Thermoelectric energy recovery is an important technology for recovering waste thermal energy in high-temperature industrial, transportation and military energy systems. Thermoelectric (TE) power systems in these applications require high performance hot-side and cold-side heat exchangers to provide the critical temperature differential and transfer the required thermal energy to create the power output. Hot-side and cold-side heat exchanger performance is typically characterized by hot-side and cold-side thermal resistances, R h,th and R c,th , respectively. Heat exchanger performance determines the hot-side temperature, T h , and cold-side temperature, T c , conditions when operating in energy recovery environments with available temperature differentials characterized by exhaust temperatures, T exh , and ambient temperature, T amb . This work analytically defined a crucially important design relationship between (P/P max ) and (R h,th / R c,th ) in TE power generation systems to determine the optimum ratio of (R h,th / R c,th ) maximizing TE system power. A sophisticated integrated TE device / heat exchanger analysis was used, which simultaneously integrates hot-and cold-side heat exchanger models with TE device optimization models incorporating temperature-dependent TE material properties for p-type and n-type materials, thermal and electrical contact resistances, and hot side and cold side heat loss factors. This work examined the (P/P max ) -(R h,th / R c,th ) relationship for system designs employing singlematerial and segmented-material TE couple legs with various TE material combinations, including bismuth telluride alloys, skutterudite compounds, and skutterudite / bismuth telluride segmented combinations. This work defined the non-dimensional functional relationships and found the optimum thermal resistance condition:(R h,th / R c,th ) opt > 10 to 30 created the maximum power output in TE optimized designs for various TE material combinations investigated. The non-dimensional relationships were investigated for various electrical contact resistances, differing thermal loss factors, and at various hot-side/cold-side temperature conditions. This work showed that the non-dimensional functional relationships were invariant under these differing conditions. It was determined that a condition of (R h,th / R c,th ) = 1 creates power output far below maximum power conditions. The (P/P max ) -(R h,th / R c,th ) relationship also dictated certain temperature profile conditions, defined by the parameter, (T h -T c ) / (T exh -T amb ) , which were directly associated with design points in this relationship including maximum power points. The value of (T h -T c ) / (T exh -T amb ) was generally less than 0.5 at maximum power conditions in TE energy recovery designs using TE materials investigated here. The wide-ranging ramifications on TE energy recovery systems and their design optimization for industrial and transportationrelated applications are discussed.
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