Optimization-Based Strategies for Optimal Inverse Parameters Estimation for Heat Transfer Systems

Abstract

Thermal design for electronic devices approached through the solution analysis of the Inverse Heat Transfer Problem (IHTP) has not been extensively explored. This article proposes an alternative strategy and a contrasting approach for the optimal inverse parameters' estimation of heat transfer systems, particularly in designing heat sinks. A framework to tackle a Rectangular Microchannel Heat Sink (RMCHS) design modeled by the Entropy Generation Minimization (EGM) criterion is developed. This framework comprises two strategies to be compared. The serial proposal works sequentially depending on the parameters' sensitivity into the RMCHS model, backpropagating estimated parameters to all processes. The parallel strategy processes all parameters simultaneously. Instead of focusing efforts on a typical optimization process, a sequential procedure takes advantage of the most influential parameters in the heat sink model and the excellent exploration-exploitation rate of Metaheuristic Optimization Algorithms (MOAs). The most sensitive design variables are prioritized in the serial strategy. The implemented estimation-optimization strategies are addressed through an IHTP's inverse analysis. Thereby, global MOAs are implemented to solve the specific application and become an alternative to the gradient-based methods when their efficiency and effectiveness are at stake. MOAs show overall relative errors related to minimal entropy generation rate inferior to 0.07% for data with 30 dB of SNR and less than 7.63% of error for data with 10 dB of SNR compared with the Levenberg-Marquardt method. Numerical results show that serial strategy provided a stable and reliable design solution even with contaminated data, obtaining better performances than the multiparametric strategy. Additionally, parametric and nonparametric statistical tests were used to validate the appropriate optimization algorithm and the most reliable strategy. The statistical tests confirmed the optimal-inverse problem estimation and optimization improvement by combining the serial strategy and analyzed MOAs to design the RMCHS based on the EGM criterion.