For one of the M = 48 modules of Example 3.13, determine a variety of different efficiency values concerning the conversion of waste heat to electrical energy.

(a) Determine the thermodynamic efficiency, η_therm  = P_{M = 1}/q₁.

(b) Determine the figure of merit ZT for one module, and the thermoelectric efficiency,η_TE using Equation 3.128.

(c) Determine the Carnot efficiency,η_Carnot = 1 – T₂/T₁.
(d) Determine both the thermoelectric efficiency and the Carnot efficiency for the case where h₁ = h₂ → ∞.
(e) The energy conversion efficiency of thermoelectric devices is commonly reported by evaluating Equation 3.128, but with T_∞,1 and T_∞,2 used instead of T₁ and T₂, respectively. Determine the value of η_TE based on the inappropriate use of Tc_,1 and T_∞,2, and compare with your answers for parts (b) and (d).

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:

MTE 1 T₂ VI+ZT-1 T₁ V1+ZT+T₂/T₁