Inverse Method for Estimating Thermal Properties of Phase Change Material Using Levenberg-Marquardt Method

This paper investigates the application of the Inverse method to a 1-D semi-infinite melting problem in order to estimate thermal properties of of Phase Change Material (PCM), including the melting point <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Tₘ</tex> , density <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ρ</tex> , and latent heat capacity <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</tex> . The problem predicts temperature using an analytical solution based on Stefan's problem that uses Neumann's similarity solution. It then estimates the unknown parameters using nonlinear inverse method based on the Levenberg-Marquardt Optimization (LMO). Two PCMs, sodium sulfate and water, were used to validate and evaluate the efficiency of the proposed model. Numerical results show that the model is robust as it converges quickly to exact values - 34 iterations for sodium sulfate case and 22 for water - indicating high reliability with negliglble error.