Optimal Length of a fin
In general, the longer the fin, the higher the heat transfer. However, a long fin means more material and increased size and cost. Question: how do we determine the optimal fin length? Use the rectangular fin as an example:
Note: heat transfer increases with mL as expected. Initially the rate of change is large and slows down drastically when mL> 2.
R(1)=0.762, means any increase beyond mL=1 will increase no more than 23.8% of the fin heat transfer.