A quadrilateral optimization method for non-linear thermal properties determination in materials at high temperatures

Abstract The actual experimental methods applied to determine the materials' thermal properties at high temperatures usually do not provide good quality values for matching simulations to experimental data. To solve this problem, this work proposes an alternative inverse methodology to estimate the thermal properties of a material at high temperatures. The developed technique is called Quadrilateral Optimization Method (QOM). The QOM is a multivariable estimation technique developed to determine the function's parameters. To regularize the results, the Time Traveling Regularization (TTR) was applied in the objective function. To prove the methodology efficiency, the specific heat is estimated through this inverse approach for a LASER welding problem. In this case, the specific heat was treated as an exponential function. Then, the QOM estimates the parameters of this function. A sensitivity analysis is performed to determine the estimation range. To minimize the computational time, in the direct model the non-linear heat diffusion equation was solved through the Finite Volume Method in an in-house CUDA-C code. A numerical welding experiment was performed to eliminate the real experimental errors. The results demonstrated that the proposed approach had an average error of less than 0.075% in the parameters' estimation in the best-case-scenario. The new methodology was validated, and it proved to be an easier and cheaper way to determine the thermal properties at high temperatures without the need to use advanced experimental apparatus.