Question

Consider the following statements:

An increase in pin fin effectiveness is caused by high value of

1. Convective coefficient

2. Thermal conductivity

3. Sectional area

4. Circumference

Which of the above statements are correct?
1. 1 and 3
2. 1 and 4
3. 2 and 3
4. 2 and 4

Answer 1

Correct Answer - Option 4 : 2 and 4

Concept:

Fin effectiveness is the ratio of actual heat transfer that takes place from the fin to the heat that would be dissipated from the same surface area without fin i.e. 

Calculation:

\({\rm{\varepsilon }} = \frac{{{\rm{heat\;transfer\;from\;the\;fin\;}}}}{{{\rm{eat\;transfer\;without\;fin}}}}\)

\({\rm{\varepsilon }} = \frac{{\sqrt {hpk{A_c}} {\rm{\Delta }}T}}{{h{A_c}{\rm{\Delta T}}}}\)

\({\rm{\varepsilon }} = \frac{{pk}}{{\sqrt {h{A_c}} }}\)

Where, h = heat transfer coefficient, k = Thermal conductivity of fin, p = perimeter of a fin

Ac = cross-sectional area of a fin

From equation obtained of the effectiveness it can be found that, effectiveness increases with increase in thermal conductivity and circumference.