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<p>In this analysis, the consequence of internal heat generation on the thermal performance of wavy profiled permeable fin wetted with ternary nanofluid of various shapes is examined. Nanoparticles with spherical, cylindrical, and platelet shapes have been considered. The temperature equation that describes the heat dispersal in a wavy fin is modeled and that equation is non-dimensionalized using suitable -dimensionless terms. A novel technique is introduced for solving the obtained non-dimensional temperature equation with related boundary conditions using Laguerre polynomial integrated with single-layer physics-informed neural network (L-PINN). Further, the L-PINN results are compared with the findings of Runge–Kutta–Fehlberg’s fourth-fifth-order (RKF-45) approach for validation purposes. The integration of Laguerre polynomial transformations with the Gaussian error linear unit (gelu) activation function enables the creation of compact neural architectures by reducing dependency on deep network designs. This approach leverages mathematical properties of orthogonal polynomials and modern activation functions to balance expressivity and computational efficiency. Also, an analysis is conducted between the temperature dispersal of the rectangular and wavy fins. The influence of the various parameters that affect the wavy fins’ thermal profile is displayed with graphical illustrations. The rise in the values of porous parameter diminishes the thermal profile. As the convection–conduction parameter and radiation–conduction parameter upsurge, the fins’ temperature declines. The growth in the internal heat generation number increases the thermal profile. The network parameters are updated using the error backpropagation algorithm, and the obtained results are compared with numerically obtained RKF-45 results demonstrating good agreement.</p>

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Shape factor effect on the thermal variation of a wavy fin wetted by ternary hybrid nanofluid using an extended physics-informed Laguerre neural network

  • 期刊论文

  • 发表日期：

    2025年9月20日

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  • R. S. Varun Kumar,
  • G. Sowmya,
  • Chander Prakash,
  • K. Chandan,
  • B. C. Prasannakumara

摘要

In this analysis, the consequence of internal heat generation on the thermal performance of wavy profiled permeable fin wetted with ternary nanofluid of various shapes is examined. Nanoparticles with spherical, cylindrical, and platelet shapes have been considered. The temperature equation that describes the heat dispersal in a wavy fin is modeled and that equation is non-dimensionalized using suitable -dimensionless terms. A novel technique is introduced for solving the obtained non-dimensional temperature equation with related boundary conditions using Laguerre polynomial integrated with single-layer physics-informed neural network (L-PINN). Further, the L-PINN results are compared with the findings of Runge–Kutta–Fehlberg’s fourth-fifth-order (RKF-45) approach for validation purposes. The integration of Laguerre polynomial transformations with the Gaussian error linear unit (gelu) activation function enables the creation of compact neural architectures by reducing dependency on deep network designs. This approach leverages mathematical properties of orthogonal polynomials and modern activation functions to balance expressivity and computational efficiency. Also, an analysis is conducted between the temperature dispersal of the rectangular and wavy fins. The influence of the various parameters that affect the wavy fins’ thermal profile is displayed with graphical illustrations. The rise in the values of porous parameter diminishes the thermal profile. As the convection–conduction parameter and radiation–conduction parameter upsurge, the fins’ temperature declines. The growth in the internal heat generation number increases the thermal profile. The network parameters are updated using the error backpropagation algorithm, and the obtained results are compared with numerically obtained RKF-45 results demonstrating good agreement.