As the fin efficiency is related to m,and $$m=\sqrt{\frac{hP}{kA}}$$
so we have:
$$m=\sqrt{\frac{2hπr}{kπr^2}}$$
so
$$m=\sqrt{\frac{2h}{kr}}$$
and finally the efficiency is related to m:
$$η=exp(-0.32\sqrt{\frac{2h}{kr}}L)$$
Please note:
1. L is the effective length
2. Volume of Fin is...
As the fin has circular cross section (cylindrical fin), and the volume is constant, increasing length causes decreasing in perimeter and cross sectional area.
The relation can be determined by the following equation:
(Cylinder Volume = Length * Circular Cross Sectional Area)
Assume we have a cylindrical fin which has the effective length of L and its efficiency is given by the equation: $$η=exp(-0.32mL)$$ where $$m=\sqrt{\frac{hP}{kA}}$$ where P is perimeter and A is the cross sectional area of the fin.
If the volume of the fin remains constant, which of the...