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.

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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