Simulation of a thermoelectric element using B-spline collocation methods

Many authors have described ways of calculating the efficiency of thermoelectric devices. These calculations usually make simplifying assumptions to define the behavior of the device. The most common of these is to make the thermoelectric material properties constant. This paper presents work in progress toward simulating the behavior of real thermoelectric devices. We present the steady state differential equations defining the behavior of thermoelectric materials and the associated boundary conditions required to solve power generation and cooling element problems. We implemented a simple one-dimensional simulation of a power-generating device using B-spline collocation methods. The results of the simulation are compared to an example presented by Angrist (1976).