Solve heat transfer problem:

$10($ten$)$ pin fins of $30$ mm length and $5$ mm diameter randomly placed on the top surface of

the insulation. The fins are made from the same material as insulation.

A$.$ Do these fins behave like infinitely long fins?

B$.$ What is the efficiency of the finned surface?

C$.$ What is the effectiveness of the finned surface?

D$.$ What is the new heat transfer rate toward the top and the bottom?

E$.$ How much time does it take to melt the ice? Based on this analysis $-$ do you think it was a good idea or a bad idea to attach these fins?