Functional estimation of space and time varying thermal properties using modified conjugate gradient method
Authors :- Parth Sathavara, Ajit Kumar Parwani, Paritosh Chaudhuri
Publication :- International Journal of Thermal Sciences, Volume 185, 2023, 108116
Estimation of thermal properties is essential for composite or newly invented materials used in various industries such as nuclear, aerospace, chemical, medical etc. In this work, the conjugate gradient method (CGM) with adjoint problem has been applied for the functional estimation of space and time varying thermal properties. No prior knowledge of the functional form of thermal properties is available. To overcome the divergence issue and relatively low derivative value during the start of CGM algorithm, a scaling factor based on Levenberg-Marquardt method (LM) has been applied. To test the efficacy of the proposed method for estimating thermal properties in actual applications, a numerical experiment with added artificial Gaussian error (noise) in simulated temperature measurements of standard deviation (θ) 0.01 °C and 0.1 °C is carried out. Three test cases of estimation have been considered in this study: (1) function estimation of space and time varying (temperature-dependent) thermal conductivity (k(T)) with known specific heat (c(T)) (2) function estimation of c(T) with known k(T) and (3) simultaneous function estimation of k(T) and c(T). The Root Mean Square (RMS) error is calculated for evaluating the accuracy of modified CGM. The RMS error for the individual estimation of k(T) and c(T) with θ = 0.1 °C is 0.1527 W/m°C and 4.0933 J/kg°C, respectively. While, when k(T) and c(T) are estimated simultaneously the RMS error with θ = 0.1 °C is 0.3531 W/m°C for k(T) and 5.2252 J/kg°C for c(T).