Question

Two plate fins of constant rectangular cross section are identical, except that the thickness of one of them is twice the thickness of the other. For which fin is the \((a)\) fin effectiveness and (b) fin efficiency higher? Explain.

Short answer

(a) The fin with larger thickness (twice the thickness of the other fin) has higher fin effectiveness. (b) The fin with smaller thickness has higher fin efficiency.

Step-by-step solution

Definitions

Recall the following definitions: (a) Fin effectiveness: The ratio of the fin heat transfer rate to the base (or reference) heat transfer rate. (b) Fin efficiency: The ratio of the fin temperature rise to the temperature rise of an ideal fin (i.e., a fin with perfect thermal conductivity).

Comparing Fin Effectiveness

The fin effectiveness depends on the heat transfer rate, which, in turn, depends on the heat transfer area. A larger heat transfer area increases the effectiveness of the fin. In this case, both fins have the same height, and the fin with twice the thickness has more area available for heat transfer. Therefore, the fin with thicker cross section will have a higher fin effectiveness.

Comparing Fin Efficiency

The fin efficiency depends on the material's thermal conductivity and the fin geometry. A higher thermal conductivity and a thinner fin geometry will result in a fin that approaches the temperature profile of an ideal fin, resulting in higher fin efficiency. While both fins have the same material (and thus the same thermal conductivity), the fin with the smaller thickness has a thinner geometry. As a result, the fin with the smaller thickness should have higher fin efficiency.

Conclusion

In conclusion: (a) The fin with the larger thickness (twice the thickness of the other fin) has a higher fin effectiveness. (b) The fin with the smaller thickness has a higher fin efficiency.