A thin film 500 W electrical heater of negligible thickness and dimensions 100 mm 100 mm

Question:

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.