Consider an aluminum alloy fin (k= 180 W/m·K) of triangular cross section whose length is...

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 IV 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 Tsurr = 290 K. Using the finite difference method with six equally spaced nodes along the tin in the x-direction. determine (a) the temperatures at the nodes and (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.

Answers: (a) 177.0°C, 174.1°C, 171.2°C. 168.4°C. 165,5°C:

(b) 537 W

FIGURE P 5-26