One of the thermoelectric modules of Example 3.13 is installed between a hot gas at T_∞,1 = 450°C and a cold gas at T_∞,2 = 20°C. The convection coefficient associated with the flowing gases is h = h₁ = h₂ = 80 W/m² · K while the electrical resistance of the load is R_e,load 
= 4Ω.

(a) Sketch the equivalent thermal circuit and determine the electric power generated by the module for the situation where the hot and cold gases provide convective heating and cooling directly to the module (no heat sinks).
(b) Two heat sinks (k = 180 W/m
· K; see sketch), each with a base thickness of L_b = 4 mm and fin length L_f  = 20 mm, are soldered to the upper and lower sides of the module. The fin spacing is 3 mm, while the solder joints each have a thermal resistance of R"_t,c = 2.5  X 10^–6 m² · K/W. Each heat sink has N = 11 fins, so that t = 2.182 mm and S = 5.182 mm, as determined from the requirements that W = (N — 1)S + t and S– t– 3 mm. Sketch the equivalent thermal circuit and determine the electric power generated by the module. Compare the electric power generated to your answer for part (a). Assume adiabatic fin tips and convection coefficients that are the same as in part (a).

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:

- Cover plate Heat sink 1, k Lip ↓ 4 Air T1, h₂ E Thermoelectric module на на Air T2¹₂ HUL W S 12L Reload Solder, R 4,c Heat sink 2, k Cover plate