ICT2014 Abstracts

This work describes a semi–analytical model to obtain the temperature distribution and the energy conversion efficiency for functionally graded thermoelectric materials (FGTEMs) with arbitrary variations of material properties along the direction of the thermoelectric generator (TEG) leg. This work employs a multilayered material model in which the FGTEM is divided into many layers along the TEG leg where each layer is treated as a homogeneous material. The thermoelectric properties (Seebeck coefficient S, electrical resistivity ρ and thermal conductivity k) in each layer are independent of the spatial coordinate, but may depend on the average temperature across the layer. An approximate, closed-form temperature solution is obtained by solving the heat conduction equation in each homogeneous layer with the continuity conditions of temperature and heat flux across the interfaces between the homogeneous layers. The energy conversion efficiency is subsequently obtained using the approximate temperature solution. The peak efficiency and the optimal current density are determined from the efficiency solution. The numerical simulations are focused on the effects of property gradation profile on the efficiency of FGTEMs with power-law property gradients. It is found that the peak efficiency may be increased significantly using appropriately designed property gradients. For example, for a constant Seebeck coefficient the efficiency may be increased by more than 35% when both the thermal conductivity and electrical resistivity decrease linearly from the cold end towards the hot end. The efficiency enhancement may be improved or degraded depending on the property variation profiles. The present model may be used to quantitatively investigate the effects of arbitrary material gradation on the FGTEM efficiency.