Consider steady two-dimensional heat transfer in a long solid bar of

(a) Square

(b) Rectangular cross sections as shown in the figure. The measured temperatures at selected points of the outer surfaces are as shown. The thermal conductivity of the body is k = 20 W/m · K, and there is no heat generation. Using the finite difference method with a mesh size of Δx = Δy = 1.0 cm, determine the temperatures at the indicated points in the medium.

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150 180 200 180 200°C 1 2 3 (4) Insulation (a) Insulation 100 120 140 120 120 1 (3) Insulation (b) 2 4 100°C 120 140