Functionally Graded Thermoelectric Materials with Arbitrary Property Gradations: A One-Dimensional Semianalytical Study

This paper presents a semianalytical model to obtain the temperature distribution and energy conversion efficiency for functionally graded thermoelectric materials (FGTEMs) with arbitrary property gradients along the direction of the thermoelectric (TE) device leg. A multilayered material model is employed in which the FGTEM is divided into many layers throughout the length of the TE element where each layer is treated as a homogeneous material with constant Seebeck coefficient, electrical resistivity, and thermal conductivity. An approximate, closed-form temperature solution is obtained by solving the heat conduction equation in each homogeneous layer with the conditions of temperature and heat flux continuity across the interfaces between the homogeneous layers. The energy conversion efficiency is subsequently obtained using the approximate temperature solution. Numerical simulations are focused on the effects of the property gradation profile on the efficiency of FGTEMs with sigmoid property gradients. It is found that the peak efficiency may be increased significantly by using appropriately designed property gradients. The present model provides a convenient analytical tool for optimal design of FGTEMs with improved efficiency.