For one of the M = 48 modules of Example 3.13, determine a variety of different efficiency

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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, ηtherm  = P= 1/q1.

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

(c) Determine the Carnot efficiency,ηCarnot = 1 – T2/T1.
(d) Determine both the thermoelectric efficiency and the Carnot efficiency for the case where h= h→ ∞.
(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 ηTE 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 Sp-n,eff = 0.1435 V/K, and an internal electrical resistance of Re,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 Ac,s = 1.2 10-5 mand is characterized by a thermal conductivity of k= 1.2 W/m· K. The hot side of each module is exposed to exhaust gases at T∞,1 = 550°C with h= 40 W/m· K, while the opposite side of each module is cooled by pressurized water at T∞,2  = 105°C with h2 = 500 W/m· K. If the modules are wired in series, and the load resistance is Re,load = 400Ω, what is the electric power harvested from the hot exhaust gases?

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Fundamentals Of Heat And Mass Transfer

ISBN: 9780470501979

7th Edition

Authors: Theodore L. Bergman, Adrienne S. Lavine, Frank P. Incropera, David P. DeWitt

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