Abstract
In this paper, the mathematical modeling of heat transfer in two aluminum cylinders controlled by a Peltier element is presented. The corresponding initial-boundary value problem is derived based on the Peltier and Seebeck thermoelectric effects in the scope of the linear theory of heat transfer. To validate the reliability of the mathematical model and identify its parameters, several sets of experiments have been performed on an originally designed test rig. The method of separation of variables is used to reduce the original three-dimensional system with distributed parameters to a spatially one-dimensional system which is nonlinear with respect to the input voltage as control function. The eigenvalues and eigenforms for the linearized problem are found by applying a Fourier analysis. The steady-state heat flow under a constant input signal is obtained for the considered structure as well. The corresponding numerical results are discussed.
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