The flat base of the bottom of an electric water heater is made of a 2 mm thick steel plate. thermal conductivity of 40 W/(m. oC), and an insulating plate with a thickness of 4 mm and thermal conductivity of 0.06 W/(m. oC). Between the steel and insulating plates there is an electrical resistance (RE) that dissipates a power of 800 W. Consider the steady state situation with boiling water at a temperature of 100 oC and with a coefficient of heat transfer by convection of 3000 W/(m2. oC), while the ambient air, which is in contact with the insulator, it remains at a temperature of 25oC and a convection heat transfer coefficient of 10 W/(m2.oC).

Considering a perfect thermal contact between the electrical resistance and the steel and insulating sheets and that the base of the heater has an area of 0.018 m2, determine:

a) The temperature (TR) of the electrical resistance;

b) The rate of heat lost to the air through of the insulating plate;

ç). The rate of heat lost to water through the steel plate.