Parameter estimation for a thin layer by measuring temperature induced by a heat source

Abstract

We study the temperature profile for a semi-infinite thin layer due to a Gaussian heat source. We follow the time-dependent temperature profile at the center of the top surface of the layer, deriving the asymptotic behavior and both the short time and long time behaviors. We also show that one can estimate thermal properites from various time measurements of the temperature at the center of the top surface. Finally, we investigate the statistical uncertainty in estimating parameter values from temperature measurements.