Analysis of the fractional order system in the thermal diffusive interface - Part 1: Application to a semi-infinite plane medium

Abstract

The recognition of fractional order behavior when identifying physical systems is relatively new. One of these fields where the fractional order integration can show up is the thermal diffusive interfaces. In fact, for some special conditions, an integration of order 0.5 appears when identifying the system. So, the objective of this work, divided into two parts, is to study the presence and the effects of the fractional order on the system behavior, and to determine the relation between the applied flux, the conduction and the point of measurement of the temperature. Accordingly, this first part will treat the case of homogeneous semi-infinite aluminum bar. Results show that the fractional order behavior of the bar disappears whenever the temperature sensor is far from the boundary where the flux is applied. Keywords-fractional order integration; thermal diffusive interface; homogeneous semi-infinite aluminum bar; modeling process.I.

Time domain response for the fractional order transfer function characterizing the thermal diffusive interface

“…In fact, when presenting the transfer function of the thermal diffusive interface of a semi-infinite or of a finite homogeneous plane, an integration of order 0.5 appears which yields to a fractional order behavior [4] [5].…”