RESEARCH ARTICLE Segmented thermoelectric generator: exponential area variation in leg Haider Ali 1 | Bekir Sami Yilbas 1,2 | Abdullah Al‐Sharafi 1 1 Department of Mechanical Engineering, King Fahd University of Petroleum and Mineral, Dhahran 31261, Saudi Arabia 2 Center of Research Excellence in Renewable Energy, Research Institute, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia Correspondence Bekir Sami Yilbas, Center of Research Excellence in Renewable Energy, Research Institute, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia. Email: bsyilbas@kfupm.edu.sa Funding information King Fahd University of Petroleum and Minerals, Grant/Award Number: RG 1501 Summary The innovative design of segmented thermoelectric generator with exponential area variation is introduced. Thermal efficiency and power output are assessed for various values of the design parameter (a =(L/x) ln[A a /A(x)], where A a is constant, and a is the dimensionless geometric parameter, L is the pin length, and A(x) is the pin cross‐sectional area), external load parameter (R L /R 0 , ratio of external electrical resistance to reference electrical resistance), and tempera- ture parameter (θ = T low /T high , ratio of cold junction temperature to high junc- tion temperature). The device efficiency obtained is validated through the previous experimental data for various hot and cold junction temperature dif- ferences. The findings reveal that thermal efficiency resulted from the current study agrees well with the experimental data. The innovative design of the seg- mented thermoelectric generator with exponentially decaying pin configuration enhances the thermal efficiency and output power as compared with the device having a single material pin configuration. Increasing temperature ratio results in the reduction in the thermal efficiency and the output power of thermoelec- tric generator. In addition, lowering the external load parameter improves the thermal efficiency and the output power of the thermoelectric device. The design parameter that maximizes the thermal efficiency of the thermoelectric generator does not maximize the device output power. KEYWORDS performance, pin configuration, segmented thermoelectric generator Nomenclature: a, Dimensionless geometric factor; A 0 , Area of rectangular geometry of thermoelectric generator (m 2 ); A(x), Cross‐sectional area variation of thermoelectric generator (m 2 ); I, Electrical current (A); k eff , n , Effective thermal conductivity of n‐type semi‐conductor (W/mK); k eff , p , Effective thermal conductivity of p‐type semi‐conductor (W/mK); k n , Thermal conductivity of n‐type semi‐conductor (W/mK); k p , Thermal conductivity of p‐type semi‐conductor (W/mK); K eff , Overall effective thermal conductance of thermoelectric generator (W/K); K 0 , Reference thermal conductivity for thermoelectric generator (W/K); L, Total length of the leg of thermoelectric generator (m); R L , External load resistance (Ω); R n , Electrical resistance of n‐type leg of semi‐conductor (Ω); R p , Electrical resistance of p‐type leg of semi‐conductor (Ω); R 0 , Reference electrical resistance (Ω); R TEG , Overall electrical resistance in of the thermoelectric generator (Ω); T high , Hot side temperature of the thermoelectric generator (K); T low , Cold side temperature of the thermoelectric generator (K); T int , n , Temperature at the interface of 2 n‐type materials (K); T int , p , Temperature at the interface of 2 p‐type materials (K); V, Voltage (V); V o , Volume of thermoelectric generator (m 3 ); W, Power output of the thermoelectric generator (W); ZT avg , Dimensionless figure of merit (1/K); α n , Seebeck coefficient of n‐type semi‐conductor (V/K); α n , eff , Effective Seebeck coefficient of n‐type leg of semi‐conductor (V/K); α p , Seebeck coefficient of p‐type semi‐conductor (V/K); α p , eff , Effective Seebeck coefficient of p‐type leg of semi‐conductor (V/K); α eff , Overall effective Seebeck coefficient of the thermoelectric generator (V/K); μ n , (=L n ,1 /L) Dimensionless ratio of n‐type material 1 to total length of thermoelectric generator; μ p , (=L p ,1 /L) Dimensionless ratio of p‐type material 1 to total length of thermoelectric generator.; η, Efficiency; σ p , Electrical conductivity of p‐type semi‐conductor (S/m); σ n , Electrical conductivity of n‐type semi‐conductor (S/m); θ, (=T low /T high ) Dimensionless ratio of the low and high temperature of the thermoelectric generator. Received: 28 April 2017 Revised: 8 June 2017 Accepted: 23 June 2017 DOI: 10.1002/er.3825 Int J Energy Res. 2017;1–13. Copyright © 2017 John Wiley & Sons, Ltd. wileyonlinelibrary.com/journal/er 1