A thin film 500 W electrical heater of negligible thickness and dimensions 100 mm × 100 mm is sandwiched between two slabs made of copper alloy (k = 120 W/m · K) and stainless steel (15 W/m · K). The two plates, copper and stainless steel with thickness 50 mm and 50 mm are surrounded by air with heat transfer coefficients of 75 W/m² · K and 25 W/m² · K, respectively. The plates are subjected to a constant temperature of 50°C and 30°C at the top and the bottom surface, respectively as shown in Fig. P5–75. The temperature of the surrounding air is maintained at 20°C. Determine (a) finite difference formulation at each node and (b) the location of maximum temperature.

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T = 20°C h₁ = 75 W/m².K 1 6 11 2 7 12 Copper alloy Electric film heater 3 8 13 T = 50°C + 9 14 T = 30°C 5 10 Stainless steel 15 T% = 20°C h₂= 25 W/m².K