Material property effect on conical semiconductor element temperatures in inhomogeneous thermoelectric coolers

The temperature-dependent material property effects, including the thermal conductivity, Seebeck coefficient, and electrical resistivity, on the thermoelectric element (TE) temperature profiles are assessed in this study. The nonlinear partial differential equation governing energy transport within a one-dimensional TE is solved using a finite difference method. The solution of the TE temperature field is obtained by solving the resulting finite difference equation in the form of a third-order polynomial. The effects of key variables on the cooling process are discussed using a practical example. Results indicate that internal constrictive resistance and Joule heat generation can be reduced with conical elements when compared to conventional free-standing elements. The cooling efficiency can be improved by incorporating a temporarily transient current pulse before it reaches a steady-state condition. This additional transient cooling and steady-state recovery time strongly depend on the magnitude of the current pulsed, duration, and pulse shape, as well as material properties. Strategies for cooling are investigated in this study; the knowledge gained from this study can be utilized by engineers in the thermoelectric industry for design optimization.