Simultaneous determination of spatially varying thermal conductivity and specific heat using boundary temperature measurements

Abstract

ABSTRACTAn inverse parameter estimation methodology for non-destructive simultaneous estimation of spatially varying thermal conductivity and specific heat in arbitrary 2D solid objects was developed that requires only boundary measurements of temperature. The spatial distributions of the two physical properties were specified by analytic functions involving unknown parameters that need to be determined by minimizing the normalized sum of the least-squares differences between measured and calculated values of the boundary temperatures. The minimization was performed using a combination of particle swarm optimization and the Broyden–Fletcher–Goldfarb–Shanno (BFGS) optimization algorithm and a hybrid optimization algorithm. Computing time was significantly reduced for the entire inverse parameter identification process by utilizing a metamodel created by an analytical response surface supported by an affordable number of high fidelity numerical solutions of the temperature fields for different guesses of the values of the parameters. The methodology was shown to accurately simultaneously predict linear and nonlinear spatial distributions of thermal conductivity and specific heat in arbitrarily shaped multiply connected 2D objects even in situations with noisy temperature measurements, thus proving that it is robust.