C11. Consider a cylindrical reservoir 0.6 m high, with inside diameter of 0.4 m and negligible wall thickness. The
bottom and the top of the reservoir are perfectly insulated. The reservoir is exposed to an air current at 15 °C. In
this reservoir, full of liquid, an electrical heating resistance is introduced dissipating continuously 200 W. The
reservoir side wall is covered by an insulating material.
Once the steady state is attained the liquid temperature stabilizes at 70 °C. The liquid side heat transfer coefficient
is $h_i = 40 \text{ W/(m}^2 \text{.K)}$ and the air side heat transfer coefficient is $h_e = 10 \text{ W/(m}^2 \text{.K)}$.
According to the given data and the operating conditions described, answer the following questions:
a) Draw the equivalent thermal resistance circuit of the system presented.
b) Determine the overall heat transfer coefficient.
c) Determine the inside reservoir wall temperature.
d) If the insulating material has 2 cm thickness, determine the value of the respective thermal conductivity
to guarantee the operating conditions described above.
e) Obtain the temperature profile equation along the insulating material wall. Sketch the temperature
profile obtained, conveniently justifying. Note: if you did not solve d) use $k_{isol} = 0.2 \text{ W/(m.K)}$
