Thermal Diffusivity Analysis of Metallic Conductors Using a Hybrid RK6 and Neural Network for Heat Transfer Simulation

Abstract

Understanding heat transfer in metallic conductors is fundamental to many engineering and scientific applications, especially where precise thermal management is crucial. Conventional numerical methods, although effective, may be computationally demanding or insufficient in accurately representing complex temperature dynamics. This study addresses the challenge of accurately and efficiently simulating transient heat conduction in materials by developing a hybrid approach that combines the Method of Lines (MOL), a sixth-order Runge-Kutta (RK6) integration scheme, and a Feed-Forward Neural Network (FFNN). The aim is to improve the accuracy of temperature distribution predictions over time by utilising numerical precision and data-driven learning methods. The MOL is first used to discretise the heat equation spatially, reducing it to a system of ordinary differential equations, which is then solved using the RK6 method. The numerical solutions obtained are utilised as input data for training the FFNN, while the precise analytical solution functions as the output target. The trained network is utilised for efficient and accurate temperature predictions over various time intervals. The results show that this hybrid FFNN_RK6 model not only captures the dynamic thermal response of various metals, such as copper and silver, but also improves prediction accuracy and computational efficiency. This method provides an effective and scalable framework for addressing heat equations, with potential applications in material science, thermal engineering, and simulation-based learning.