Abstract
Stochastic heat transfer simulations play a pivotal role in capturing real-world uncertainties, where randomness in material properties and boundary conditions is present. Traditional methods, such as Monte Carlo simulation, perturbation methods, and polynomial chaos expansion, have provided valuable insights but face challenges in efficiency and accuracy, particularly in high-dimensional systems. This paper introduces a methodology for one-dimensional heat transfer modeling that incorporates random boundary conditions and treats thermal conductivity as a random process The proposed approach integrates Monte Carlo simulation with Cholesky decomposition to generate a vector of thermal conductivity realizations, capturing the inherent randomness in material properties. Finite element method (FEM) simulations based on these realizations yield rich datasets of temperatures at various locations. A deep neural network (DNN) is then trained on this FEM data, enabling not only rapid and accurate temperature predictions but also bidirectional computations—predicting temperatures based on thermal conductivity and inversely estimating thermal conductivity from observed temperatures.
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Data Availability
The data that support the findings of this study are available upon request from the corresponding author. Please contact Rakesh Kumar at kumar.137@iitj.ac.in for access to the data.
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Acknowledgements
I would like to express my gratitude to Dr. Vivek Vijay, Assistant Professor in the Department of Mathematics at the Indian Institute of Technology Jodhpur (IITJ), for his invaluable assistance in helping me understand the lognormal distribution of random processes. Additionally, I extend my heartfelt thanks to Prof. B. Ravindran Professor in the Department of Mechanical Engineering at IITJ, for his consistent support in preparing this manuscript. I am also deeply grateful to my supervisors, Prof. C. Venkataesan from the Department of Mechanical Engineering at IITJ, and Dr. Abir Bhattacharyya from the Department of Metallurgical and Materials Engineering at IITJ, for their guidance and mentorship throughout this research endeavor.
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Kumar, R. Heat transfer in material having random thermal conductivity using Monte Carlo simulation and deep neural network. Multiscale and Multidiscip. Model. Exp. and Des. (2024). https://doi.org/10.1007/s41939-024-00388-5
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DOI: https://doi.org/10.1007/s41939-024-00388-5