Abstract :

Thermal Systems That Arise In Mechanical, Electronic, And Process Engineering Are Governed By Nonlinear Partial Differential Equations Whose Classical Solution By Finite Element (FEM) Or Finite Difference (FDM) Methods Is Computationally Expensive, Particularly For Design Optimisation, Real-time Control, And Digitaltwin Applications That Require Thousands Of Repeated Evaluations. This Paper Proposes A Machine Learning-assisted Mathematical Framework That Couples The Governing Heat Conduction And Convection Equations With A Data-driven Neural Surrogate Trained Under A Physics-informed Loss. The Governing Fourier Heat Equation, Boundary Conditions, And The Non-dimensional Biot And Fourier Numbers Are First Formulated Analytically; A Feed-forward Neural Network Is Then Trained To Approximate The Temperature Field By Minimising A Composite Loss Consisting Of A Physics Residual Term, A Boundary-condition Term, And A Data-fitting Term. The Framework Is Validated On A Benchmark Conduction– Convection Problem And Compared Against A Conventional FEM Solver. Results Indicate That The Proposed Hybrid Model Reduces Computation Time By More Than Three Orders Of Magnitude While Keeping The Mean Absolute Percentage Error Below 2.1% Relative To The FEM Baseline, Demonstrating That Machine Learning Can Substantially Accelerate Thermal Analysis Without A Significant Loss Of Physical Accuracy. Keywords: Machine Learning, Thermal Systems, Physics-Informed Neural Networks, Heat Transfer, Mathematical Modelling, Surrogate Modelling, Fouriers Law, Regression Analysis.

Published:

31-12-2024

Issue:

Vol. 24 No. 12 (2024)

Page Nos:

192 - 199

Section:

Articles

License:

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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