Thermoelectric device and optimum external load parameter and slenderness ratio

Thermodynamic formulation of efficiency of thermoelectric power generator is presented in terms of the slenderness ratio (X=(A_p/L_p)/(A_n/L_n)) and the external load parameter (Y=(R_L)/(L_n/k_e,nA_n)). The optimum values of the slenderness ratio and external load parameter, maximizing the device efficiency, are formulated and predicted for several values of the thermal conductivity and the electrical conductivity ratios. The study is extended to include the influence of the dimensionless figure of merit (ZT_avg) and the temperature ratio on the maximum efficiency of the generator. It is found that for a fixed thermal conductivity ratio, the external load parameter increases with increasing the slenderness ratio while the electrical conductivity ratio of the p and n pins in the device reduces.