Question

Which one of the following configurations has the highest fin effectiveness?

• A.
  Thin, closely spaced fins
• B.
  Thin, widely spaced fins
• C.
  Thick, widely spaced fins
• D.
  Thick, closely spaced fins

Answer 1

The correct option is A

Thin, closely spaced fins
Fin effectiveness,

$ϵ=\frac{\text{Heat transfer with fin:}{Q}_{Fin}}{\text{Heat transfer without fin:}Q}=\frac{Q_{Fin}}{Q}$

$Q_{Fin}=\sqrt{KPhP}{\theta }_{\circ }$ for long fin

$Q_{Fin}=hA{\theta }_{\circ }$

$ϵ=\frac{\sqrt{KAhP}{\theta }_{\circ }}{hA{\theta }_{\circ }}=\frac{\sqrt{KAhP}}{hA}=\sqrt{\frac{kP}{hA}}$

$ϵ\propto \sqrt{P};\text{and}ϵ\propto \frac{1}{\sqrt{A}}$

For highest fin effectiveness, the perimeter of fin should be large and cross- sectional area should be low. It means, for a large value of perimeter, fins should be closely spaced (to increase the total number of fins ) and for lower value of cross-sectional area, it should be thin.