A Nonlinear Model of Heat Transfer for Cylindrical Bodies Controlled by a Thermoelectric Converter

Abstract

A boundary control problem for heat transfer processes in solid bodies is considered. The bodies are actuated by applying a voltage to a thermoelectric converter — the Peltier element. A nonlinear model describing the processes both in the Peltier element and heated or cooled bodies is proposed. The model takes into account the recuperation of the heat energy into electric one due to the Seebeck effect and the Joule heating. It is also assumed that there is an exchange of heat with the surrounding medium. As an example, we consider a structure consisting of two coaxial cylinders. A thin Peltier element is placed between them in contact with the ends of the cylinders. By using linearization with respect to the temperature, eigenfunctions are analytically constructed and eigenvalues are found for the resulting nonlinear control problem. Based on the feedback linearization, a feedforward control strategy and feedback compensation of the external disturbances are proposed.