Estimation of Spatially Distributed Thermal Properties of Heterogeneous Media with Non-Intrusive Measurement

Abstract

This article deals with estimation of spatially distributed thermal properties of two-dimensional heterogeneous media from the solution of inverse heat conduction problem. The experimental procedure involves sequential heating of sample at four discrete locations on one side and recording transient temperature on the other side non-intrusively. The inverse problem formulation is carried out as parameter estimation problem and the unknown parameters are estimated through minimization of sum of squared error between measured and simulated temperatures using Levenberg–Marquardt algorithm. The huge computational time required to calculate sensitivity matrix is reduced through parallel computation strategy. Numerical estimations are carried out with synthetic temperature and it is found that the resolution and accuracy of estimated spatially distributed thermal conductivity is in better agreement with the exact distribution when compared to volumetric heat capacity even at an error level of ± 0.1 K. Transient temperature response of the fabricated heterogeneous prototype is recorded using infrared radiation camera and the same is used for estimation of unknown parameters. The estimated thermal conductivity closely mimics the actual distribution. Therefore, this simple proposed method can be directly used in thermal tomography applications for identifying the shape and size of inclusions/inhomogeneities from the estimated thermal conductivity distribution alone.