Consider a 5-m-long constantan block (k = 23 W/m · K) 30 cm high and 50 cm wide (Fig. P5–70). The block is completely submerged in iced water at 0°C that is well stirred, and the heat transfer coefficient is so high that the temperatures on both sides of the block can be taken to be 0°C. The bottom surface of the bar is covered with a low-conductivity material so that heat transfer through the bottom surface is negligible. The top surface of the block is heated uniformly by a 8-kW resistance heater. Using the finite difference method with a mesh size of Δx = Δy = 10 cm and taking advantage of symmetry,

(a) Obtain the finite difference formulation of this problem for steady two dimensional heat transfer,

(b) Determine the unknown nodal temperatures by solving those equations,

(c) Determine the rate of heat transfer from the block to the iced water.

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8 kW heater 0°C Insulation >10cm 10cm ↓↓↓↓↓↓↓↓↓↓↓↓↓↓ 0000 Insulation 0°C