas/air side).
- To achieve maximum thermal effectiveness:
1. Thin Fins (Small Thickness $\delta$): Minimizes conducting material cross-sectional area ($A_c = w \delta$) and maximizes the perimeter-to-area ratio ($P/A_c \approx 2/\delta$), allowing rapid heat conduction into the fin base with minimal conductive resistance.
2. Large Number of Fins: Multiplies total external convective surface area by 10- to 20-fold.
- Therefore, the provision of fins is most effective when they are Large in number and thin in size (Large and thin) (C).

Step 3: Final Answer:
Hence, fins are more effective if they are Large and thin, matching option (C).