The Fractional Order Models of a Thermal Trace on a Heat-Insulating Surface

The paper deals with a modeling of thermal trace at heat insulating surface with the use of two Fractional Order (FO) state space models. The fundamental distributed-parameter model was compared to simplified, lumped-parameter model, built with the assumption that the spatial heat transfer can be omitted. Such a comparison has not been presented yet. The simplifying assumption was confirmed experimentally in two ways. Firstly, the proposed lumped-parameter model assures the same accuracy in the sense of Integral Absolute Error (IAE) cost function as distributed-parameter model. Next, identified values of the heat transfer coefficient in the heat transfer equation are close to zero.