Consider an aluminum alloy fin (k = 180 W/m · K) of triangular cross section whose length is L = 5 cm, base thickness is b = 1 cm, and width w in the direction normal to the plane of paper is very large. The base of the fin is maintained at a temperature of T₀ = 180°C. The fin is losing heat by convection to the ambient air at T∞ = 25°C with a heat transfer coefficient of h = 25 W/m² · K and by radiation to the surrounding surfaces at an average temperature of T_surr = 290 K. Using the finite difference method with six equally spaced nodes along the fin in the x-direction, determine

(a) The temperatures at the nodes

(b) The rate of heat transfer from the fin for w = 1 m. Take the emissivity of the fin surface to be 0.9 and assume steady one-dimensional heat transfer in the fin.

Transcribed Image Text:

To k. b 0 W 0 2 -Triangular fin h, To tan 0 b/2 L X