It is desired to estimate the effectiveness of a horizontal, straight fin of rectangular cross section when applied to a surface operating at 45°C in an environment for which the surroundings and ambient air are at 25°C. The fin is to be fabricated from aluminum alloy (2024- T6) with an anodized finish (B = 0.82) and is 2 mm thick and 100 mm long.

(a) Considering only free convection from the fin surface and estimating an average heat transfer coefficient, determine the effectiveness of the fin.

(b) Estimate the effectiveness of the fin, including the influence of radiation exchange with the surroundings.

(c) Using a numerical method, develop the finite-difference equations and obtain the fin effectiveness. The free convection and radiation exchange modes should be based on local, rather than average, values for the fin.