Reconsider Prob. 5–47. Using EES (or other) software, investigate the effect of the fin base temperature on the fin tip temperature and the rate of heat transfer from the fin. Let the temperature at the fin base vary from 100°C to 200°C. Plot the fin tip temperature and the rate of heat transfer as a function of the fin base temperature, and discuss the results.

Data From problem 47

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