Thermoelectric modules have been used to generate electric power by tapping the heat generated by wood stoves. Consider the installation of the thermoelectric module of Example 3.13 on a vertical surface of a wood stove that has a surface temperature of T_s = 375°C. A thermal contact resistance of R"_t,c = 5  X 10^–6 m² · K/W exists at the interface between the stove and the thermoelectric module, while the room air and walls are at T_∞ = T_sur = 25°C. The exposed surface of the thermoelectric module has an emissivity of ε = 0.90 and is subjected to a convection coefficient of h = 15 W/m²  · K. Sketch the equivalent thermal circuit and determine the electric power generated by the module. The load electrical resistance is R_e,load  =  3 Ω.

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?