Reconsider Prob. 5–65. Using EES (or other) software, investigate the effects of the thermal conductivity and the heat generation rate on the temperatures at nodes 1 and 3, and the rate of heat loss from the top surface. Let the thermal conductivity vary from 10 W/m · K to 400 W/m · K and the heat generation rate from 10⁵ W/m³ to 10⁸ W/m³. Plot the temperatures at nodes 1 and 3, and the rate of heat loss as functions of thermal conductivity and heat generation rate, and discuss the results.

Data from problem 65

Consider steady two-dimensional heat transfer in a long solid body whose cross section is given in Fig. P5–65. The temperatures at the selected nodes and the thermal conditions on the boundaries are as shown. The thermal conductivity of the body is k = 180 W/m · K, and heat is generated in the body uniformly at a rate of ė = 10⁷ W/m³. Using the finite difference method with a mesh size of Δx = Δy = 10 cm, determine
(a) The temperatures at nodes 1, 2, 3, and 4

(b) The rate of heat loss from the top surface through a 1-m-long section of the body.

Transcribed Image Text:

100 120 150 200 100 è = 107 W/m³ 0.1 m 0.1 m (3) 200 100 2 4 200 100°C 120 150 200