The electric power generator for an orbiting satellite is composed of a long, cylindrical uranium heat source that is housed within an enclosure of square cross section. The only way for heat that is generated by the uranium to leave the enclosure is through four rows of the thermoelectric modules of Example 3.13. The thermoelectric modules generate electric power and also radiate heat into deep space characterized by T_sur = 4K. Consider the situation for which there are 20 modules in each row for a total of M = 4 = 20 = 80 modules. The modules are wired in series with an electrical load of R_e,load = 250Ω, and have an emissivity of ε = 0.93. Determine the electric power generated for E_g  = 1,10, and 100 kW. Also determine the surface temperatures of the modules for the three thermal energy generation rates.

Example 3.13

An array of M = 48 thermoelectric modules is installed on the exhaust of a sports car. Each module has an effective Seebeck coefficient of S_p-n,eff =
0.1435 V/K, and an internal electrical resistance of R_e,eff = 4Ω. In addition, each module is of width and length W = 54 mm and contains N = 100 pairs of semiconducting pellets. Each pellet has an overall length of 2L = 5mm and cross-sectional area A_c,s = 1.2 10^-5 m² and is characterized by a thermal conductivity of k_s = 1.2 W/m
· K. The hot side of each module is exposed to exhaust gases at T_∞,1 = 550°C with h₁ = 40 W/m₂ · K, while the opposite side of each module is cooled by pressurized water at T_∞,2  = 105°C with h₂ = 500 W/m² · K. If the modules are wired in series, and the load resistance is R_e,load = 400Ω, what is the electric power harvested from the hot exhaust gases?

Transcribed Image Text:

2L- Heat source, E- Insulation Thermoelectric module, s Tsur Re, load tw