When raised to very high temperatures, many conventional liquid fuels dissociate into hydrogen and other components. Thus the advantage of a solid oxide fuel cell is that such a device can internally reform readily available liquid fuels into hydrogen that can then be used to produce electrical power in a manner similar to Example 1.4. Consider a portable solid oxide fuel cell, operating at a temperature of T_fc = 800°C. The fuel cell is housed within a cylindrical canister of diameter D = 75 mm and length L = 120 mm. The outer surface of the canister is insulated with a low-thermal-conductivity material. For a particular application, it is desired that the thermal signature of the canister be small, to avoid its detection by infrared sensors. The degree to which the canister can be detected with an infrared sensor may be estimated by equating the radiation heat flux emitted from the exterior surface of the canister (Equation 1.5; Es = ε_sσT⁴_s) to the heat flux emitted from an equivalent black surface, (E_b = σT⁴_b). If the equivalent black surface temperature, T_b, is near the surroundings temperature, the thermal signature of the canister is too small to be detected-the canister is indistinguishable from the surroundings.

(a) Determine the required thickness of insulation to be applied to the cylindrical wall of the canister to ensure that the canister does not become highly visible to an infrared sensor (i.e., T_b – T_sur < 5 K). Consider cases where (i) the outer surface is covered with a very thin layer of dirt (e s = 0.90) and (ii) the outer surface is comprised of a very thin polished aluminum sheet (e s = 0.08). Calculate the required thicknesses for two types of insulating material calcium silicate (k = 0.09 W/m ∙ K) and aero-gel (k = 0.006 W/m ∙ K) the temperatures of the surroundings and the ambient are T_sur = 300 K and T_∞ = 298 K, respectively. The outer surface is characterized by a convective heat transfer coefficient of h = 12 W/m² ∙ K.

(b) Calculate the outer surface temperature of the canister for the four cases (high and low thermal conductivity; high and low surface emissivity).

(c) Calculate the heat loss from the cylindrical walls of the canister for the four cases.