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<p>This study investigates the thermal behavior of a radial porous fin influenced by a magnetic field and internal heat generation. The nonlinear governing ordinary differential equation (ODE) is solved using two advanced methodologies: The Taylor wavelet method and the physics-informed neural networks (PINNs). The Taylor wavelet method provides a semi-analytical solution by converting the ODE into algebraic equations, ensuring accuracy and computational efficiency. PINNs integrate physical laws directly into the neural network framework, employing automatic differentiation to minimize residual errors while solving the ODE. A comparative analysis of the fin’s thermal performance with and without the magnetic field is conducted. The results demonstrate that the Hartmann number <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((H)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>H</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> significantly enhances the heat transfer rate. Furthermore, higher values of the heat generation parameter <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\((Q)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>Q</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> lead to elevated temperature profiles, as increased internal heat production slows the rate of temperature decay along the fin’s length. This trend is consistent across both scenarios. The PINN approach offers a notable advantage by embedding physics equations within its architecture, eliminating the need for extensive mathematical computations often required by traditional numerical methods. This capability ensures accurate results with minimal training data, making it a time-efficient and resource-saving solution for complex thermal analyses. This approach effectively addresses complex nonlinear thermal problems with high precision and reliability.</p>

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Physics-informed neural networks and wavelet technique for heat transfer analysis in radial porous fins with magnetic and internal heat effects

  • 期刊论文

  • 发表日期：

    2026年1月13日

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  • K. J. Gowtham,
  • B. J. Gireesha

摘要

This study investigates the thermal behavior of a radial porous fin influenced by a magnetic field and internal heat generation. The nonlinear governing ordinary differential equation (ODE) is solved using two advanced methodologies: The Taylor wavelet method and the physics-informed neural networks (PINNs). The Taylor wavelet method provides a semi-analytical solution by converting the ODE into algebraic equations, ensuring accuracy and computational efficiency. PINNs integrate physical laws directly into the neural network framework, employing automatic differentiation to minimize residual errors while solving the ODE. A comparative analysis of the fin’s thermal performance with and without the magnetic field is conducted. The results demonstrate that the Hartmann number \((H)\) ( H ) significantly enhances the heat transfer rate. Furthermore, higher values of the heat generation parameter \((Q)\) ( Q ) lead to elevated temperature profiles, as increased internal heat production slows the rate of temperature decay along the fin’s length. This trend is consistent across both scenarios. The PINN approach offers a notable advantage by embedding physics equations within its architecture, eliminating the need for extensive mathematical computations often required by traditional numerical methods. This capability ensures accurate results with minimal training data, making it a time-efficient and resource-saving solution for complex thermal analyses. This approach effectively addresses complex nonlinear thermal problems with high precision and reliability.