C. Baker, Vuppuluri, P., Shi, L., and Hall, M. J., “Model of Heat Exchangers for Waste Heat Recovery from Diesel Engine Exhaust for Thermoelectric Power Generation,” Journal of Electronic Materials , vol. 41, pp. 1290–1297, 2012.
The performance and operating characteristics of a hypothetical thermoelectric generator system designed to extract waste heat from the exhaust of a medium-duty turbocharged diesel engine were modeled. The finite-difference model consisted of two integrated submodels: a heat exchanger model and a thermoelectric device model. The heat exchanger model specified a rectangular cross-sectional geometry with liquid coolant on the cold side, and accounted for the difference between the heat transfer rate from the exhaust and that to the coolant. With the spatial variation of the thermoelectric properties accounted for, the thermoelectric device model calculated the hot-side and cold-side heat flux for the temperature boundary conditions given for the thermoelectric elements, iterating until temperature and heat flux boundary conditions satisfied the convection conditions for both exhaust and coolant, and heat transfer in the thermoelectric device. A downhill simplex method was used to optimize the parameters that affected the electrical power output, including the thermoelectric leg height, thermoelectric n-type to p-type leg area ratio, thermoelectric leg area to void area ratio, load electrical resistance, exhaust duct height, coolant duct height, fin spacing in the exhaust duct, location in the engine exhaust system, and number of flow paths within the constrained package volume. The calculation results showed that the configuration with 32 straight fins was optimal across the 30-cm-wide duct for the case of a single duct with total height of 5.5 cm. In addition, three counterflow parallel ducts or flow paths were found to be an optimum number for the given size constraint of 5.5 cm total height, and parallel ducts with counterflow were a better configuration than serpentine flow. Based on the reported thermoelectric properties of MnSi1.75 and Mg2Si0.5Sn0.5, the maximum net electrical power achieved for the three parallel flow paths in a counterflow arrangement was 1.06 kW for package volume of 16.5 L and exhaust flow enthalpy flux of 122 kW.