Stepwise Sequential Inverse Function Estimation Approach for Simultaneous Estimation of Temperature‐Dependent Thermophysical Properties

ABSTRACT Accurate determination of temperature‐dependent thermophysical properties is important for thermal analysis and engineering design. However, many existing inverse estimation approaches rely on predefined functional forms or require complex adjoint formulations. This study proposes a simple novel stepwise sequential inverse function estimation approach for the simultaneous estimation of temperature‐dependent thermal conductivity and specific heat capacity , without assuming predefined functional forms. The methodology involves estimating the unknown parameters at each 1 s interval. Initially, the parameters are estimated for the first interval using temperature data recorded in intermediate time steps using the Levenberg–Marquardt algorithm. The estimated values of and for the first interval are used as initial guesses for the next interval, and this procedure is repeated for the subsequent intervals. Both the forward and inverse models were implemented using in‐house MATLAB code. To evaluate the algorithm, synthetic temperature data were generated using various function forms for and . The estimated profiles had values ranging from 0.99 to 1.0. However, the algorithm exhibited limitations when applied to low materials. In such cases, the values of dropped to 0.536 for and −3.909 for . By performing the modifications described in the article, the values improved to 0.96 for and 0.99 for .