Analysis of the fractional order system in the thermal diffusive interface - Part 2: Application to a finite plane medium

Abstract

After presenting, in the first part of this work, the homogeneous aluminum linear semi-infinite bar, and having shown that the fractional behavior of order 0.5 appears for relatively high instances which represents low frequencies (it depends in fact on the location of the temperature sensor), this part aims to do almost the same study but for a homogeneous aluminum linear finite bar. In this case, we realize that the fractional order behavior, when found, occupies a limited frequency band within medium frequencies. In fact, for medium frequencies, the fractional order behavior appears when the measured temperature is near the boundary where the flux is applied. Whenever the temperature sensor is placed far than the critical distance, the fractional behavior is no more recognized.