Derivation of the non-integer system identification method for the adiabatic boundary condition using Laplace transform

Abstract

The determination of surface heat flux from in-depth temperature measurements on the basis of calibration measurements is reported for a system with an adiabatic wall boundary condition. The Non-Integer System Identification (NISI) method - originally developed for the semi-infinite problem - is mathematically derived based on a one-dimensional heat conduction problem with adiabatic wall condition. This is of particular interest for heat shield characterization in thermal protection systems, e.g. in re-entry space flight. Because the actual sensor system is calibrated, the NISI approach neither requires any material parameter nor temperature sensor position information in order to solve the inverse heat conduction problem to measure the net surface heat flux. In this study, the NISI approach was analytically derived using the Laplace transformation of the heat equation, the same approach as used for a semi-infinite system. It is found that the resulting transfer function in the time domain is the same for the semi-infinite problem and the adiabatic wall boundary condition. However, the calibration parameters of the systems are different. This work shows that the application of NISI is possible using a variety of boundary conditions and can thus serve as one unique transfer function relating net surface heat flux to in-depth temperature data.