Modeling, Experimental Identification, and Optimization of Heat Transfer in a Metal Bar Controlled by Peltier Elements

Abstract In this paper, a problem for heat conduction in a metal bar heated and cooled by Peltier elements attached to its bottom surface is investigated. The bar has the shape of an elongated cuboid, the vertical sides of which are insulated, whereas the heat exchange with the environment takes place on the upper and lower surfaces. A 4D PDE model of heat transfer in the cuboid body is considered and an experimental identification of unknown system parameters is performed. The optimal control problem is to find the time law for the elements’ heat powers transferring the system to a stationary terminal state and minimizing a quadratic cost function.