Low-frequency heat waves transport in graded Si–Ge alloys

Abstract

In this work, we consider a rigid heat conductor graded material subjected to an oscillating thermal signal applied on its boundary. We use a recently proposed novel concept, the so-called spectral diffusivity, to characterize the response of the material to an externally applied variable temperature difference. The spectral diffusivity has the physical meaning of an effective transport coefficient. We found a frequency window between 10−2 and 102 Hz wherein the spectral diffusivity increases, showing a maximum. The transport equation was numerically solved to calculate the average heat flowing through the material. We found that it also increased having a maximum in the mentioned range of frequencies. We then investigated the thermal rectification of the material finding a maximum in the same frequency range. The thermal rectification, as well as the spectral diffusivity, improved as the inhomogeneity of the heat conductivity of the material was higher. The spectral diffusivity enables a more in-depth analysis of heat wave transfer, and it contributes to a better understanding of the material response in front of periodic thermal disturbances.