Energy Payback Optimization of Thermoelectric Power Generator Systems

An analytic model for optimizing thermoelectric power generation system is developed and utilized for parametric studies. This model takes into account the external thermal resistances with hot and cold reservoirs. In addition, the spreading thermal resistance in the module substrates is considered to find the impact of designing small fraction of thermo elements per unit area. Previous studies are expanded by a full optimization of the electrical and thermal circuits. The optimum condition satisfies both electrical load resistance match with the internal resistance and the thermal resistance match with the heat source and the heat sink. Thermoelectric element aspect ratio and fill factor are found to be key parameters to optimize. The optimum leg length and the maximum output power are determined by a simple formula. The output power density per mass of the thermoelectric material has a peak when thermo elements cover a fractional area of ~1%. The role of the substrate heat spreading for thermoelectric power generation is equally significant as thermoelement. For a given heat source, the co-optimization of the heat sink and the thermoelectric module should be performed. Active cooling and the design of the heat sink are customized to find the energy payback for the power generation system. The model includes both the air cooled heat sinks and the water cooled micro channels. We find that one can reduce the mass of thermoelement to around 3~10% of that in commercial modules for the same output power, as long as the module and elements are designed properly. Also one notes that higher heat flux sources have significantly larger energy payback and reduced cost per output power. NOMENCLATURE A: Area (TE substrate or fin) [m 2 ] C: Thermal resistance ratio [(W/K)/(K/W)] Cp: Specific heat [W/mK] D: Width of heat sink or channel [m] d: Leg length [m] F: Fill factor (fraction of element) I: Current [A] L: Length of fluid passage of heat sink or channel [m] m: Electric resistance ratio [ohm/ohm] q: Heat flow [W/m 2 ] R: Electrical resistance of element [ohm] S: Seebeck coefficient [V/K] T: Temperature [K] U: Heat transfer coefficient [W/m2K] u: Fluid flow speed [m/s] w: Power per unit area [W/m 2 ] Z: Figure of merit [1/K] GREEK SYMBOLS : Thermal conductivity [W/mK] : fin spacing [m] : Spreading angle [deg] : Efficiency : Dimension thickness of substrate : Density [kg/m3] : Electrical conductivity [S] : Thermal resistance [K/W] SUBSCRIPTS a: ambient BASE: heat sink foot print Proceedings of the ASME 2010 International Mechanical Engineering Congress & Exposition IMECE2010 November 12-18, 2010, Vancouver, British Columbia, Canada