Triangular and parabolic straight fins are subjected to the same thermal conditions as the rectangular straight fin of Problem 3.134.
(a) Determine the length of a triangular fin of unit width and base thickness t = 3 mm that will provide the same fin heat rate as the straight rectangular fin. Determine the ratio of the mass of the triangular straight fin to that of the rectangular straight fin.

(b) Repeat part (a) for a parabolic straight fin.

Data From Problem 3.134

A straight fin fabricated from 2024 aluminum alloy  (k = 185 W/m
· K) has a base thickness of t = 3 mm  and a length of L = 15 mm. Its base temperature is  T_b = 100°C, and it is exposed to a fluid for which  T_∞ =  20°C and h = 50 W/m² · K. For the foregoing  conditions and a fin of unit width, compare the fin heat rate, efficiency, and volume for rectangular, triangular, and parabolic profiles.