Consider the engine block of a car made of cast iron (k = 52 W/m · K and α = 1.7 × 10^-5 m²/s). The engine can be considered to be a rectangular block whose sides are 80 cm, 40 cm, and 40 cm. The engine is at a temperature of 150°C when it is turned off. The engine is then exposed to atmospheric air at 17°C with a heat transfer coefficient of 6 W/m² · K. Determine

(a) The center temperature of the top surface whose sides are 80 cm and 40 cm

(b) The corner temperature after 45 min of cooling.