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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
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/m^{2} ∙ 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.
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